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B. N COLLEGE OF ENGINEERING AND TECHNOLOGY, LUCKNOW

Department of Electronics & Communication Engineering

DIGITAL SIGNAL PROCESSING LAB (EEC 652)

LIST OF EXPERIMENTS:

1. To Study Circular Convolution

2. Study of FIR Filter and plotting frequency response

3. Generate Amplitude Modulation and observe the Characteristic

4. Evaluation of DFT of a given sequence.

5. Implement the filter function

6. Generate a Random Binary Data Stream

7. Study of Sampling and study of Aliasing of signal using Mat lab

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EXPERIMENT NO 1

Object: To Study Circular Convolution

Apparatus Required: DSP KIT with processor DSK6713

Personal computer CRO

Procedure:

1. Creating a new project

2. Creating a new configuration file

3. Adding files to a project

4. Reviving the source code

5. Building the program

6. Enabling the RTDX channel

7. Displaying the graphs

Mat lab program:

function y=circular_convolution(x,h)

x= input ('enter the first sequence');

h= input ('enter the second sequence');

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N1= length(x);

N2= length(h);

N=max(N1,N2);%length of sequence

x=[x zeros(1,N-N1)]; %modified first sequence

h=[h zeros(1,N-N2)]; %modified second sequence

for n=0:N-1;

y(n+1)=0;

for i=0:N-1

j=mod(n-i,N);

y(n+1)=y(n+1)+x(i+1)*h(j+1); %shifting and addingend

%to display and plot circular convolution

n=1:N;

disp('output sequence of circular convolution');

disp(y);%to view output in command window

pause;

stem(n,y);%plotting circular convolution

grid minor;

xlabel('time index');

ylabel('amplitude');

title('circular convolution sequence of x and h');

RESULT : We observe the desired output.

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EXPERIMENT NO 2

Object: Study of FIR Filter and plotting frequency response.



Procedure:








Mat lab program:

Fs=10000; % Sampling frequency

N=41; % Filter length

WT=[10 3 10]; % Weights of the deviations in the bands

Hd=[0 0 1 1 0 0]; % Desired magnitude response in the bands

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F=[0 0.1 0.2 0.3 0.4 1]; % Band edge frequencies

b = remez(N-1, F, Hd, WT); % Compute the filter coefficients

[H, f] = freqz(b, 1, 512, Fs);% Compute the frequency response

mag = 20*log10(abs(H)); % of filter and plot it

plot(f, mag), grid on

xlabel('Frequency (Hz)')

ylabel('Magnitude (dB)')


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EXPERIMENT NO 3

Object: Generate Amplitude Modulation and observe the Characteristic



Procedure:








Mat lab program:

t=0:0.001:1;

vd=8*cos(2*pi*5*t);

vc=0.1*cos(2*pi*15*t);

ft=vc.*vd;

am=ft+vc;

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figure(1)

plot(t,vd);

figure(2)

plot(t,vc);

figure(3)

plot(t,am);


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EXPERIMENT NO 4

Object: Evaluation of DFT of a given sequence.



Procedure:








Mat lab program:

%DFT by Direct Method (dsp8t3.m)

disp('Performs DFT on windowed cosine wave');

disp('Set relative frequency of cosine wave: ');

W=pi/4;

N = 64 ; % DFT order;

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Invers = 0; % Specifies DFT rather than inverse DFT

% Store N samples of cos(W*n) as test signal:- }

for n =0 : N-1

x(n+1) = cos(n*W) + j* 0 ;

end;

figure (1); plot([0:N-1],x); grid on;

% Start DFT procedure:-

if Invers ==1

E = -2*pi/N

elseE = 2*pi/N

end;

for k=0 : N-1

X(1+k) = 0 + j*0 ; Wk =k*E ;

for L = 0 : N-1

C = cos(L*Wk) + j *sin(L*Wk);

X(1+k) = X(1+k) + x(1+L) * C;

end;

if (Invers == 1)

X(1+k)=X(1+k)/N;

end;

end;

figure(2); plot([0:N-1] , abs(X),'r* '); grid on;


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EXPERIMENT NO 5

Object: Implement the filter function



Procedure:








Mat lab program:

N=10; % length of test input signal

NB=N/2; % block length

x = 1:N; % test input signal

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B = [1,1]; % feedforward coefficients

A = 1; % feedback coefficients (no-feedback case)

[y1, Sf] = filter(B,A,x(1:NB)); % process block 1

y2 = filter(B,A,x(NB+1:N),Sf); % process block 2

for i=1:NB % print input and output for block 1

disp(sprintf('x(%d)=%f\ty(%d)=%f',i,x(i),i,y1(i)));

end

for i=NB+1:N % print input and output for block 2disp(sprintf('x(%d)=%f\ty(%d)=%f',i,x(i),i,y2(i-NB)));

end


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EXPERIMENT NO 6

Object: Generate a Random Binary Data Stream



Procedure:








Mat lab program:

% Setup

% Define parameters.

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M = 16; % Size of signal constellation

k = log2(M); % Number of bits per symbol

n = 3e4; % Number of bits to process = 30,000

Fd=1;Fs=1; %Input message sampling frequency, output message sampling

frequency

nsamp = 1; % Oversampling rate

%% Signal Source

% Create a binary data stream as a column vector.

x = randint(n,1); % Random binary data stream

% Plot first 40 bits in a stem plot.

stem(x(1:40),'filled');title('Random Bits');

xlabel('Bit Index');

ylabel('Binary Value');


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EXPERIMENT NO 7

Object: Study of Sampling and study of Aliasing of signal using Mat lab



Procedure:








Mat lab program:

Sampling:

x(n) = xa(nTs)

x is a discrete signal sampled from the analog signal xa with a sample periodof Ts and a

sample frequency of Fs = 1/Ts.

Try:

Fs = 100;

N = 1000;

stoptime = 9.99;

t1 = (0:N-1)/Fs;

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t2 = 0:1/Fs:stoptime;

x1 = sin(2*pi*2*t1);

x2 = sin(2*pi*3*t2);

plot(x1)

figure, plot(x2)

Aliasing:

Digital signals are often derived by sampling a continuous-time signal with

an analog-to digital (A/D) converter. If the continuous signal, xa(t), is band

limited, meaning that it does not contain any frequencies higher than a

maximum frequency fM, the Shannon sampling theorem says that it can be

completely recovered from a set of samples if the sampling frequency fs is

greater than two times the maximum frequency of the signal to be sampled:

Fs > 2fM

This maximum frequency fM is known as the Nyquist frequency. If the

sampling frequency is not greater than two times the Nyquist frequency, the

continuous signal cannot be uniquely recovered and aliasing occurs. (You

heard examples of aliased signals in Homework No.1).

fs > 2fM: Original signal and sampled signal have the same frequency.

fs _ 2fM: Sampled signal is aliased to half the original frequency.

t = 0:0.001:2;xa = sin(2*pi*5*t);

plot(t,xa)

hold on

fs = 15;

ts = 0:1/fs:2;

xs1 = sin(2*pi*5*ts);

plot(ts,xs1,ro-)

fs = 7.5;

ts = 0:1/fs:2;

xs2 = sin(2*pi*5*ts);

plot(ts,xs2,ro-)

hold off

RESULT: We observe the desired output.

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