dtsp extc viva questions answer

Name :

What & Why ?

Sr No TOPIC [PAGE

1

Basic Concepts 2

2

Discrete Time signals 3

3

Discrete Fourier Transform and Fast Fourier Transform 7

4

Analysis of DT system using Z-Transform 19

5 Digital Filters 26

When you study DSP, so many questions come in mind. The more you study more questions come. Those question needs to be resolved, I have made

the list of few FAQ questions. After you study DSP, you should be in a position to answer these questions.

You need to Study. Kiran Talele

[email protected] 9987030881

1. BASIC CONCEPTS

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What & Why (1) What is DSP?

Ans : Digital Signal Processing is a technique that converts signals from real world sources (usually in analog form) into digital data that can then be analyzed. Analysis is performed in digital form because once a signal has been reduced to numbers, its components can be isolated, analyzed and rearranged more easily than in analog form.

Eventually, when the DSP has finished its work, the digital data can be turned back into an analog signal, with improved quality. For example, a DSP can filter noise from a signal, remove interference, amplify frequencies and suppress others, encrypt information, or analyze a complex waveform into its spectral components. This process must be handled in real-time - which is often very quickly. For instance, stereo equipment handles sound signals of up to 20 kilohertz (20,000 cycles per second), requiring a DSP to perform hundreds of millions of operations per second.

(2) What are the applications of DSP ? Ans :

Speech coding & Decoding

Speech encryption & decryption Speech recognition

Speech Synthesis Speaker identification Hi-fi audio encoding & decoding Noise cancellation AAuuddiioo eeqquuaalliizzaattiioonn

AAuuddiioo mmiixxiinngg && eeddiittiinngg VViissiioonn Image compression & decompression IImmaaggee ccoommppoossiittiinngg EEcchhoo ccaanncceellllaattiioonn SSppeeccttrraall eessttiimmaattiioonn

(3) What do you mean by real time signal ? Give example. Ans : Signal is processed with the same speed it is captured. Signal is captured, sampled and processed

with the same speed. Signal is not stored before processing. Entire input signal never available before processing. Processed signal can be stored.

For example, in digital telephone system, Signal is captured, Sampled, Processed , Transmitted and Made it available to the end user. Real Time Processing is Online Processing.

(4) Give one Real Time practical example of DSP system. Ans : Digital Telephone System.


(5) What do you know about Analog Signal, Digital Signal, CT signal, DT Signal ? Ans : i] Analog Signal : Signal value can be anything. NO fixed signal level. Eg x(t) =cos(100π t). continuous Sinusoidal signal x[n] = 10.5, 4.7, 3.5, 5.7, 3.8 sampled signal

ii] Digital Signal : Only two levels +5v and 0. ie. Logically High and Low.

Eg. Binary data

iii] Continuous Time Signal : Signal is defined for every value of time. Signal value can be

anything. Eg. x(t) =cos(100π t). continuous Sinusoidal signal

Bilevel Signal

iv] Discrete Time Signal : Signal is defined for Discrete instant of Time. NOT for every value of time. Signal value can be anything.

Eg. x[n] = 10.5, 4.7, 3.5, 5.7, 3.8 sampled signal (6) How Discrete Time signal is obtained ?

Ans : DT signal is obtained by sampling CT signal at regular intervals of time.

]n[x]nTs[x)t(xnTst

===

In practical application sampling is implemented using S/H circuit. (7) What is antialising filter? Can it be Digital filter ? justify. Ans : When processing the analog signal using DSP System, it is sampled at some rate depending

upon the bandwidth. The rate of sampling is decided by the Nyquist criterion. However, signals that are found in physical systems will never be strictly bandlimited. To eliminate signal content beyond the desired bandwidth, antialiasing filter is used.

The filter cannot be a digital filter. This is because antialias filtering is required to be performed in the analog domain prior to applying the signal to A/D converter where aliasing would take place.

(8) Let x[t] = 10 cos(100π) + 20 cos( 120πt)-5 sin(50πt). If x(t) is sampled with sampling frequency Fs = 200 Hz. What will be Discrete Time Signal x[n] at n=0 ?

Ans : 30

3Kiran Talele ( )


2. DISCRETE TIME SIGNALS

What & Why (9) What are the classification of signals ? Ans : DT signal are classified as

(i) Causal Signal, Anti-causal Signal, Bothsided Signal. (ii) Even Signal, Odd Signal (iii) Energy Signal, Power Signal (iv) Periodic Signal, Non periodic Signal (v) Symmetric, Anti-symmetric (vi) Finite Length Signal, Infinite Length Signal

(10) What do you mean by Causal signal, Anti-causal Signal and Both-sided signal ? Ans : If x[n] = 0 for all n < 0 Then x[n] is causal signal.

If x[n] = 0 for all n ≥ 0 Then x[n] is anticausal signal. If x[n] is neither causal nor anticausal Then x[n] is bothsided signal.

(11) Give one example of Causal, Anticausal and Bothesided signal. Ans : Examples :

(i) Causal signal : x1[n] = u[n] x2[n] =( ½ )n u[n] (ii) Anti-causal signal : x1[n] = u[-n-1] x2[n] =( ½ )n u[–n–1] (iii) Both sided signal : x1[n] = u[n] + u[-n-1] x2[n] = (2)n u[n] + (3)n u[–n–1]

(12) What is an energy signal ? Give example.

Ans : Energy of signal is defined as, E =1

2

0[ ]

N

nx n

−

=∑

If Energy of DT signal is finite (0<E<∞ ) then x[n] is an energy signal. Ex : x[n] = ( ½ )n u[n] E = 2 ( finite)

4321][

↑=nx E = 30 (finite)

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(13) Consider x1[n] is periodic with period = 4 and x2[n] is periodic with period = 6 . Let x[n] = x1[n] + x2[n]. What will be the period of x[n] ?


(14) What is power signal ? Give example.

Ans : The average power of the x[n] is given as P = 1

2

0

1lim [ ]N

N nx n

N

−

→∞=

∑

If P is finite and nonzero then x[n ] is a power signal.

Ex x[n] = u[n] (15) What is symmetric signal ? Give example. Ans : If x [ n ] = x [ N-1-n ] Then x[n] is causal symmetric

Ex. Causal Symmetric signal : ⎭⎬⎫

⎩⎨⎧

−−−−=↑

12321][nx

(16) What is Anti-symmetric signal ? Give example. Ans : If x [ n ] = - x [ N-1-n ]

Then x[n] is causal anti-symmetric.

Ex. Causal Anti-Symmetric signal : ⎭⎬⎫

⎩⎨⎧

−−=↑

12021][nx

(17) What is an Even signal ? Give example. Ans : If x[ n ] = x [-n ] Then x [n ] is even signal.

Ex. Even signal : Nonperiodic ⎭⎬⎫

⎩⎨⎧

−−−−=↑

12321][nx

Periodic

⎭⎬⎫

⎩⎨⎧

−−−=↑

23321][nx

(18) What is an odd signal ? Give example. Ans :

If x[ n ] = – x [–n ] Then x [n ] is odd signal

Ex. Odd signal : Nonperiodic

⎭⎬⎫

⎩⎨⎧

−−=↑

12021][nx

Periodic

⎭⎬⎫

⎩⎨⎧

−−=↑

23320][nxp

(19) What is the sum of odd signal values ? Ans : Sum of odd signal value is 0.

Ex Sum = 0 ⎭⎬⎫

⎩⎨⎧

−−=↑

12021][nx

Sum = 0 ⎭⎬⎫

⎩⎨⎧

−−=↑

23320][nxp

5Kiran Talele ( )


(20) How to check whether the given signal is periodic or not ? Ans : If the digital frequency of the signal is rational number then the signal

is periodic. Otherwise signal is nonperiodic.

Ex x[n] = cos (0.6 π n) where w = 0.6π and f = 0.3 = 103

Here f is a rational number, so x[n] is periodic signal with period = 10

(21) What is the concept of digital frequency f ?

Ans : Digital Frequency is ratio of Analog Frequency to Sampling frequency. FsFfei =..

(22) What is the range of w and f ? Ans : Range of Digital frequency ω is ( –π , π ]

Range of Digital frequency f is ⎥⎦

⎤⎜⎜⎝

⎛ −21,

21

(23) What is the unit of digital frequency w and f ? Ans : Unit of digital frequency w is radians and f is unit less quantity.

(24) Classify the following signal : Finite Length or Infinite Length :- x[n] = u[n] + 2 u[n-1] – 3 u[n-5]

Ans : Finite length with length N = 5

(25) What is correlation ? Ans : Correlation gives a measure of similarity between two data sequences. In this process, two signals

are compared and the degree to which the two signals are similar is computed.

(26) What are the applications of Correlation ?

Ans : Typical applications of correlation include speech processing, image processing and radar systems.

In a radar system, the transmitted signal is correlated with the echo signal to locate the position of the target. Similarly, in speech processing systems, different waveforms are compared for voice recognition.

(27) What is the application of Convolution ? Ans : Application of Convolution is to find output of Digital Filter for any given input signal.

Output of Digital filter y[n] is linear Convolution of input signal x[n] and impulse response of the filter h[n].

(28) What are the properties of Convolution ? Ans :

i) Commutative x [n] * h[n] = h[n] * x[n]

ii) Associative ( x [n] * h1[n] * h2[n] ) = ( x [n] * h1[n] ) * h2[n]

iii) Distributive

x[n] * [ = x [n] * h]]n[h]n[h 21 + 1[n] + x[n] * h2[n].

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(29) Consider x1[n] is periodic with period N1 = 4 and x2[n] is periodic with period N2 = 6 . Let x[n] = x 1[n] + x2[n]. What will be the period of x[n] ?

Ans : Period N = LCM N1, N2 = 12

(30) Let x[n] = δ[n] + 2 u[n] – 2 u[n-4] . Determine which of the following classification is true for x[n]. (a) Periodic, Finite length (b) Periodic, Infinite length (c) Non periodic, Finite length (d) Non-periodic, Infinite length

Ans : Non periodic, finite length

NOTE :

Linear Shifting of NON-Periodic DT Signals

1) x[ n ] = ⎭⎬⎫

⎩⎨⎧

↑4321

2) x[ n –1 ] = ⎭⎬⎫

⎩⎨⎧

↑43210

3) x[ n + 1 ] = ⎭⎬⎫

⎩⎨⎧

↑4321

4) x[ –n ] = ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

↑1234

5) x[ –n + 1 ] = ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

↑1234

6) x[ –n – 1 ] = ⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

↑01234

----------------------------------------------------------------------------------------------------

Circular Shifting of Periodic DT Signals

1) x[ n ] = 1, 2, 3, 4

2) x[ n-1 ] = 4, 1, 2, 3

3) x[ n+1 ] = 2, 3, 4, 1

4) x[ –n ] = 1, 4, 3, 2

5) x[ –n+1 ] = 2, 1, 4, 3

6) x[ –n–1 ] = 4, 3, 2, 1

-----------------------------------------------------------------------------------------------------------

7Kiran Talele ( )


3. D F T and F F T

What & Why

(31) Define Discrete Fourier Transform of x[n].

Ans : nkn

N

nWnxkX ][][

1

0∑

−

=

=

(32) What is the interpretations of DFT coefficients ?

Ans : DFT gives N values of Fourier Transforms of DT signal x[n] at 1......,2,1,02−== Nkfor

Nkw π

.

They are equally spaced with frequency spacing of Nπ2

(33) How many complex multiplications and additions are required to find DFT ? Ans : By DFT

(i) Complex Multiplications 2N=

(ii) Complex Additions )1( −= NN

(34) How many real multiplications and additions are required to find DFT. Ans :

Let P = a + j b and Q = c + j d (1) P X Q = ( a + j b ) ( c + j d ) = (ab – bd )+ j ( bc + ad ) 4 Real Multiplications and 2 Real Additions

For 1 Complex Multiplications we require 4 Real Multiplications. and 2 Real Additions (2) P + Q = ( a + j b ) + ( c + j d ) = (a + c )+ j ( b + d ) 2 Real Additions

For 1 Complex Addition we require 2 Real Additions Now, In DFT, Total Complex Multiplications = N2 and Total Complex Additions )1( −= NN So, For N2 Complex Multi. we require 4 N2 Real Multi. and 2 N2 Real Additions For ( N2-N) Complex Additions we require 2( N2-N) Real Additions. In suumary, Total Real Mulitplications = 4 N2

Total Real Additions = 2 N2 + 2( N2-N) == 4 N2– 2N (35) How many real multiplications and additions are required to find DFT of 32 point signal.? Ans : By DFT

(i) Real Multiplications 4096)32(4N4 22 ===

(i) Real Additions 4032124 2 =−= NN

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(36) How many complex multiplications and additions are required to find FFT ? Ans : By DFT

(i) Complex Multiplications NN2log

2=

(ii) Complex Additions NN 2log= (37) How many real multiplications and additions are required to find DFT of 32 point signal using FFT

algorithm? Ans : By FFT (i) Real Multiplications 320NlogN2 2 ==

(ii) Real Additions 480NlogN3 2 == (38) What is Scaling and Linearity property of DFT ? Ans : Scaling Property : If signal is multiplied by constant Then DFT is also multiplied by the same

constant. i .e. DFT a x1[n] = a X1[k]

Linearity Property : If signals are added, Then DFT’s are also added. i .e. DFT a x1[n] + b x2[n] = a X1[k] + b X2[k

(39) What is the DFT of δ[n] ? Ans : DFT δ[n] = 1 (40) What is the DFT of N pt signal u[n] ? Ans : DFT u[n] = N δ[k] (41) What is the DFT of 4 pt x[n] where x[n] = δ[n] + u[n] ? Ans : X[k] = 1+ 4 δ[k] = 5, 1, 1, 1 (42) What is periodicity property of DFT ? Ans : DFT equation produces periodic results with period = N i.e. X[k] = X[k+N] = X[k MOD N] = X[((k))] Inverse DFT equation produces periodic results with period = N i.e. x[n] = x[n+N] = x[n MOD N] = x[((n))] (43) Why DFT results are periodic ? Ans : DFT results are periodic because twiddle factor is periodic with period = N (44) DFT gives discrete spectrum or continuous spectrum ? Justify ? Ans : DFT gives discrete spectrum.

If the signal is periodic then spectrum is discrete and if the signal is non-periodic then spectrum is continuous. DFT assumes that input signal is periodic and therefore DFT gives discrete spectrum.

9Kiran Talele ( )


(45) What do you mean by spectrum is Discrete or continuous? Ans : Continuous spectrum is defined for every value of frequency. Discrete spectrum is

defined only at discrete values of frequencies ie. Not defined for every value of frequency.

(46) Find DFT of x[n] where x[n] = u[n] + 2 u[n-2] – 3 u[n-4] Ans : Here x[n] = 1, 1, 3, 3 By DFT X[k] = 8, -2+2j, 2, -2-2j (47) Find DFT of 10 pt x[n] where x[n] = δ[n] + δ[n-5] ?

Ans : kNWkX 51][ += k)1(1 −+=

(48) What is Time shift and frequency shift property of DFT ?

Ans : ][][ kXWmnxDFT mkN=−

][][ mkXnxWDFT mnN −=−

(49) What is symmetry property of DFT ? Ans : If x[n] X[k] Then X[k] = X*[-k]. i.e. If x[n] is real valued signal, then real part of X[k] is symmetric about

k = N/2 and Imaginary part of X[k] is Anti-symmetric about k = N/2.

(50) What is DFT property of EVEN signal ? Ans : If x[n] is Even , Then X[k] is also Even i.e.. If x[n] = x[–n] Then X[k] = X[–k]

(51) What is the DFT of real and even signal.? Ans : If x[n] is Real and Even, Then X[k] is also Real and Even Eg. x[n] = 1, 2, 3, 2 X[k] = 8, -2, 0, -2

(52) What is the DFT of Imaginary and Even signal ? Ans : If x[n] is Imaginary and Even Then X[k] is also Imaginary and Even Eg. x[n] = j, 2j, 3j, 2j X[k] = 8j, -2j, 0, -2j

(53) What is DFT property of ODD signal ? Ans : If x[n] = – x[–n] Then X[k] = – X[–k] i.e. If x[n] is Odd , Then X[k] is also Odd.

(54) What is the DFT of real and Odd signal ? Ans : If x[n] is Real and Odd, Then X[k] is also Imaginary and Odd Eg. x[n] = 0, 2, 0, –2 X[k] = 0, – 4j, 0, 4j

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(55) What is the DFT of Imaginary and Odd signal ? Ans : If x[n] is Imaginary and Odd Then X[k] is also Real and Odd Eg. x[n]= 0, 2j, 0, – 2j X[k] = 0, 4, 0, – 4 (56) If DT signal is expanded in time domain what will be the effect in frequency domain? Ans : Expansion in time domain corresponds to Compression in frequency domain. Eg. x[n] = 1,2,3,2 X[k] = 8, –2, 0, –2 Let p[n] = 1, 0, 2, 0, 3, 0, 2,0 Then P[k] = 8, –2, 0, –2, 8, –2, 0, –2

0 0.5π π 1.5π 2π

|P[k]||X[k]|

0 0.5π π 1.5π 2π

(57) If DT signal is compressed in time domain what will be the effect in frequency domain? Ans : Compression in time domain corresponds to Expansion in frequency domain. Eg. x[n] = 1, 0, 2, 0, 3, 0, 2,0 X[k] = 8, –2, 0, –2, 8, –2, 0, –2 Let p[n] = 1,2,3,2 Then P[k] = 8, –2, 0, –2

0 0.5π π 1.5π 2π

|P[k]||X[k]|

0 0.5π π 1.5π 2π

(58) If DT signal is appended by zeros in time domain what will be the effect in frequency domain? Ans : Eg. x[n] = 1,2,3,2 X[k] = 8, –2, 0, –2 N=4 pt Let p[n] = 1, 2, 3, 2, 0, 0, 0, 0 N=8 pt

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0 0.5π π 1.5π 2π

|P[k]||X[k]|

0 0.5π π 1.5π 2π

As the length of signal increases, the frequency spacing decreases. The number of points per unit length i.e. resolution of the spectrum increases. Therefore the approximation error in the representation of the spectrum decreases.


(59) What is convolution property of DFT ? Ans : Convolution in time domain corresponds to multiplication in frequency domain. I f x[n] X[k] and h[n] H[k] Then

DFT x[n] ⊗ h[n] = X[k] H[k] (60) What is correlation property of DFT ? Ans : I f x[n] X[k] and h[n] H[k] Then

DFT x[n] o h[n] = X[k] H*[k]

(61) How to find energy of signal from its DFT ? Ans : According to parseval’s energy theorem, Energy of the signal is given by,

21

0|][|1 kX

NE

N

k∑

−

==

(62) Are FFT's limited to sizes that are powers of 2? Ans : No. The most common and familiar FFT's are "radix 2". However, other radices are

sometimes used, which are usually small numbers less than 10. For example, radix-4 is especially attractive because the "twiddle factors" are all 1, -1, j, or -j, which can be applied without any multiplications at all.

Also, "mixed radix" FFT's also can be done on "composite" sizes. In this case, you break a non-prime size down into its prime factors, and do an FFT whose stages use those factors. For example, an FFT of siz 1000 might be done in six stages using radices of 2 and 5, since 1000 = 2 * 2 * 2 * 5 * 5 * 5. It might also be done in three stages using radix 10, since 1000 = 10 * 10 * 10.

(63) What is an FFT "radix"? Ans : The "radix" is the size of an FFT decomposition. In the example above, the radix was 2.

For single-radix FFT's, the transform size must be a power of the radix. In the example above, the size was 32, which is 2 to the 5th power.

(64) What is an "in place" FFT?

Ans : An "in place" FFT is simply an FFT that is calculated entirely inside its original sample memory. In other words, calculating an "in place" FFT does not require additional buffer memory (as some FFT's do.)

(65) What is "bit reversal"? Ans : "Bit reversal" is just what it sounds like: reversing the bits in a binary word from left to

write. Therefore the MSB's become LSB's and the LSB's become MSB's. But what does that have to do with FFT's? Well, the data ordering required by radix-2 FFT's turns out to be in "bit reversed" order, so bit-reversed indexes are used to find order of input and output.

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It is possible (but slow) to calculate these bit-reversed indices in software; however, bit reversals are trivial when implemented in hardware. Therefore, almost all DSP processors include a hardware bit-reversal

indexing capability (which is one of the things that distinguishes them from other microprocessors.)


(66) How efficient is the FFT? Ans : The DFT takes N2 operations for N points. Since at any stage the computation

required to combine smaller DFTs into larger DFTs is proportional to N, and there are log2(N) stages (for radix 2), the total computation is proportional to N log2(N). Therefore, the ratio between a DFT computation and an FFT computation for the same N is proportional to N / log2(N). In cases where N is small this ratio is not very significant, but when N becomes large, this ratio gets very large. (Every time you double N, the numerator doubles, but the denominator only increases by 1.)

(67) FFT is faster than DFT. Justify. Ans : FFT produces fast results because calculations are reduced by decomposition technique.

In FFT, N pt DFT is decomposed into two N/2 pt DFT’s, N/2 pt DFT is decomposed into N/4 pt DFT’s and so on… Decomposition reduces calculations. FFT algorithms are implemented using parallel processing techniques. Because calculations are done in parallel, FFT produces fast results.

Complex Multiplications : DFT FFT

N 2N NN2log

2

16 256 32 32 1,024 80 64 4,096 192 256 65,536 1,024 512 2,62,144 2,304 1024 10,48,576 5,120

(68) What do you mean by Decimation ? Ans : Decimation means Sampling.

(69) Why Radix-2 algorithms are fast compared to radix-3 algorithms. ? Ans : In FFT, N pt DFT is decomposed into two N/2 pt DFT’s, N/2 pt DFT is decomposed into N/4 pt

DFT’s and so on… Decomposition reduces calculations This process continues till further decomposition is not possible. In radix-2 last level of decomposition is when the length of signal becomes 2 pt.

For minimum calculations there must be maximum levels of decompositions. In Radix-2 algorithms, we get maximum levels of decompositions and therefore radix-2 algorithms requires less calculations. Radix-2 algorithms are fast algorithms.

(70) Which algorithm is more powerful : DIT-FFT or DIF-FFT ?

Ans : Computationally, both the algorithms are exactly same.

(71) What is the order of input and output sequence in 8 pt DIT-FFT ? Ans : x[n] = x[0], x[4], x[2], x[6], x[1], x[5], x[3], x[7] X[k] = X[0], X[1], X[2], X[3], X[4], X[5], X[6], X[7]

13

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(72) What is the order of input and output sequence in 8 pt DIF-FFT? Ans : x[n] = x[0], x[1], x[2], x[3], x[4], x[5], x[6], x[7] X[k] = X[0], X[4], X[2], X[6], X[1], X[5], X[3], X[7] (73) How to find CC using DFT ? Ans : To find CC of x[n] and h[n] using DFT,

(i) Select N Let N = max(L,M) where L is the length of x[n] and M is length of h[n],

(ii) Append x[n] by (N-L) zeros and Append h[n] by (N-M) zeros

(iii) Find X[k] where ∑−

==

1

0][][

N

n

nkNWnxkX

(iv) Find H[k] where ∑−

==

1

0][][

N

n

nkNWnhkH

(v) Let Y[k] = X[k] H[k].

(vi) Find y[n] where ∑−

=

−=1

0][][

N

K

nkNWkY

Niny

Always explain wrt diagram

DFT/FFT

DFT/FFT

y[n] Y[k]

x[n]

H[k]

X[k]

h[n]

× iDFT /

(74) How to find CC using FFT ? Ans : To find CC of x[n] and h[n] using FFT,

(i) Select N Let N = max(L,M) where L is the length of x[n] and M is length of h[n],

(ii) Append x[n] by (N-L) zeros and Append h[n] by (N-M) zeros

(iii) Find X[k] by using N point DIT-FFT / DIF-FFT flowgraph (iv) Find H[k] by using N point DIT-FFT / DIF-FFT flowgraph (v) Let Y[k] = X[k] H[k]. (vi) Find y[n] by Inverse FFT.

By Inverse FFT, y[n] = ( )** ][1 kYFFTN

Always explain wrt diagram.

Kiran Talele ( ) 14


(75) How to find LC using CC ? Ans : To find LC of x[n] and h[n] using CC,

(i) Select N: Let N ≥ L + M – 1 where L is the length of x[n] and M is length of h[n], (ii) Append x[n] by (N-L) zeros and Append h[n] by (N-M) zeros (iii) Perform N point Circular convolution of x[n] and h[n]

(76) How to find LC using DFT /FFT ? Ans : : To find LC of x[n] and h[n] using DFT/FFT,

(i) Select N Let N ≥ L + M – 1 where L is the length of x[n] and M is length of h[n],

(ii) Append x[n] by (N-L) zeros and Append h[n] by (N-M) zeros (iii) Perform N point Circular convolution of x[n] and h[n] using DFT/FFT. Find N point X[k] and H[k] Let Y[k] = X[k] H[k]. Find y[n] by Inverse DFT/FFT.

Always explain wrt diagram. (77) What are the applications of FFT. ? Ans : (i) Linear Filtering i.e. to find output of digital filter for any given input sequence (ii) Spectral Analysis i.e. to find magnitude spectrum and phase spectrum

(iii) Circular Correlation ie to find degree of similarity between two signals. (78) How to find output of the filter using DFT ? Ans : Output of the filter is Linear convolution of impulse response with the input of the signal. To find output means to find LC by DFT. (79) How to find output of the FIR filter using FFT ? Ans : In FIR filter length of h[n] is finite. Output of the filter is always Linear convolution of impulse

response with the input of the signal. To find output i.e. to find LC by FFT (i) Select N

Let N ≥ L + M – 1 where L is the length of x[n] and M is length of h[n], (ii) Append x[n] by (N-L) zeros and Append h[n] by (N-M) zeros (iii) Perform N point Circular convolution of x[n] and h[n] using FFT. * Find N point X[k] and H[k] by using FFT flowgraph. * Let Y[k] = X[k] H[k].

* Find y[n] by Inverse FFT. y[n] = ( )** ][1 kYFFTN

Always explain wrt diagram.

15

Kiran Talele ( )

[email protected] 9987030881 Kiran Talele ( ) 16

(80) How to find output of the IIR filter using DFT / FFT? Ans : Output of the filter is Linear convolution of impulse response with the input of the

signal. To find output means to find LC by DFT/FFT. Length of h[n] in IIR filter is infinite. So, DFT/FFT implementation of infinite length signals is not possible.

(81) What is the length of linearly convolved signals ? Ans : Length of linearly convolved signal is always equal to N = L + M – 1 where L is length of first

signal and M is length of second signal.

(82) What is periodic convolution ? Ans : Periodic convolution is convolution of two periodic signals of the same period. When two

periodic signals are periodic with common period, periodic convolution is similar to circular convolution.

(83) What is the difference between circular convolution and periodic convolution ? Ans : In periodic convolution input signals are originally periodic with common value of period. In circular convolution, if input signals are not periodic then they are assumed to be periodic

with period = N where N = max(L,M) where L is the length of first signal and M is length of second signal.

(84) What do you mean by aliasing in circular convolution ? Ans : In circular convolution if value of N < L+M-1 then last M-1 values of y[n] wraps around gets

added with first M-1 values of y[n]. This is called aliasing.

(85) Why FFT is used to find output of FIR filter ? Justify. Ans : FFT produces fast results because in practical applications FFT algorithms are implemented

using parallel processing techniques. Because in FFT calculations are done in parallel, FFT produces fast results.

(86) What are the limitations of filtering by FFT algorithms? Justify. Ans : (i) NOT suitable for real time applications :

FFT algorithms are implemented using parallel processing techniques. When FFT is used input is applied in parallel i.e simultaneously. For real time applications entire input signal is not available. So FFT algorithms can not be used.

(ii) NOT suitable for Long Data Sequence. As the length of the input sequence increases, the no of stages in FFT will also increase proportionally and so the delay increases, processing time at each stage increases.

(87) How to find output of FIR filter for long input sequence. Ans : In FIR filter length of h[n] is finite. Output of the filter is always Linear Convolution of impulse

response with the input of the signal. To find output of digital FIR filter FFT technique is used. But for Long data sequence, direct FFT technique is not suitable. For long data sequence, Overlap Add Method using FFT or Overlap Save Method using FFT is used.

(88) What is Overlap Add Method? (89) What is Overlap Save Method?


(90) How to find output of FIR filter for real time input signal.? Ans : In real time application entire input is not available and input signal has to be

processed online. Length of input signal depends on application. It can be long sequence also.

In FIR filter length of h[n] is finite. Output of the filter is always Linear Convolution of impulse response with the input of the signal. To find output of digital FIR filter, Overlap Add Method using FFT or Overlap Save Method using FFT is used.

(91) How to find output of IIR filter for real time input signal.? Ans : In real time application entire input is not available and input signal has to be processed online.

Length of input signal depends on application. It can be long sequence also. In IIR filter length of h[n] is infinite. Output of the filter is always Linear Convolution of impulse response with the input of the signal. To find output of digital IIR filter, Overlap Add Method using FFT or Overlap Save Method using FFT can not be used.

Output of digital IIR filter is calculated using difference equation recursively. (92) How to find output of IIR filter for long input sequence.? Ans : In IIR filter length of h[n] is infinite. Output of the filter is always Linear Convolution of impulse

response with the input of the signal. To find output of digital IIR filter, Overlap Add Method using FFT or Overlap Save Method using FFT can not be used.

Output of digital IIR filter is calculated using difference equation recursively. (93) What is DTFT ? Ans : DTFT is Fourier Transform of DT signal that converts the sampled DT signal from time domain

to frequency domain. Frequency domain representation parameters are magnitude and phase. DTFT gives frequency response that includes magnitude response and phase response.

(94) If DTFT is Fourier Transform of DT signal then What is DFT ? Ans : DFT is frequency sampling of DTFT. When DTFT is sampled in frequency domain we get DFT. (95) Describe the relat ion between DFT and DTFT. Ans : DFT is frequency sampling of DTFT. When DTFT is sampled in frequency domain with frequency

spacing of N

w π2= we get DFT coefficients.

Nkw

wXkX π2)(][=

=

(96) Derive DFT equation . [ Refer note book ] (97) Why DFT ? What is need of Sampling DTFT ? Ans : In digital domain for processing, input has to be discrete. For frequency domain analysis, DT

signal is converted to frequency domain. Frequency domain representation of DT signal is continuous, NOT discrete. For processing in digital domain we need to take sampled values. The frequency samples thus obtained are called DFT coefficient. That is what DFT is.

17

Kiran Talele ( )


(98) How to find DFT of infinite length sequence ? Ans : To find DFT of infinite length sequence x[n]:

(i) Find DTFT of x[n] i.e. ∑∞

−∞=

−=n

jnwenxwX ][)(

(ii) Find DFT by frequency sampling DTFT. i .e. N

kwwXkX π2)(][

==

DFT coefficients can be obtained by evaluating DFT equation.

(99) What is Power Density Spectrum of Periodic DT Signals ? Ans :

The average power of periodic DT signal is given by ∑−

==

1

0

2][1 N

nnx

NP

According to Parseval’s theorem, 21

0

1

0

2][1 ∑ ∑−

=

−

===

N

n

N

kkCnx

NP

The coefficients 2kC for k =0, 1, 2…..N-1 is the distribution of power as a function of

frequency is called the power density spectrum of the DT periodic signal (100) What is Energy Density Spectrum of DT Aperiodic Signals Ans :

The energy of DT signal x[n] is ∑∞

∞−==

nnxE 2][

According to parseval’s theorem, ∑∞

∞−= 2][nxE dwwX

2

)(21

∫−

=π

ππ

Let *2 )()()()( wXwXwXwSx == Sx (w) is the function of frequency and it is called energy density spectrum of x [n].

∑∞

∞−

= 2][nxE = ∫−

=π

ππ

.)(21 dwwSx

(101) Find DTFT and Energy Density Spectrum of x[n] = u[n].

Ans : Energy of u[n] is infinite. Therefore u[n] is not energy signal.

Fourier Transform is defined only for energy signal.

Kiran Talele ( ) 18


(102) What is the necessary condition to find DTFT of any signal. ? Ans : To find DTFT of any signal the necessary condition is, signal must be an energy

signal. It must be absolutely summable. (103) DTFT gives continuous spectra or discrete spectra?. Ans : When signal is periodic spectrum is Discrete. If the signal is not-

periodic then spectrum is always continuous. DTFT is fourier transform of Non-periodic signals. Therefore DTFT gives

continuous spectra. (104) How to use FFT algorithm to find IDFT ?

Ans : By IFFT equation we get, ( )** ][1][ kXFFTN

nx =

Algo : (i) Find X*[k] (ii) Find FFT (X*[k] ) using DIT-FFT/DIF-FFT flowgraph,

Here same flowgraph is required to find FFT X*[k]result.. (iii) Find x[n]

(105) What is the difference between DFT and DTFS ? [Refer Notes] (106) What is the relat ion between DFT and DTFS ? [Refer Notes] (107) What is the relat ion between DFT and DTFT ? [Refer Notes] (108) What is the relat ion between DTFT and ZT ? [Refer Notes] (109) What is the relat ion between DFT and ZT ? [Refer Notes] (110) How to find DFT of Two N point Real Sequence using a single N point FFT ? (111) How to find DFT of 2N point DFT of real valued sequence using a single N point FFT

algorithm? [Refer Notes] ---------------------------------------------------------------------

19Kiran Talele ( )


What & Why

Kiran Talele ( ) 20

(112) Why ZT is used for frequency domain analysis of DT systems

instead of DTFT ? Ans : DTFT of every input signal is not possible. DTFT of u[n] is not possible because

u[n] is not an energy signal. However ZT of u[n] is possible. Therefore ZT is used for analysis.

(113) What is the ZT of δ[n] and u[n] Ans : ZT δ[n]=1 and ZTu[n] = z/(z-1)

(114) What is the ZT of x[n] = (2)n u[n] Ans : X(z) = z/(z-2) ROC : |z| > 2

(115) Let x[n] = (4)n u[n] What is X(z) at z = 6 and z = 2 ?

Ans : X(z) = z/(z-4) ROC : |z| > 4 (i) At z = 6 X(z) = 6/2 = 3

4. ANALYSIS OF DT SYSTEM

( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ ⟩

−=Otherwise

azaz

znuaZT n

0][

( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧ ⟨

−−

=−−Otherwise

azaz

znuaZT n

0]1[

(ii) At z = 2 X(z) = ∞

(116) What is the concept of ROC ? Ans : ROC gives the set of values of Z for which X(z) is finite. Every value of Z in the

ROC gives X(z) finite. (117) What is the ROC condition for causal signal. ? Why ? Justify with

example. Ans : ROC is |z| > | Largest value of POLE | Ex x[n] = (2)n u[n] + (3)n u[n]

NOTE : If x[n] is right handed sequence, the ROC extends outward from the outermost finite pole in ∞=ztozX )(

Sequence ROC 1 x[n] = Entire Z-plane

2 x[n] = |Z| > 0

3 x[n] = an u[n] |Z| > |a|

4 x[n] = an u[n] + bn u[n] |Z|> max |a |,|b| 5 x[n] = (-3)n u[n] + (2)n u[n] |Z| > 3


(118) What is the ROC condition for Anti-causal signal? Why ? Justify with example.

Ans : ROC is |z| < | Lowest value of POLE | Ex x[n] = (2)n u[-n–1] + (3)n u[-n–1]

NOTE : If x[n] is Left handed sequence, the ROC extends inward from the innermost finite pole in 0zto)z(X =

Sequence ROC 1 x[n] = 1, 2, 3, 0

|Z| < ∞

2 x[n] = an u[-n-1] |Z| < |a|

3 x[n] = an u[-n-1] + bn u[-n-1] |Z| < min |a|, |b| 4 x[n] = (-3)n u[-n-1] + (2)n u[-n-1] |Z| < 2

Kiran Talele ( ) 21

(119) What is the ROC condition for Both-sided signal. ? Why ? Justify with example.

Ans : ROC condition for both sided signal is bounded between two POLES. Ex x[n] = (2)n u[n] + (3)n u[-n]

NOTE : If x[n] is two sided sequence, the ROC consist of a ring in the Z plane, bounded by interior and exterior pole.]

Sequence ROC

1 x[n] = an u[n] + bn u[-n-1] |b| > |z| > |a|

2 x[n] = (2)n u[n] + (3)n u[-n-1] 3 > |z| > 2

3 x[n] = (3)n u[n] + (2)n u[-n-1] Not possible

4 x[n] = (2)n u[n] + (3)n u[n] + (–4)nu[-n-1] + (5)nu[-n-1] 4 > |z| > 3

(120) What is DT system ? Ans : A DT system is a device or algorithm that operates on a DT signal according to some well defined

rule, to produce another DT signal. In general a DT system can be thought as a set of operations performed on the input signal x[n] to produce the output signal y[n].

(121) What are the classif ication of DT systems ? Ans : Systems are classif ied as,

(1) Static (Memorylees ) / Dynamic (Memory System) :-

(2) Linear / Non Linear System.

(3) Causal / Non Causal System

(4) Time Invariant / Time Variant System.

(5) Stable / Unstable system

(122) Explain classif ication of DT system

(123Ans

(124Ans

(125Ans

(1) Static (Memorylees ) / Dynamic (Memory System) :-

A DT system is called static or memoryless if it output at any instant depends on the input sample at the same time and not on past or future samples of the input. If the system is not static then it is dynamic.

(2) Linear / Non Linear System.

A system that satisfies the superposition principle is called Linear System.

If a system is Linear then,

T a . x1[n] + b x2[n] = a1 T x1 [n] + a2 T x2 [n]

If a system does not satisfy the superposition principle then it is Non Linear System.

(3) Causal / Non Causal System

A system is said to be causal if the output of the system at any time depends only on present and past values of input and does not depend on future values of input.

If the system is not causal then it is Non casual. For non causal system output depends onfuture values of input.

(4) Time Invariant / Time Variant System.

A system is called Time Invariant if a time shift in the input signal causes a time shift in the output signal. Otherwise the system is Time Variant System.

(5) Stable / Unstable system.

A system is said to be bounded input, bounded output stable if and only if every bounded input produces a bounded output.


) What is Impulse response ? Step response ? : Impulse Response is output of the system when input is δ[n]. Step Response is output of the system when input is u[n].

) What is zero input response ? : If the initial state of the system is NOT zero and the input x[n] = 0 to all n, then the output of the

system with zero input is called the zero input response or natural response or free response of the system.

) What is zero state response ? : If the initial state of the system is zero and the input x[n] ≠ 0 then the output of the system with

non zero input is called the zero state response or forced response of the system.

Kiran Talele ( ) 22


(126) What is zero state step response ? Ans : If the initial state of the system is zero and the input x[n]=u[n] then the output of the

system is called zero step response of the system.

(127) What is Transient response ? Ans : Transient response of the system is the response of the system that decays to zero. (128) What is Steady State Response ? Ans : Everlasting response of the system that depends on magnitude response and phase response of the

system is steady state response of the system. (129) What is Infinite Impulse Response ? Ans : When length of h[n] is infinite it is called infinite impulse response. E.g. h[n] = ( ½ )n u[n] (130) What is Finite Impulse Response ? Ans : When length of h[n] is finite it is called finite impulse response, E.g. 4,3,21][

↑=nh

(131) What is frequency response ? Ans : Frequency response means magnitude response and phase response. (132) What is Magnitude Response ? Ans : Magnitude Response = rDenominatoof

NumeratorofMagnitudeMagnitude

Where 22 )(Imaginary(Real)Magnitude +=

(133) What is Phase Response? Ans : Phase Response = Angle of Numerator – Angle of Denominator

Where

⎢⎢⎢⎢

⎣

⎡

<⎟⎠⎞

⎜⎝⎛+

>⎟⎠⎞

⎜⎝⎛

=−

−

0RealWhenReal

Imaginarytan180

0RealWhenReal

Imaginarytan

1

1

Angle

(134) How to obtain Frequency Response Graphically ? Ans : In Graphical method, the frequency response at a given frequency w is determined by

the ratio of the product of the zero vectors with the product of pole vectors.

Magnitude Response = polesfromdistanceofProductzerosfromdistanceofProduct

Phase Response = Summation of angles from ZEROS – Summation of angles from POLES.

23 Kiran Talele ( )


(135) Magnitude spectrum is continuous or discrete ? Ans : If the signal is periodic then magnitude spectrum is discrete and If the signal is not-

periodic then spectrum is continuous function of w.

(136) What is a digital resonator ? Ans : A digital resonator is essentially a narrowband bandpass filter.

(137) What is eigen value of the system ?

Ans : Eigen-function of a system is an input signal that produces an output that differs from the input by a constant multiplicative factor. The multiplicative factor is called an eigen value of the system.

(138) How to find value of DT signal at infini ty. ?

Ans : By final value theorem we can find x[∞]. )(1lim)(1

zXz

zxz

⎟⎠⎞

⎜⎝⎛ −

=∞→

(139) What is Transfer function of DT system ? Ans : The Z – Transform H(z) of an impulse response h[n] is known as the system function or

transfer function of the system

(140) What are different real ization methods of digital f i l ters ? Ans :

IIR FILTER LINEAR PHASE FIR FILTER. 1 Direct Form Realization

a) DF-I b) DF-II

Direct Form Realization -DF-I -DF-II

2 Lattice Realization Lattice Realization 3 Linear Phase Realization 4 Frequency Sampling Realization

(141) What is canonic structure ? Ans : If the number of delays in the realizat ion block diagram is equal to the order

of the transfer function, then the realization structure is called canonic otherwise i t is called non-canonic.

(142) What is the advantage of direct form –II method of realization ? Ans : DF-II method of real izat ion requires LESS no of delay block.

(143) What is the advantage of Linear Phase Realization ? Ans : Linear Phase method of realization requires LESS no of multipliers.

(144) What is the advantage of cascade connection of systems? Ans : In cascade form, the shift from the actual POLE location due to quantizat ion is

LESS. So, quantization error is less.

Kiran Talele ( ) 24


(145) What is the difference equation of DT system ?

Ans : Output in terms of past/present , input/output of the system is called difference of the system.

Eg y[n] = y[n–1] + y[n–1] + x[n] + x[n–1]

(146) What is t ransform domain stabili ty condit ion ? Ans : If ROC includes unit circle, then system is stable.

(147) What is s tabili ty condit ion for causal and stable system? Ans : For causal and stable system, al l the POLES must l ie INSIDE the unit circle.

(148) What do you mean by stable system ? Ans : If the system is stable then output of the system depends on the input that is

applied and characterist ics of the system. Mathematically, output should be always finite.

(149) What will happen if the system is not stable. ? Ans : If the system is stable then output of the system depends on the input that is

applied and characterist ics of the system. Mathematically, output should be always f inite. We get f ini te desirable output only when system is stable. If the system is not stable, output will not depend on the input, output will not depend on the characterist ics of the system. In that case we get undesired, distorted, noisy output.

(150) What is Minimum Phase System ? Ans : For any system If ∠ H(π) – ∠ H(0) = 0 Then system is called a Minimum Phase

System. When All zeros are inside the unit circle, the net phase change θ1(π) – θ1(0) = 0

i.e. minimum phase.

(151) What is Maximum Phase System ? Ans : For any system If ∠ H(π) – ∠ H(0) = Mπ Then system is called a Maximum

Phase System. When All zeros are outside the unit circle, the net phase change θ1(π)–θ1(0) = Mπ

i.e. Maximum phase.

NOTE : If the system is Neither Minimum Phase NOR Maximum Phase Then System is Mixed Phase System. Minimum Phase characteristic implies a min. delay function while a maximum phase characteristic implies that the delay characteristic is also maximum.

Kiran Talele ( ) 25

(152) Find the output of the following system

Z-1

10 y[n]x[n]


Always remember this →

[i] To find Zero State Response (ZSR)

Kiran Talele ( ) 26

(i) h[n] (ii) H[z] (iii) Difference Equation (iv) Realization Diagram (v) Pole Zero Plot

H(z) Y(z) X(z)

ZT IZT

x[n] y[n]

[ i i] Relationship Diagram `

P.Z.

H(z)

R.D.

h[n] D.E. IZT

(i) Take ZT (ii) Group the terms

with Y(z) & X(z) (iii) Arrange in terms

of Y(z)/X(z)

H(ejw) OR H(w) Freq. Response

i.e. DTFT

Put z = ejw

ZT

(i) Write H(z) in –ve powers of z (ii) Let H(z)=Y(z)/X(z) (iii) Cross Multiply (iv) Take IZT

(153) Impulse response of Digital Low Pass filter is given by h[n] = 3, 2, 1, 2, 3 . What will be the output of the filter for any given input x[n] ?

Digital Filter y[n]x[n]


5. DIGITAL FILTERS

What & Why (154) What is Digital filter ? Ans :

Digital filter is a discrete time System which produces a discrete time output sequence y[n] for the discrete time input sequence x [n]. Digital filter is nothing but mathematical algorithm implemented in hardware or software.

(155) What is Real time Digital filter? Ans : Real time digital filter consist of processing of real time signal using digital device called

digital processor. (156) What are the Advantages of digital filters-? Ans : The following list gives some of the main advantages of digital over analog filters.

1. A digital filter is programmable, i.e. its operation is determined by a program stored in the processor's memory. This means the digital filter can easily be changed without affecting the circuitry (hardware). An analog filter can only be changed by redesigning the filter circuit.

( i.e. Flexibility in parameter setting )

2. Digital filters are easily designed, tested and implemented on a general-purpose computer or workstation.

3. The characteristics of analog filter circuits (particularly those containing active components) are subject to drift and are dependent on temperature. Digital filters do not suffer from these problems, and so are extremely stable with respect both to time and temperature.

(157) What is Infinite Impulse Response (I I R) filter ? Ans : If the impulse response of the system is of infinite duration, the system is said to be I I R

filter system.

∞=⎟⎠⎞

⎜⎝⎛= Lenth].n[u

21]n[

nh Ex.

(158) What is Finite Impulse Response (FIR) filter ? Ans : If the impulse response of the system s of finite duration then the system is said to be FIR

system. Ex : 4,3,2,1]n[h1 = Length = 4 (finite)

Length = 5 (fnite)

↑⎭⎬⎫

⎩⎨⎧

=↑

1,2,3,2,1]n[h 2

27

Kiran Talele ( )


(159) What are Advantages of FIR Filters-? [Refer Theory Notes ] Ans:

1) They can easily be designed to be "linear phase" 2) They are suited to multi-rate applications. 3) They have desirable numeric properties. 4) They can be implemented using fractional arithmetic. 5) They are simple to implement.

(160) What are the disadvantages of FIR Filters (compared to IIR filters)? Ans : Compared to IIR filters, FIR filters sometimes have the disadvantage that they require more

memory and/or calculation to achieve a given filter response characteristic.

(161) What are the advantages of IIR filters (compared to FIR filters)? Ans : IIR filters can achieve a given filtering characteristic using less memory and calculations than a

similar FIR filter. (162) What are the disadvantages of IIR filters (compared to FIR filters)?

Ans : 1) They are more susceptible to problems of finite-length arithmetic, such as noise generated by calculations, and limit cycles. (This is a direct consequence of feedback: when the output isn't computed perfectly and is fed back, the imperfection can compound.)

2) They are harder to implement using fixed-point arithmetic. 3) They don't offer the computational advantages of FIR filters for multirate (decimation and

interpolation) applications.

(163) Compare FIR filters and IIR filters

FIR filter IIR filter 1 Provides exact linear phase. Not linear phase. 2 Provides good stability. Stability is not guaranteed. 3 Order required is higher. Order required is lower. 4 Computationally not efficient. Computationally more efficient. 5 More memory required for the storage

of coefficients. Less memory required fro storage of coefficients.

6 Requires more processing time. Requires less processing time. 7 Requires N multiplications per output

sample Requires 2N + 1 multiplications per output sample.

(164) What is the relation between Analog filter pole and digital filter pole when impulse invariant

technique is used for filter design. Ans : Z = e ST (165) What is the relationship between Analog filter frequency and digital filter frequency when

impulse invariant technique is used for filter design.

Kiran Talele ( ) 28

Ans : TW Ω=


(166) Why Impulse Invariant method is not suitable for HPF / BPF design? Ans : The the mapping from the analog frequency Ω to the freq. variable w in the digital domain is

many to one. which reflects the effect of aliasing due to sampling. A one to one mapping is

thus possible only if freq. lies in the principle range of ΩTTππ

≤Ω≤− .

That means if cut off frequency of analog filter Ω c is greater than .Tπ

then one to one

mapping from analog filter frequency to digital filter frequency is not possible. Therefore the

filter such as HPF or BPF with cut off frequency of analog filter c greater than Ω .Tπ

can not be designed using impulse invariant method. (167) What do you mean by invariant ? Ans : Invariant means, Not variant, ie. Doesn’t change. (168) Explain the Mapping of points from s-plane to z–plane when Impulse Invariant Method is used

for filter design.

Case-I When 1r,0 ==σ Analog poles which lies on imaginary axis gets mapped onto the unit circle in

the z-plane. Case-II When ,1r,0 <<σ

Analog poles that lies on LEFT half of s-plane gets mapped INSIDE the unit circle in the z–plane.

Case–III When .1r,0 >>σ

Analog poles that lies on RIGHT half of s-plane gets mapped OUTSIDE the unit circle in the z–plane.

Always explain wrt diagram. [ Refer theory notes ] (169) What is the relation between Analog filter pole and digital filter pole when BLT method is used

for filter design.

Ans : )1()1(2

+−

=zTzS

(170) What is the relationship between Analog filter frequency and digital filter frequency when

BLT method is used for filter design.

Ans : ⎟⎠⎞

⎜⎝⎛=Ω

2tan2 w

T(171) Explain frequency warping in BLT. Ans : [ Refer theory notes ]

29Kiran Talele ( )


(172) Frequency warping is needed to perform in BLT technique but not in impulse invariance techniqueOR In BLT there is no aliasing

Ans : Bilinear Transformation is a mapping of points from s-plane to corresponding points

in the z-plane. The BLT transforms, the entire j Ω axis in the s-plane into one revolution of the unit circle in the z-plane ie. only once and therefore avoids the aliasing of frequency components.

Always Remember This……..

[A] For Linear Phase filter h[n] must be either Symmetric or Antisymmetric.

Examples of Linear phase filters Examples of non Linear phase filters h[n] = 3, 2, 1, 2, 3 h[n] = 1, 2, 3, 1, 2, 3 h[n] = 1, 2, 2, 1 h[n] = 3, 2, 1, -2, -3 h[n] = 1, -2, 0, 2, -1 h[n] = 3, 2, 0, -2, 3 h[n] = δ[n] + δ[n-3] h[n] = 1, 2, 3, 4

[B] When h[n] is either Symmetric OR Antisymmetric, ZEROS of the filter are always in Reciprocal order.

i.e. If Z1 is ZERO of the filter, Then 1

1z

is also a ZERO of the filter.

[C] If ZEROS of the filter are in reciprocal order, then filter is Linear Phase FIR filter

[D] For linear Phase FIR filter.

a) ZEROS are always in reciprocal order (ie linear Phase) b) POLES are always only at origin (ie FIR)

ex h[n] = 1, –2.5, 1 ( )

2Z

2z21z

)z(H−⎟

⎠⎞

⎜⎝⎛ −

=

h [n] = 1, 0, -1 2Z)1z()1z()z(H −+

=

h [n] = 1, -1.5, -1.5, 1 3Z

)2z(21Z)1z(

)z(H−⎟

⎠⎞

⎜⎝⎛ −+

=

[E] When zeros of the filter are INSIDE the unit circle filter is called Minimum Phase Filter.

Concept : For Minimum Phase filter φ(π) - φ(0) = 0 [F] When all zeros of the filter are OUTSIDE the unit circle filter is called maximum phase filter.

Concept : For Maximum Phase filter φ(π) - φ(0) = ± m π

Kiran Talele ( ) 30


[G] When System is Neither Minimum Phase Nor Maximum Phase, Then System is Mixed Phase System

[H] When all zeros of the FIR filter are LEFT side of POLES, filter is LOW PASS FIR

FILTER.

eg. FIR Filter

[I] When all zeros of the FIR filter are RIGHT side of ZEROS, filter is HIGH PASS FIR FILTER.

eg. FIR Filter

[J] When zeros of the FIR filter are Both sides of POLES, Then filter is BAND PASS FIR

FILTER.

eg. FIR Filter

[K] When All ZEROS are on Left side of POLES , then filter is LPF

eg. IIR Filter [L] When All ZEROS are on Right side of POLES , then filter is HPF

eg. IIR Filter

[M] When ZEROS of the filter are outer sides of POLES, then filter is BPF

e.g. (i) ( )0.5z0.5)-(z 1)-(z 1)+(z )(

+=zH

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Kiran Talele ( )


[N] When POLES and ZEROS of the filter are in reciprocal order, filter is ALL PASS FILTER.

Eg. IIR filter , 5.0Z

2Z)z(H−−

= POLE P1 = 0.5 ZERO Z1 = 2

Here, ZERO = 1/POLE ∴ Filter is All Pass IIR Filter.

[O] When Numerator Coefficients and Denominator coefficients of H(z) are in Reverse Order Filter is ALL PASS FILTER.

Eg. H(z) = 21

21

32123

−−

−−

++++

zzzz (IIR)

Numerator Coefficients : [ 3, 2, 1 ] Denominator Coefficients : [ 1, 2, 3 ]

∴ Filter is All Pass IIR Filter.

(173) What is a linear phase filter? Ans : "Linear Phase" refers to the condition where the phase response of the filter is a linear (straight-

line) function of frequency.

(174) What is the advantage of Linear Phase ? Ans : This results in the delay through the filter being the same at all frequencies. Therefore, the filter

does not cause "phase distortion" or "delay distortion".

(175) Explain the concept of Linear Phase and its importance.

Ans : I. If the Phase Response is Linear the output of the Filter during pass-band is delayed input. II. If the phase Response is non Linear the output of the filter during pass-band is distorted one

The linear Phase characteristic is important when the phase distortion is not tolerable. FIR Filter can be designed with linear phase characteristic. In application like data transmission, speech processing etc phase distortion can not be tolerated and here linear phase characteristic of FIR filter is useful

(176) Show that if the Phase Response is Linear the output of the Filter during pass-band is delayed input. Consider a LPF with frequency response H(e–jwα) given by

⎪⎩

⎪⎨⎧

≤<

≤=

−

π

α

wwcwwe

eH cjw

jw

0||

)(

Kiran Talele ( ) 32

)(][

)(][

wYny

wXnx

H(ejw )

Let X(w) = DTFT X[n] ,

The FT of y[n] is then given by

Y(w) =X(w) . H(w)

Y(w) = X(w) . e–jwα

By iDTFT, y[n] = x[n – α] ← o/p of filter

[email protected] 9987030881 Kiran Talele ( ) 33

(177) What is the role of window in the design of FIR filter ? Name the few types of windows.

Ans : FIR filter is designed by truncating infinite samples of hd[n] by using window function. Examples of window function include, Hamming window, Bartlet Window, Hanning window, Blackman window etc.

(178) Why rectangular window is not preferred for FIR fi l ter design ? Ans : Rectangular window function has As = 21 db which is very small compared to other window

function. Larger value of As desired. (179) Is the following filter a linear phase filter. If yes, what is the type of filter ? It’s transfer

function is given by H(z) = 1 – z –4 . Ans : By IZT h[n] = 1, 0, 0, 0, –1 Since h[n] is anti-symmetric, filter is a linear phase FIR filter. Antisymmetric h[n] with N odd is suitable only for Band Pass Filter.

(i) At w = 0, z = 1 : H(w) = 0 (ii) At w = π, z = – 1: H(w) = 0 (iii) At w = π/2, z = j: H(w) = 2

(180) Why antisymmetric h[n] is not suitable for LPF fil ter design ? Ans : [ Refer notes ]

(181) Why symmetric h[n] with N even and anti-symm h[n] with N odd is not

suitable for HPF design ? Ans : [ Refer notes ]

(182) Explain Linear phase FIR fi l ter design using window. Ans : [ Refer class note book ]

(183) Explain frequency sampling method of FIR filter design ? Ans : [ Refer class note book ] (184) What is the advantage of frequency sampling realization ? Ans : The frequency sampling realization of filter is computationally more efficient than the direct

form realization. Justification : When the desired frequency response characterization of the FIR filter is

narrowband, most of the coefficients H[k] are zero. The corresponding filter sections can be eliminated and only the filters with non zero coefficients need to be retained. The net result is a filter that requires fewer computations (multiplications and additions) than the corresponding direct form realization. Thus frequency Sampling realization is more efficient realization.

(185) Why IIR filters are called as recursive filters ? Ans : In IIR filter output dépends on output values. e.g. y[n] = x[n] + x[n-1] + y[n] + y[n-1]. Therefore IIR filters are also called as Recursive Filters


(186) Why FIR filters are called as Non-recursive filters? Ans : In FIR filter output depends only on input values. It doesn’t depend on output values. e.g. y[n] = x[n] + x[n-1] Therefore FIR filters are also called as Non-Recursive Filters.

(187) Explain how to find output of digital FIR filter in real time application.

Ans : In real time applications, output of FIR filter is obtained using overlap add method / overlap save method.

(188) Explain how to find output of digital IIR filter in real time application.

Ans : In real time applications, output of IIR filter can be obtained by evaluating difference equation.

(189) Can we use Overlap Add Method and Overlap Save Method to find output of IIR filter for long data sequence. Ans : No.

(190) What is Phase Delay and Group Delay ? Ans : The phase delay and group delay. The phase delay (Tp) and group delay (Tg) of the filter are

given by,

dwTgand

wTp ==

)w(d)w( φφ−

The group delay Tg, is defined as the delayed response of the filter as a function of w to the signal. Linear Phase Filters are those Filters in which the phase delay and group delay are constant, ie independent of frequency. Linear Phase Filters are also called as constant time delay Filters.

(191) What are the desirable characteristics of window Function ? Ans : (i) . The Fourier Transform of the window function W(ejw) should have a small width of

main lobe containing as much of the total energy.

(ii) . The Fourier Transition of the window function W(ejw) should have side lobes that decrease in energy rapidly as w tends to π .

(192) Why IIR filter cannot have a linear phase : Ans : The physically realizable and stable IIR filter cannot have a linear phase. For a filter to

have a linear phase, the condition is h (n) = h (N-1-n) and the filter would have a mirror image pole outside the unit circle for every pole inside the unit circle. This results in an unstable filter. As a result, a causal and stable IIR filter cannot have a linear phase.

Kiran Talele ( ) 34


6. Miscellaneous

What & Why

(193) What is Hilbert Transform? Ans : Relationship between real and imaginary parts of complex functions is known as Hilbert

Transform Relationship.

(194) What is signal flow graph? Ans : A signal flow graph is basically a set of directed branches that connect at nodes.

This signal out of a branch is equal to the branch gain times the signal into the branch. (195) What is notch f i l ter? Give Applications of Notch filter :

Ans : A notch filter is a filter that contain one or more deep notches or ideally perfect nulls in its

frequency response characteristic. They are useful in application where specific frequency components must be eliminated. For

example instrumentation and recording systems required that the power line frequency of 60 Hz and its harmonics to be eliminated.

(196) What is comb fi l ter? Give Applications of comb filter :

Ans : A comb filter can be viewed as a notch filter in which the null occur periodically across the frequency band.

. Comb filters find applications in a wide range of practical systems such as in the rejection of power line harmonics, is the separation of solar and lunar components from ionosphere measurements of electron concentration and is the suppression of cluster from fixed objects in moving target indicates (MTI) radars.

(197) Explain Chirp Z – Transform Ans : The chirp Z–Transform is an efficient algorithm for evaluating the z – Transform of a

finite length sequence at spaced samples along a generalized couture in the z plane.

(198) What is Digital Signal Processor ? Ans : A Digital Signal Processor is a special-purpose CPU (Central Processing Unit) that

provides ultra-fast instruction sequences, such as shift and add, and multiply and add, which are commonly used in math-intensive signal processing applications.

(199) What is the Need of DSP Processor? Ans : DSPs are not the same as typical microprocessors. Microprocessors are typically general-

purpose devices that run large blocks of software. They are not often called upon for real-time computation and they work at a slower pace, choosing a course of action, then waiting to finish the present job before responding to the next user command. A DSP, on the other hand, is often used as a type of embedded controller or processor that is built into another piece of equipment and is dedicated to a single group of tasks. In this environment, the DSP assists the general-purpose host microprocessor.

35

Kiran Talele ( )


(200) What is the difference between Pentium Processor and DSP Processor ? [ Refer Notes ]

(201) What is the application of DSP chips ? Ans : DSP chips are used in sound cards; fax machines, modems, cellular phones, high-capacity

hard disks and digital TVs. According to Texas Instruments, DSPs are used as the engine in 70% of the world's digital cellular phones, and with the increase in wireless applications, this number will only increase. Digital signal processing is used in many fields including biomedicine, sonar, radar, seismology, speech and music, processing imaging and communications.

(202) What is the use of All pass f i l ter ?

Ans : All pass f i l ter is used for phase compensation. Whenever sinusoidal signal is passed through All Pass Fil ter , the phase value of the input signal is modified.

Kiran Talele ( ) 36

X(t) Analog Input

Y(t) Anolog output

(203) Explain real time digital filter.

ADC

Anti aliasing

Alter

Digital Processor

DAC

Reconstruction Filter

As shown in figure, analog input signal is band limited using antialiasing filter which is then sampled and DT signal thus obtained is converted into digital signal using AdC. Digital processor, perform the operation depending upon the algorithm programmed in digital processor. The output of the digital processor is converted inot analog signal using Dac. Reconstruction filter is used to obtain the corresponding analog signal from the output DT signal.

dtsp extc viva questions answer

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