07a6ec01 digital signal processing

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SET-1R07Code.No: 07A6EC01

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD III B.TECH II SEM–REGULAR/SUPPLEMENTARY EXAMINATIONS MAY - 2010

DIGITAL SIGNAL PROCESSING (COMMON TO EEE, ECE, EIE, E.CON.E, ETM, ICE)

Time: 3hours Max.Marks:80 Answer any FIVE questions

All questions carry equal marks - - -

1.a) Verify the following system is stable or not Y(n) = sin[x(n)] b) Determine whether the following system is linear or not Y(n) = log10[x(n)] c) A LTI system is described by

3 1( ) ( 1) ( 2) ( )4 8

y n y n y n x n− − + − =

Determine the frequency response of the system. [16] 2.a) Compute the convolution of the following two sequences using DFT 1( ) {1,2,1, 1}x n = − 2 ( ) {1, 1,2, 1}x n = − − b) Consider the sequence x(n) = 4 ( ) 3 ( 1) 2 ( 2) ( 3)n n n nδ δ δ δ+ − + − + − . Find 6-point DFT of x(n) [8+8] 3.a) Compute the DFT using Radix -2, DIT-FFT algorithm x(n) = { 1, 1, 1, 1, 0, 0, 0, 0, } b) Compare DIT-FFT and DIF-FFT algorithms in calculating DFT of a sequence. [16]

4.a) Consider the system H(z) = 1 2 3

1 1 1

1 2 0.5 1(1 )(1 0.5 )(1 0.2 )

Z Z Z ZZ Z Z

− − −

− − −

− + −< <

− − −. Sketch the

pole zero pattern and determine stability of system. b) Realize the following system in direct form I and II

11 2

1( )1

H Za z a z−=

+ + 2− [8+8]

5. Design a Digital Butterworth Low pass filter with pass band cut off frequency 0.35 & 0.01p pw π δ= = and stop band frequency of 0.5 & 0.01s sw π δ= =

use Bilinear transformation. [16] 6.a) Explain why FIR filter is called as a linear phase filter? b) Use a hamming window to find fourth order linear phase FIR filter to approximate ideal

low pass filter e-j2w for a 1w ≤ and zero for 1 w π≤ ≤ . [16]

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7.a) What are the applications of multirate digital signal processing. b) Design a interpolator which meet the following specifications. Interpolation factor = 20 Pass band : 0 90f≤ < Transitions band : 90 100f< < Input sampling rate : 10 KHz Ripple : 2

1 210 , 10δ δ 3− −= = [8+8] 8. Explain the on chip peripherals available on TMS 320C5X processor and explain the

function of each. [16]

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1.a) State what is the necessary condition for stability of a linear time invariant system. b) Determine and sketch the magnitude and phase response of the following system.

[1( ) ( ) ( 1) ( 2)3

y n x n x n x n= + − + − ] [8+8]

2.a) Distinguish between linear convolution and circular convolution and compute the

convolution for the following sequences. 1( ) {1,1, 1,2 }x n = − 2 ( ) {1, 1,1, 1}x n = − − b) Find the DFT of the following sequence ( ) ( ) 2 ( 5)x n n nδ δ= = − . [8+8] 3.a) Compute the DFT of the following sequence using radix-2 DIT-FFT ( ) {2,1, 2, 1,1,1, 2,1 }x n = b) Explain the inverse DFT using DIF-FFT radix-2 algorithm. [8+8] 4.a) A causal LT1 system is described by the difference equation

here ( ) ( 1) ( 2) ( 1y n y n y n x n= − + − + − ) w ( )x n is the input and is the output. Find the H(z) for the system.

( )y n

b) Realize the following system in Cascade form

( )( )

1 2

2

1( )3 1 1z zH z

z z z

− −

−

− −=

− − − [8+8]

5.a) Design a digital low pass Butterworth filter using bilinear transformation to meet the

following specification. Pass band edge frequency = 1.KHz. Stop band edge frequency = 2 KHz Pass band ripple 0.2 dB ≥ Stopband attenuation ≥ 10 dB Sampling frequency = 5 KHz. b) Draw and explain the frequency response of type-I Chebyshev filter. [8+8] 6. Design a band stop filter with desired frequency response ( ) 02

1 2jw j wn

d c cH e e w w w−= − ≤ ≤

2& cw w π≤ ≤

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0 otherwise. N = 7 & cutoff frequency 1 4cw π= and 2

34cw π= using Hamming window.

[16] 7.a) Describe the decimation process with a neat block diagram. b) Consider a signal ( ) sin ( )x n n u nπ= . Obtain a signal with an interpolation factor of ‘2’

[8+8] 8. Write short notes on the following with respect to digital signal processor. a) Barrel shifter b) MAC. [8+8]

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1.a) Determine whether the following systems are linear, causal and stable. (i) ( ) ( )y n nu n= (ii) 2( ) ( 1)y n n u n= − b) Determine the frequency response of the system described by the following difference

equation with ( ) 0.8 ( 2) ( 1)y n y n x n− − = −

[8+8] ( 1) 1, ( 2) 0 & ( ) ( )y y x n u− = − = = n 2.a) Prove the following properties (i) *( ) *(( )) ( )N Nx n x K R K→ − (ii) ( )* ( ) ( ) ( )N eN

x n R k x K− → b) Find the discrete Fourier series for the following function shown in fig.1 [8+8]

3.a) Draw the Butterfly diagram for a 16-point DIF-FFT algorithm. b) Compute 8-point DFT using radix-2 DIT-FFT algorithm for the following sequence

x(n) = { 1, 2, 3, 0, -1, -2, 1, 1 } [8+8] 4.a) Determine the stability of the system described by

1

1 2( )1

zH zz z

−

− −=− −

b) Realize the following system in parallel form

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( )( )( )2

1( )

1 2z

H zz z z

−=

+ + +1 [8+8]

5. Determine the system function H(z) of the lowest order Chebyshev digital filter that

meets the following specifications. (a) d.B ripple in the pass band 0 0.w 3π≤ ≤

(b) At least 60 dB attenuation in the stop band 0.35 wπ π≤ ≤ . Use bilinear transformation method. [8+8]

6. Design a Band stop filter with desired frequency response ( ) 02

1 2jw j wn

d c cH e e w w w−= − ≤ ≤

2& cw w π≤ ≤ 0 otherwise. For N = 7 & cut off frequency 1 4cw π= and 2

34cw π= using Barlett window.

[16] 7.a) Why multirate digital signal processing is needed? b) Design a two state decimator for the following specifications. Decimation factor = 50 Pass band = 0 5f 0≤ ≤ Transitive band = 50 55f≤ ≤ Input sampling = 10 KHz Ripple = 1

1 210 & 10δ δ 3− −= = [8+8] 8.a) What are the advantages of DSP processors. Compare to other conventional processor? b) Explain the architecture of TMS 320C5X processor with suitable block diagram.

[8+8]

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1.a) Define the following terms for the LTI system (i) Linearity (ii) Causality (iii) Stability. b) Solve the following difference equation for the given initial conditions

3 1( ) ( 1) ( 2) 04 8

y n y n y n+ − + − =

y(0) = 1 and y(-1) = -6 and all other initial conditions are zero. [8+8] 2.a) Define DFT and prove its any four properties. b) Find the convolution of the following two sequences using DFT. 1( ) {1, 2, 2, 1}x n = − − [8+8] 2 ( ) {1, 1, 1,1}x n = − 3.a) Compute the 8-point DFT for the following sequence using DIT-FFT algorithm

1 3

( )0

for xx n

otherwise4− ≤ ≤⎧

= ⎨⎩

b) What ‘Bit-reversal’ and ‘in-place computation’? c) Calculate the number of multiplications needed in the calculations of DFT using

FFT algorithm with 32 point sequence. [16] 4.a) Determine the inverse Z transform of the following function

X(z) = 2

21 12 4

z z

z z

+

⎛ ⎞ ⎛ ⎞− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

b) Realize the following system is parallel form H(z) = 1

11z

z z

−

2− −− −. [8+8]

5. Design a digital chebyshev filter to meet the following specifications. ( )0.8 1jH e ω≤ ≤ 0 0.2ω π≤ ≤

( ) 0.2jH e 0.6ω ≤ π ω π≤ ≤

Using (a) Bilinear transformation method. (b) Impulse invariant method. [8+8] 6.a) Design high pass linear phase filter with frequency response.

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( ) 02j njcH e e ωω ω ω π−= ≤ ≤

0 otherwise. For N = 7 and Cω = 4

π use rectangular window.

b) Compare 11R and FIR filter. [8+8] 7.a) What are the advantages and drawbacks of multirate digital signal processing b) Design a decimator with the following specification D = 5, 0.025pδ = , 0.0035sδ = , 0.2sω π= Assume any other required data.

[8+8] 8.a) Explain the various interrupt types available in TMS 320C5X processor. b) What are different address modes in digital signal processor TMS 320C5X. [8+8]

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07a6ec01 digital signal processing

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