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LABORATORY MANUAL

SUBJECT: DIGITAL SIGNAL PROCESSING

STUDENT NAME : ……………………………………………………..

ROLL NUMBER :

…………………………………………………………

EXAM NUMBER : …………………………………………………………

SEMESTER : …………………………………………………………

YEAR : …………………………………………………………

Department of Electronics and Communication Engineering,

L.D.R.P. Institute of Technology and Research,

Gandhinagar,



July – December 2009.



CERTIFICATE

This is to certify that Shri....................................................................... Roll

no. ....................... of B.E. semester................................class has satisfactorily

completed the course in ........................................................................... within

four walls of L.D.R.P. Institute of Technology and Research, Gandhinagar.

Date: Staff-in-charge Head of the dept.

CERTIFICATE

This is to certify that the above term work of

Shri.............................................................. University Exam. No. .................... of

B.E. Semester................................ is assessed for University examination.

Date: Examiner



INDEX

Sr.

No. Objective DatePage

No SignatureRemarks

1 Generation of Unit

Sample Sequence.

2 Generation of a complex

exponential sequence

3 Generation of a realexponential sequence

4 Generation of asinusoidal sequence

5 Signal Smoothing by

Averaging

6 Generation of amplitude

modulated sequence

7 Generation of a swept

frequency sinusoidalsequence

8 Generation of theensemble average

9 Generation of complexexponential sequence

10 Generation of realexponential sequence

11 Signal Smoothing by a

Moving-Average Filter

12 Illustration of Median

Filtering

13 Illustration of

Convolution

14 Computation of

Autocorrelation of a

Noise CorruptedSinusoidal Sequence

15 Illustration of Up-

Sampling by an IntegerFactor

16 Illustration of Down-

Sampling by an Integer

Factor





Practical: 1

Date: ________

Aim: Generation of Unit Sample Sequence.

Program Code:

% Generate a vector from -10 to 20n = -10:20;

% Generate the unit sample sequenceu = [zeros(1, 10) 1 zeros(1,20)];

% Plot the unit sample sequencestem(n,u);

xlabel(’Time index n’);ylabel(’Amplitude’);

title(’Unit Sample Sequence’);

axis([-10 20 0 1.2]);

Output:

-10 -5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

Timeindexn

A m p l i t u d e

Unit SampleSequence



Signature:__________

Practical: 2

Date:__________

Aim: Generation of a complex exponential sequence

Program Code:

c = -(1/12)+(pi/6)*i;

K = 2;n = 0:40;

x = K*exp(c*n);

subplot(2,1,1);

stem(n,real(x));

xlabel(’Time index n’);ylabel(’Amplitude’);title(’Real part’);

subplot(2,1,2);stem(n,imag(x));

xlabel(’Time index n’);ylabel(’Amplitude’);title(’Imaginary part’);

Output:

0 5 10 15 20 25 30 35 40-2

-1

0

1

2

Timeindexn

A m p l i t u d e

Real part

0 5 10 15 20 25 30 35 40-1

0

1

2

Timeindexn

A m p l i t u d e

Imaginarypart



Signature:_________

Practical: 3

Date:_________

Aim: Generation of a real exponential sequence

Program Code:

n = 0:35; a = 1.2; K = 0.2;

x = K*a.^+n;

stem(n,x);


Output:

0 5 10 15 20 25 30 350

20

40

60

80

100

120

Time index n

A m p l i t u d e




Practical: 4

Date:__________

Aim: Generation of a sinusoidal sequence

Program Code:

n = 0:40;f = 0.1;

phase = 0;A = 1.5;

arg = 2*pi*f*n - phase;x = A*cos(arg);

clf; % Clear old graphstem(n,x); % Plot the generated sequence

axis([0 40 -2 2]);grid;

title(’Sinusoidal Sequence’);xlabel(’Time index n’);ylabel(’Amplitude’);axis;

Output:



0 5 10 15 20 25 30 35 40-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Sinusoidal Sequence

Timeindexn

A m p l i t u d e


Practical: 5

Date:__________

Aim: Signal Smoothing by Averaging

Program Code:

R = 51;d = 0.8*(rand(R,1) - 0.5); % Generate random noise

m = 0:R-1;s = 2*m.*(0.9.^m); % Generate uncorrupted signal

x = s + d’; % Generate noise corrupted signalsubplot(2,1,1);

plot(m,d’,’r-’,m,s,’g--’,m,x,’b-.’);xlabel(’Time index n’);ylabel(’Amplitude’);

legend(’d[n] ’,’s[n] ’,’x[n] ’);x1 = [0 0 x];x2 = [0 x 0];x3 = [x 0 0];y = (x1 + x2 + x3)/3;

subplot(2,1,2);plot(m,y(2:R+1),’r-’,m,s,’g--’);

legend(’y[n] ’,’s[n] ’);




Output:

0 5 10 15 20 25 30 35 40 45 50-5

0

5

10

Timeindexn

A m p l i t u d e

d[n]

s[n]x[n]

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

Timeindexn

A m p l i t u d e

y[n]

s[n]

Signature:_________

Practical: 6

Date:_________

Aim: Generation of amplitude modulated sequence

Program Code:

n = 0:100;m = 0.4;fH = 0.1; fL = 0.01;

xH = sin(2*pi*fH*n);xL = sin(2*pi*fL*n);

y = (1+m*xL).*xH;

stem(n,y);grid;xlabel(’Time index n’);ylabel(’Amplitude’);

Output:



0 10 20 30 40 50 60 70 80 90 100-1.5

-1

-0.5

0

0.5

1

1.5

Time index n

A m p l i t u d e

Signature:________

Practical: 7

Date:__________

Aim: Generation of a swept frequency sinusoidal sequence

Program Code:

n = 0:100;a = pi/2/100;

b = 0;arg = a*n.*n + b*n;

x = cos(arg);clf;

stem(n, x);axis([0,100,-1.5,1.5]);

title(’Swept-Frequency Sinusoidal Signal’);xlabel(’Time index n’);





d = rand(R,1)-0.5;x = s + d';x1 = x1 + x;

end

x1 = x1/50;stem(m,x1);

xlabel('Time index n');ylabel('Amplitude'); title('Ensemble average');

Output:

0 5 10 15 20 25 30 35 40 45 50-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Timeindexn

A m p l i t u

d e

Noise

Signature:________

Practical: 9

Date:__________

Aim: Generation of complex exponential sequence

Program Code:

a = input('Type in real exponent = ');b = input('Type in imaginary exponent = ');

c = a + b*i;

K = input('Type in the gain constant = ');N = input ('Type in length of sequence = ');n = 1:N;

x = K*exp(c*n); %Generate the sequence

stem(n,real(x)); %Plot the real part



xlabel('Time index n');ylabel('Amplitude');title('Real part');

disp('PRESS RETURN for imaginary part');pause

stem(n,imag(x)); %Plot the imaginary partxlabel('Time index n');ylabel('Amplitude');title('Imaginary part');

Observation:

Type in real exponent = 5

Type in imaginary exponent = 6

Type in the gain constant = 67

Type in length of sequence = 68

Output:



0 10 20 30 40 50 60 70-0.5

0

0.5

1

1.5

2

2.5

3x 10

149

Time index n

A m p l i t u d e

Real part


Practical: 10

Date:__________



Aim: Generation of real exponential sequence

Program Code:

a = input('Type in argument = ');K = input('Type in the gain constant = ');

N = input ('Type in length of sequence = ');

n = 0:N;x = K*a.^n;

stem(n,x);xlabel('Time index n');ylabel('Amplitude');title(['\alpha = ',num2str(a)]);

Observation:-

Type in argument = 3Type in the gain constant = 5Type in length of sequence = 6

Output:

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5x10

4

Timeindexn

A m p l i t u d e

α= 4


Practical: 11

Date:__________



Aim: Signal Smoothing by a Moving-Average Filter

Program Code:

R = 50;

d = rand(R,1)-0.5;

m = 0:1:R-1;s = 2*m.*(0.9.^m);x = s + d';

plot(m,d,'r-',m,s,'b--',m,x,'g:')

xlabel('Time index n'); ylabel('Amplitude')legend('d[n]','s[n]','x[n]');

pause

M = input('Number of input samples = ');b = ones(M,1)/M;

y = filter(b,1,x);

plot(m,s,'r-',m,y,'b--')legend('s[n]','y[n]');

xlabel ('Time index n');ylabel('Amplitude')

Output:

0 5 10 15 20 25 30 35 40 45 50-1

0

1

2

3

4

5

6

7

8

Timeindexn

A m p l i t u d e

d[n]

s[n]

x[n]

Signature:_________

Practical: 12

Date:__________



Aim: Illustration of Median Filtering

Program Code:

N = input('Median Filter Length = ');

R = 50; a = rand(1,R)-0.4;

b = round(a); % Generate impulse noisem = 0:R-1;s = 2*m.*(0.9.^m); % Generate signalx = s + b; % Impulse noise corrupted signaly = medfilt1(x,3); % Median filtering

subplot(2,1,1)

stem(m,x);axis([0 50 -1 8]);xlabel('n');ylabel('Amplitude');

title('Impulse Noise Corrupted Signal');

subplot(2,1,2)stem(m,y);xlabel('n');ylabel('Amplitude');title('Output of Median Filter');

Observation:

Number of input samples = 4

Median Filter Length = 5



Output:

0 5 10 15 20 25 30 35 40 45 50

0

2

4

6

8

n

A m p l i t u d e

ImpulseNoiseCorruptedSignal

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

n

A m

p l i t u d e

Output of MedianFilter




Practical: 13

Date:__________

Aim: Illustration of Convolution

Program Code:

a = input('Type in the first sequence = ');

b = input('Type in the second sequence = ');

c = conv(a, b);M = length(c)-1;n = 0:1:M;

disp('output sequence =');disp(c)stem(n,c)

xlabel('Time index n'); ylabel('Amplitude');

Observation:

Type in the first sequence = 3

Type in the second sequence = 4output sequence = 12

Output:

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

Timeindexn

A m p l i t u d e




Practical: 14

Date:__________

Aim: Computation of Autocorrelation of a Noise Corrupted Sinusoidal Sequence

Program Code:

N = 96;

n = 1:N;

x = cos(pi*0.25*n); % Generate the sinusoidal sequenced = rand(1,N) - 0.5; % Generate the noise sequence

y = x + d; % Generate the noise-corrupted sinusoidal sequence

r = conv(y, fliplr(y)); % Compute the correlation sequencek = -28:28;

stem(k, r(68:124));

xlabel('Lag index'); ylabel('Amplitude');

Output:

-30 -20 -10 0 10 20 30-60

-40

-20

0

20

40

60

Lagindex

A m p l i t u d e




Practical: 15

Date:__________

Aim: Illustration of Up-Sampling by an Integer Factor

Program Code:

N = input('Input length = ');L = input('Up-sampling Factor = ');

fo = input('Input signal frequency = ');

% Generate the input sinusoidal sequencen = 0:N-1;

x = sin(2*pi*fo*n);

% Generate the up-sampled sequencey = zeros(1, L*length(x));

y([1: L: length(y)]) = x;

% Plot the input and the output sequencessubplot(2,1,1)

stem(n,x);title('Input Sequence');

xlabel('Time index n');ylabel('Amplitude');

subplot(2,1,2)

stem(n,y(1:length(x)));

title(['Output sequence up-sampled by', num2str(L)]);


Observation:-

Input length = 4Up-sampling Factor = 5

Input signal frequency = 6



Output:

0 0.5 1 1.5 2 2.5 3-6

-4

-2

0x10

-15 Input Sequence

Timeindexn

A m p l i t u d e

0 0.5 1 1.5 2 2.5 3-1

-0.5

0

0.5

1

Output sequenceup-sampledby5

Timeindexn

A m p l i t u d e




Practical: 16

Date:__________

Aim: Illustration of Down-Sampling by an Integer Factor

Program Code:

N = input('Output length = ');M = input('Down-sampling Factor = ');

fo = input('Input signal frequency = ');

% Generate the input sinusoidal sequencen = 0 : N-1;

m = 0 : N*M-1;

x = sin(2*pi*fo*m);

% Generate the down-sampled sequence

y = x([1 : M : length(x)]);


stem(n, x(1:N));title('Input Sequence');


subplot(2,1,2)

stem(n, y);

title(['Output sequence down-sampled by ',num2str(M)]);

ylabel('Amplitude');xlabel('Time index n');

Observation:

Input length = 4

Up-sampling Factor = 5Input signal frequency = 6Output length = 5Down-sampling Factor = 7

Input signal frequency = 8



Output:

0 0.5 1 1.5 2 2.5 3 3.5 4-8

-6

-4

-2

0

x 10-15 Input Sequence

Time index n

A m p l i t u d e

0 0.5 1 1.5 2 2.5 3 3.5 4-6

-4

-2

0

2x 10

-14 Output sequence down-sampled by 7

A m p l i t u d e

Time index n




Practical: 17

Date:__________

Aim: Effect of Up-Sampling in the Frequency DomainUse fir2 to create a band limited input sequence

Program Code:

freq = [0 0.45 0.5 1];

mag = [0 1 0 0];x = fir2(99, freq, mag);

% Evaluate and plot the input spectrum[Xz, w] = freqz(x, 1, 512);

plot(w/pi, abs(Xz)); gridxlabel('\omega/\pi'); ylabel('Magnitude');title('Input spectrum');

pause

% Generate the up-sampled sequenceL = input('Type in the up-sampling factor = ');y = zeros(1, L*length(x));y([1: L: length(y)]) = x;

% Evaluate and plot the output spectrum

[Yz, w] = freqz(y, 1, 512);

plot(w/pi, abs(Yz)); gridxlabel('\omega/\pi'); ylabel('Magnitude');title('Output spectrum');



Output:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ω / π

M a g n i t u d e

Input spectrum




Practical: 18

Date:__________

Aim: Effect of Down-Sampling in the Frequency DomainUse fir2 to create a band limited input sequence

Program Code:

freq = [0 0.42 0.48 1];mag = [0 1 0 0];

x = fir2(101, freq, mag);

% Evaluate and plot the input spectrum

[Xz, w] = freqz(x, 1, 512);

plot(w/pi, abs(Xz)); grid

xlabel('\omega/\pi'); ylabel('Magnitude');title('Input spectrum');

pause

% Generate the down-sampled sequenceM = input('Type in the down-sampling factor = ');

y = x([1: M: length(x)]);

% Evaluate and plot the output spectrum

[Yz, w] = freqz(y, 1, 512);

plot(w/pi, abs(Yz)); gridxlabel('\omega/\pi'); ylabel('Magnitude');title('Output spectrum');



Output:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ω / π

M a g n i t u d e

Input spectrum




Practical: 19

Date:__________

Aim: Illustration of Interpolation Process

Program Code:

N = input('Length of input signal = ');L = input('Up-sampling factor = ');

f1 = input('Frequency of first sinusoid = ');f2 = input('Frequency of second sinusoid = ');

% Generate the input sequence

n = 0:N-1;

x = sin(2*pi*f1*n) + sin(2*pi*f2*n);

% Generate the interpolated output sequence

y = interp(x,L);


stem(n,x(1:N));title('Input sequence');

xlabel('Time index n'); ylabel('Amplitude');subplot(2,1,2)

m=0:N*L-1;stem(m,y(1:N*L));title('Output sequence');

xlabel('Time index n'); ylabel('Amplitude');

Observaton:

Length of input signal = 9Up-sampling factor = 9

Frequency of first sinusoid = 9Frequency of second sinusoid = 9



Output:

0 1 2 3 4 5 6 7 8-6

-4

-2

0

2x 10

-14 Input sequence

Time index n

A m p l i t u d e

0 10 20 30 40 50 60 70 80-1

-0.5

0

0.5

1x 10

-13 Output sequence

Time index n

A m p l i t u d e




Practical: 20

Date:__________

Aim: Illustration of Sampling Rate Alteration by

a Ratio of Two Integers

Program Code:

N = input('Length of input signal = ');

L = input('Up-sampling factor = ');M = input('Down-sampling factor = ');

f1 = input('Frequency of first sinusoid = ');f2 = input('Frequency of second sinusoid = ');

% Generate the input sequence

n = 0:N-1;x = sin(2*pi*f1*n) + sin(2*pi*f2*n);

% Generate the resampled output sequence

y = resample(x,L,M);


stem(n,x(1:N));title('Input sequence');

xlabel('Time index n'); ylabel('Amplitude');subplot(2,1,2)

m=0:N*L/M-1;

stem(m,y(uint8(1:N*L/M)));title('Output sequence');xlabel('Time index n'); ylabel('Amplitude');

Observation:

Length of input signal = 9Up-sampling factor = 9

Down-sampling factor = 9Frequency of first sinusoid = 9

Frequency of second sinusoid = 9



Output:

0 1 2 3 4 5 6 7 8-6

-4

-2

0

2x 10

-14 Input sequence

Time index n

A m p l i t u d e

0 1 2 3 4 5 6 7 8-6

-4

-2

0

2x 10

-14 Output sequence

Time index n

A m p l i t u d e




Practical: 21

Date:__________

Aim: Design of Lth Band FIR Filter Using theWindowed Fourier Series Approach

Program Code:

N = input('Type in the filter order = ');

L = input('Type in the value of L = ');n = -N/2:N/2;

% Generate the truncated impulse response of the ideal% lowpass filter

b = sinc(n/L)/L;

% Generate the window sequence

win = hamming(N+1);

% Generate the coefficients of the windowed filterc = b.*win';

% Plot the gain response of the windowed filter

[h,w] = freqz(c,1,512);

plot(w/pi,20*log10(abs(h)));grid

xlabel('\omega/\pi');ylabel('Gain, dB');title(['L-th band Nyquist Filter, L = ',num2str(L),]);

Observation:

Type in the filter order = 2

Type in the value of L = 3



Output:

0 1 2 3 4 5 6 7 8-6

-4

-2

0

2x 10

-14 Input sequence

Time index n

A m p l i t u d e

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-11

-10

-9

-8

ω / π

G a i n ,

d B

L-th band Nyquist Filter, L = 3




Practical: 22

Date:__________

Aim: Frequency Responses of Johnston's QMF FiltersType in prototype lowpass filter coefficients

Program Code:

B1 = input('Filter coefficients = ');B1 = [B1 fliplr(B1)];

% Generate the complementary highpass filterL = length(B1);

for k = 1:LB2(k) = ((-1)^k)*B1(k);end

% Compute the gain responses of the two filters

[H1z, w] = freqz(B1, 1, 256);h1 = abs(H1z); g1 = 20*log10(h1);[H2z, w] = freqz(B2, 1, 256);h2 = abs(H2z); g2 = 20*log10(h2);

% Plot the gain responses of the two filters

plot(w/pi, g1,'-',w/pi, g2,'--');grid

xlabel('\omega/\pi'); ylabel('Gain, dB')pause

% Compute the sum of the squared-magnitude responsesfor i = 1:256,

sum(i) = (h1(i)*h1(i)) + (h2(i)*h2(i));end

d =10*log10(sum);

% Plot the amplitude distortion

plot(w/pi,d);grid;xlabel('\omega/\pi'); ylabel('Amplitude distortion, dB')

Observation:

Filter coefficients = 5



Output:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-25

-20

-15

-10

-5

0

5

10

15

20

ω / π

G a i n ,

d B




Practical: 23

Date:__________

Aim: Spectrogram of a Speech Signal

Program Code:

load mtlb

n = 1:4001;

plot(n-1,mtlb);xlabel('Time index n');ylabel('Amplitude');pause

nfft = input('Type in the window length = ');ovlap = input('Type in the desired overlap = ');

specgram(mtlb,nfft,7418,hamming(nfft),ovlap)

Output:

0 500 1000 1500 2000 2500 3000 3500 4000-3

-2

-1

0

1

2

3

4

Time index n

A m p l i t u d e




Practical: 24

Date:__________

Aim: Power Spectrum Estimation Using Welch's Method

Program Code:

n = 0:1000;g = 2*sin(0.12*pi*n) + sin(0.28*pi*n) + randn(size(n));

nfft = input('Type in the fft size = ');window = hamming(256);noverlap =input('Type in the amount of overlap = ');

[Pxx, f] = psd(g,nfft,2,window,noverlap);

plot(f/2,10*log10(Pxx));grid

xlabel('\omega/\pi');ylabel('Power Spectrum, dB');title(['Overlap = ',num2str(noverlap),' samples']);

Output:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

ω / π

M a g n i t u d e




Practical: 25

Date:__________

Aim: Sigma-Delta Quantizer Operation

Program Code:

N = input('Type in the length of input sequence = ');n = 1:1:N;

m = n-1;

A = input('Type in the input amplitude = ');x = A*ones(1,N);

plot(m,x);axis([0 N-1 -1.2 1.2]);xlabel('Time'); ylabel('Amplitude');

title('Input analog signal');pause

y = zeros(1,N+1);

v0 = 0;for k = 2:1:N+1;

v1 = x(k-1) - y(k-1) + v0;y(k) = sign(v1);

v0 = v1;

endyn = y(2:N+1);axis([0 N-1 -1.2 1.2]);

stem(m, yn);xlabel('Time'); ylabel('Amplitude');

title('Output of sigma-delta modulator');

ave = sum(yn)/N;disp('Average value of output is = ');disp(ave);

Observation:

Type in the length of input sequence = 9

Type in the input amplitude = 6

Average value of output is =

Columns 1 through 7

11.1111 11.1111 11.1111 11.1111 11.1111 11.1111 11.1111



Columns 8 through 9 11.1111 11.1111

Output:

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time

A m p l i t u d e

Output of sigma-delta modulator




Practical: 26

Date:__________

Aim: Sigma-Delta A/D Converter Operation

Program Code:

wo = 2*pi*0.01;N = input('Type in the length of input sequence = ');n = 1:1:N;

m = n-1;

A = input('Type in the amplitude of the input = ');x = A*cos(wo*m);

axis([0 N-1 -1.2 1.2]);plot(m,x);xlabel('Time'); ylabel('Amplitude');title('Input analog signal');

pause

y = zeros(1,N+1);v0 = 0;

for k = 2:1:N+1;v1 = x(k-1) - y(k-1) + v0;

if v1 >= 0;

y(k) = 1;elsey(k) = -1;

endv0 = v1;

end

yn = y(2:N+1);axis([0 N-1 -1.2 1.2]);

stairs(m, yn);xlabel('Time'); ylabel('Amplitude');

title('Output of sigma-delta quantizer');

Y = fft(yn);pauseH = [1 1 0.5 zeros(1,N-5) 0.5 1];YF = Y.*H;

out = ifft(YF);axis([0 N-1 -1.2 1.2]);

plot(m,out);



xlabel('Time'); ylabel('Amplitude');title('Lowpass filtered output');

Observation:

Type in the length of input sequence = 3

Type in the amplitude of the input = 2

Output:

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 21.984

1.986

1.988

1.99

1.992

1.994

1.996

1.998

2

2.002

Time

A m p l i t u d e

Input analog signal


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