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PRG 1% Program to generate sinusoidal waveform based on recursive difference% equation clc;clear all ;

close all ; x = [0 0 ones(1,50)]; % input sequencey_ics =[1 1]; % initializing past outputs h = recur_diff(x,y_ics); % sub-function call plot(h); % printing outputgridtitle( 'Sinusoidal Waveform' );xlabel( 'Time' );ylabel( 'Amplitude' );

% subfunctionfunction y = recur_diff(x,y_ics);y(1) = y_ics(1);y(2) = y_ics(2);

for k=3:(length(x)+2)y(k)=1.91996*y(k-1)-0.99998*y(k-2); % recursive operation

end

OUTPUT:

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0 10 20 30 40 50 60-1.5

-1

-0.5

0

0.5

1

1.5Sinusoidal Waveform

Time

A m p

l i t u

d e

PRG 2

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% Program to find DFT of given signal

clc;clear all ;close all ;

N = input( 'Enter the value of N(Value of N in N-Point DFT): ' );x = input( 'Enter the sequence for which DFT is to be calculated: ' );n=[0:N-1];k=[0:N-1];WN=exp(-1*j*2*pi/N); %Twiddle factornk=n'*k;W=WN.^nk;X=x*W;MagX=abs(X); % Magnitude of calculated DFTPhaseX=angle(X)*180/pi; % Phase of the calculated DFTsubplot(2,1,1);plot(k,MagX);title( 'Magnitude Spectrum of calculated DFT' );xlabel( 'N' )ylabel( 'Magnitude' )subplot(2,1,2);plot(k,PhaseX);title( 'Phase Spectrum of the calculated DFT' );xlabel( 'N' )ylabel( 'phase' )

OUTPUT:

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Enter the value of N(Value of N in N-Point DFT): 8Enter the sequence for which DFT is to be calculated: [1 1 1 1 1 1 0 0]

0 1 2 3 4 5 6 70

2

4

6Magnitude Spectrum of calculated DFT

N

M a g n

i t u

d e

0 1 2 3 4 5 6 7-200

-100

0

100

200Phase Spectrum of the calculated DFT

N

p h a s e

% Program to find IDFT of given signal

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N = input( 'Enter the value of N(Value of N in N-Point DFT): ' );X = input( 'Enter the sequence for which IDFT is to be calculated: ' );n=[0:N-1];k=[0:N-1];

WN=exp(1*j*2*pi/N);nk=n'*k;W=WN.^nk;x=X*W;x = x/N;disp( 'The IDFT of given sequence is' );disp(real(x));

OUTPUT:

Enter the value of N(Value of N in N-Point DFT): 8Enter the sequence for which IDFT is to be calculated: [5, 0, 1-i, 0, 1, 0, 1+j, 0]

The IDFT of given sequence is

1.0000 0.7500 0.5000 0.2500 1.0000 0.7500 0.5000 0.2500

PRG 3

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Frequency response of a given system given in (Transfer Function/Difference equation form)

Aim :- To find the frequency response of the system given by difference equationy(n) 5 y(n1) = x(n) + 4 x(n1)

Apparatus Used:- System with MATLAB R2008

Theory:

Procedure:- 1) Open MATLAB2) Open new M-file3) Type the program4) Save in current directory5) Compile and Run the program6) For the output see command window\ Figure window

Program:-

b = [1, 4]; %Numerator coefficientsa = [1, -5]; %Denominator coefficientsw = -2*pi: pi/256: 2*pi;[h] = freqz(b, a, w);subplot(2, 1, 1),

plot(w, abs(h));xlabel('Frequency \omega'), ylabel('Magnitude');

gridsubplot(2, 1, 2), plot(w, angle(h));xlabel('Frequency \omega'), ylabel('Phase - Radians'); grid

OUTPUT:

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-8 -6 -4 -2 0 2 4 6 80.5

1

1.5

Frequency

M a g n

i t u

d e

-8 -6 -4 -2 0 2 4 6 8-4

-2

0

2

4

Frequency

P h a s e -

R a

d i a n s

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PRG 4:

% Program to determine the Power Spectrum of given signal clc;clear all ;

close all ; N = 512;fs = N; %sampling frequencyt = 0:1/fs:0.2;x = 2*sin(2*pi*200*t); %input signalplot(x);title( 'Given Signal' );xlabel( 'Time' );c = xcorr(x);c1 = c(1:length(t));F = fft(c,N);% figure,plot(t,abs(F));f = 1000*(0:N-1)/N;figure,plot(f,abs(F));title( 'Frequency content of x' );xlabel( 'frequency (Hz)' );

OUTPUT:

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0 20 40 60 80 100 120-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Given Signal

Time

0 100 200 300 400 500 600 700 800 900 10000

2000

4000

6000

8000

10000

12000Frequency content of x

frequency (Hz)

PRG 5

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System function is given by

22

11

0

1)(

++

= z a z a

b z H

% Program to generate sinusoidal signal through filtering clc;clear all ;close all ; fs = 1000; % sampling frequencyt0 = 1/fs;f = 5; imp = [1; zeros(999,1)]; %Input - Impulse

b0=2*sin(2*pi*f*t0);a1=-2*cos(2*pi*f*t0);a2=1; num = [b0];den = [1 a1 a2]; y = filter(num,den,imp);figure,plot(y);title( 'Sine Wave' )

OUTPUT:

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0 100 200 300 400 500 600 700 800 900 1000-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5Sine Wave