dsp practicals

8/4/2019 DSP Practicals

1/35

BSP Practical Lab Manual

1. AimWrite a program to display a continuous time sine waveform along with its

sampled version

Program

clcA =input('Enter the amplitude A=');

f0=input('Enter the signal frequency in hz f0 =');

ph=input('Enter the initial phase angle in radians ph =');

fs=input('Enter the sampling frequency fs=');c =input('No of cycles to be displayed c=');

t= 0:0.01/fs:c*1/f0;

x= A*sin(2*pi*f0*t +ph);

subplot(2,1,1)plot(t,x);

title('continuous sine wave');

xlabel('time ');ylabel('Amplitude');

grid

subplot(2,1,2)x1= x([1:50:length(x)]);

n=0:1:length(x1)-1;stem(n,x1)title('sampled sine wave');

xlabel('time (n)');

ylabel('Amplitude(A)');grid

Input

The given sample input for this program is:

Enter the amplitude A=5

Enter the signal frequency in hz f0 =50

Enter the initial phase angle in radians ph = 45Enter the sampling frequency fs=200

No of cycles to be displayed c=5


2/35

Output

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-5

0

5continuous sine wave

time

Amplitude

0 5 10 15 20 25 30 35 40-5

0

5sampled sine wave

time (n)

Amplitude(A

)

Conclusion

Thus we had obtained the continuous sine wave along with sampled version using sampleinput values.


3/35

2. AimWrite a program to show the convolution of two sequences x(n) & h(n) which

are input from keyboard.

Program

x = input('Enter the first sequence x(n) = ');

h = input('Enter the second sequence h(n) = ');y = conv (x,h);

k = length(x) + length(h) -1;

n = 1:k ;

stem(n,y);title('Convoluted signal ');

xlabel('Time');

ylabel('Amplitude');

grid ON;

Input


Enter the first sequence x(n) = [1 3 5 7]

Enter the second sequence h(n) = [2 4 6 8]

Output

1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90Convolutedsignal

Time

Amplitude


4/35

Conclusion

Thus we had obtained the convoluted signal output of the two sample input sequences.


5/35

3. Aimwrite a program tofind the circular convolution of two sequences input fromthe keyboard using DFT.

Program

clc;

clear all;

x = input( ' Enter the first sequence x(n)=');

h = input( ' Enter the second sequence h(n)=');

N1 = length(x);N2 = length(h);

if N1>N2

h = [h,zeros(N1-N2)];

end

if N1


6/35

ylabel('Amplitude');

grid ON;

Input


Enter the first sequence x(n) = [1 3 5 7]Enter the second sequence h(n) = [2 4 6 8]

Output

0 0.5 1 1.5 2 2.5 30

5

10Sequence x(n)

Time

Amplitude

0 0.5 1 1.5 2 2.5 30

5

10Sequence h(n)

Time

Amplitude

0 0.5 1 1.5 2 2.5 30

50

100Circular Convolution

Time

Amplitude

Conclusion

Thus we had obtained the circular convolution of two sample input sequences and

represent them individually in each graph.


7/35

4. Aim Write a program to compute the DFT of an input sequence from the

keyboard. Plot the magnitude and phase. [ Use fft and angle functions]

Program

clc ;

clear all;

x = input('Signal sequence whose DFT to be calculated x(n) : ');n = [0 : length(x)-1];

radian = 2*pi*n;

y = fft(x);

subplot(2,1,1);stem(radian,abs(y));

title( ' MAGNITUDE DFT[x(n)]');

xlabel('Radians');

ylabel('Amplitude');grid ON;

subplot(2,1,2);stem(radian,angle(y));

title( ' PHASE PLOT DFT[x(n)]');

xlabel('Radians');

ylabel('Phase');grid ON;

Input


Signal sequence whose DFT to be calculated x(n): [1 3 5 7]

Output


8/35

0 2 4 6 8 10 12 14 16 18 200

5

10

15

20MAGNITUDEDFT[x(n)]

Radians

Amplitude

0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

4PHASEPLOTDFT[x(n)]

Radians

Phase

Conclusion

Thus we had obtained the DFT of the input sequence and plotted the sequence using fftand angle function and plotted it on magnitude and phase graph.


9/35

5. AimWrite a program to design a FIR filters [LP, HP, BP, BR] using rectangular

window.

Program

clc;

choice = 0;

while(choice ~= 5)clc;

disp('**************MAIN MENU***************');

disp('------FIR Filter using rectangular window--------');

disp('1: Low pass filter');disp('2: High pass filter');

disp('3: Band pass filter');

disp('4: Band reject filter');

disp('5: Exit');choice = input('Your Choice :');

if(choice == 5)break;

end

format long;rp=input('enter the passband ripple=');

rs=input('enter the stopband riple=');

fp=input('enter the passband freq=');fs=input('enter the stopband freq=');

f=input('enter the sampling freq=');

wp=2*fp/f;ws=2*fs/f;

num=-20*log10(sqrt(rp*rs))-13;dem=14.6*(fs-fp)/f;

n=ceil(num/dem);

n1=n+1;

if(rem(n,2)~=0)n1=n;

n=n-1;

endy=boxcar(n1);

switch(choice)case 1

b=fir1(n,wp,y);


10/35

case 2

b=fir1(n,wp,'high',y);

case 3

wn=[wp ws];b=fir1(n,wn,y);

case 4

b=fir1(n,wn,'stop',y);

end

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,1,1);plot(o/pi,m);

ylabel('Gain in db-->');xlabel('(a) Normalized frequency-->');

end

Input

The given sample input for all the filters i.e. LP, HP, BP, BR in this program is:

FIR filters--rectangular window

a) Passband ripple=0.05

b) Stopband ripple=.04c) Passband frequency=1500

d) Stopband frequency=2000

e) Sampling frequency=9000

Output

Low Pass Filter (LP):


11/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-->

(a) Normalized frequency-->

High Pass Filter (HP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb

-->


Band Pass Filter (BP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-->


Band Reject Filter (BR):


12/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-20

-10

0

10

Gainindb-->


Conclusion

Thus we have obtained the filter design method for FIR filter using rectangular windowfor all types of filters viz. LP, HP, BP and BR.


13/35

6. AimWrite a program to design a FIR filters [LP,HP,BP,BR] using hamming

window.

Program

clear;

clc;

choice = 0;while(choice ~= 5)

clc;

disp('**************MAIN MENU***************');

disp('------FIR Filter using hamming window--------');disp('1: Low pass filter');

disp('2: High pass filter');


disp('4: Band reject filter');disp('5: Exit');

choice = input('Your Choice :');if(choice == 5)

break;

end

format long;

rp=input('enter the passband ripple=');

rs=input('enter the stopband ripple=');fp=input('enter the passband freq=');

fs=input('enter the stopband freq=');

f=input('enter the sampling freq=');wp=2*fp/f;

ws=2*fs/f;

num=-20*log10(sqrt(rp*rs))-13;

dem=14.6*(fs-fp)/f;

n=ceil(num/dem);

n1=n+1;if(rem(n,2)~=0)

n1=n;

n=n-1;end

y=hamming(n1);

switch(choice)

case 1

b=fir1(n,wp,y);


14/35

case 2


case 3

wn=[wp ws];

b=fir1(n,wn,y);

case 4


end

[h,o]=freqz(b,1,256);m=20*log10(abs(h));

subplot(2,1,1);plot(o/pi,m);

ylabel('Gain in db-->');

xlabel('(a) Normalized frequency-->');

end

Input


FIR filters--hamming window


b) Stopband ripple=0.02

c) Passband frequency=1500

d) Stopband frequency=2000e) Sampling frequency=8000

Output

Low pass filter (LP):


15/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-->


High pass filter (HP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-

->


Band pass filter (BP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-->


Band reject filter (BR):


16/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10

-5

0

5

Gainindb-->


Conclusion

Thus we have obtained the filter design method for FIR filter using hamming window

for all types of filters viz. LP, HP, BP and BR.


17/35

7. AimWrite a program to design of FIR filters [LP,HP,BP,BR] using hanning

window.

Program

clear;

clc;

choice = 0;while(choice ~= 5)

clc;

disp('**************MAIN MENU***************');

disp('------FIR Filter using hanning window--------');disp('1: Low pass filter');





break;

end

format long;


rs=input('enter the stopband riple=');fp=input('enter the passband freq=');

fs=input('enter the stopband freq=');

f=input('enter the sampling freq=');wp=2*fp/f;

ws=2*fs/f;

num=-20*log10(sqrt(rp*rs))-13;

dem=14.6*(fs-fp)/f;

n=ceil(num/dem);

n1=n+1;if(rem(n,2)~=0)

n1=n;

n=n-1;end

y=hanning(n1);

switch(choice)

case 1


18/35

b=fir1(n,wp,y);

case 2


case 3

wn=[wp ws];b=fir1(n,wn,y);

case 4


end

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));subplot(2,1,1);

plot(o/pi,m);



end

Input


FIR filters--hanning window


b) Stopband ripple=0.01

c) Passband frequency=1400d) Stopband frequency=2000


Output

Low pass filter (LP):


19/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-150

-100

-50

0

50

Gainindb-->


High pass filter (HP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-->


Band pass filter (BP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-150

-100

-50

0

Gainindb-->


Band reject filter (BR):


20/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-15

-10

-5

0

5

Gainindb-->


Conclusion

Thus we have obtained the filter design method for FIR filter using hanning window

for all types of filters viz. LP, HP, BP and BR.


21/35

8. AimWrite a program to design digital Butterworth filters [ LP, HP, BP, BR ] for

the following specifications

a)Pass band ripple

b)Pass band frequency

c)Stop band ripple

d)Stop band frequencye)Sampling frequeny

Use buttord, butter and freqz functions. Plot the amplitude and phase response.

Program

clear;clc;

choice = 0;

while(choice ~= 5)

clc;disp('**************MAIN MENU***************');

disp('------Butterworth Filter--------');disp('1: Low pass filter');




choice = input('Your Choice :');


end

format long;


rs=input('enter the stopband riple=');wp=input('enter the passband freq=');

ws=input('enter the stopband freq=');

fs=input('enter the sampling freq=');

w1=2*wp/fs;w2=2*ws/fs;


[n,wn]=buttord(w1,w2,rp,rs);[b,a]=butter(n,wn);

case 2


22/35

[n,wn]=buttord(w1,w2,rp,rs);

[b,a]=butter(n,wn,'high');

case 3

[n]=buttord(w1,w2,rp,rs);wn=[w1 w2];

[b,a]=butter(n,wn,'bandpass');

case 4

[n]=buttord(w1,w2,rp,rs);

wn=[w1 w2];[b,a]=butter(n,wn,'stop');

end

w=0:.01:pi;[h,om]=freqz(b,a,w);

m=20*log10(abs(h));

an=angle(h);

subplot(2,1,1);plot(om/pi,m);


xlabel('(a) Normalized frequency-->');subplot(2,1,2);

plot(om/pi,an);

xlabel('(b) Normalized frequency-->');ylabel('phase in radians-->');

end

Input

The given sample input for all the filters i.e. LP, HP, BP, BR in this program are:

1) Butterworth low pass and high pass filters (LP & HP):


b) Stopband ripple=50



2) Butterworth band pass filter (BP):


23/35


b) Stopband ripple=40c) Passband frequency=1500



3) Butterworth band reject filter (BR):





Output

1) Butterworth low pass filter (LP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-400

-200

0

200

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4

(b) Normalized frequency-->

phaseinradians-->

2) Butterworth high pass filter (HP):


24/35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-300

-200

-100

0

100

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phasein

radians-->

3) Butterworth band pass filter (BP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-800

-600

-400

-200

0

Gainindb--

>


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradia

ns-->


25/35

4) Butterworth band reject filter (BR):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-300

-200

-100

0

100

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinrad

ians-->

Conclusion

Thus we have obtained the filter design method for Butterworth filter for all types of

filters viz. LP, HP, BP and BR.


26/35

9. AimWrite a program to design digital Chebyshev Type-I filters [ LP, HP, BP, BR]

for the following specifications

a) Pass band ripple

b) Pass band frequency

c) Stop band ripple

d) Stop band frequencye) Sampling frequency

Use cheb1ord, cheby1 and freqz functions. Plot the amplitude and phase response.

Program

clear;clc;

choice = 0;

while(choice ~= 5)

clc;

disp('**************MAIN MENU***************');disp('------chebyshev type-I Filter--------');

disp('1: Low pass filter');


disp('3: Band pass filter');disp('4: Band reject filter');

disp('5: Exit');


break;

end

format long;

rp=input('enter the passband ripple=');rs=input('enter the stopband ripple=');

wp=input('enter the passband freq=');


fs=input('enter the sampling freq=');w1=2*wp/fs;

w2=2*ws/fs;

switch(choice)

case 1

[n,wn]=cheb1ord(w1,w2,rp,rs);

[b,a]=cheby1(n,rp,wn);

case 2


27/35


[b,a]=cheby1(n,rp,wn,'high');

case 3

[n]=cheb1ord(w1,w2,rp,rs);

wn=[w1 w2];

[b,a]=cheby1(n,rp,wn,'bandpass');

case 4

[n]=cheb1ord(w1,w2,rp,rs);wn=[w1 w2];

[b,a]=cheby1(n,rp,wn,'stop');

end

w=0:.01:pi;[h,om]=freqz(b,a,w);

m=20*log10(abs(h));

an=angle(h);

subplot(2,1,1);plot(om/pi,m);


xlabel('(a) Normalized frequency-->');subplot(2,1,2);

plot(om/pi,an);

xlabel('(b) Normalized frequency-->');ylabel('phase in radians-->');

end

Input


1) Chebyshev Type-I Low Pass filter (LP):


b) Stopband ripple=45c) Passband frequency=1300




28/35

2) Chebyshev Type-I High Pass filter (HP):

a) Passband ripple=0.3b) Stopband ripple=60



3) Chebyshev Type-I Band Pass filter (BP):





4) Chebyshev Type-I Band Reject filter (BR):





Output

1) Chebyshev Type-I Low Pass filter (LP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-600

-400

-200

0

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradians-->


29/35

2) Chebyshev Type-I High Pass filter (HP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-400

-300

-200

-100

0

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinrad

ians-->

3) Chebyshev Type-I Band pass filter (BP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-600

-400

-200

0

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradians-->


30/35

4) Chebyshev Type-I Band Reject filter (BR):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-150

-100

-50

0

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinrad

ians-->

Conclusion

Thus we have obtained the filter design method for Chebyshev Type-I filter for all types

of filters viz. LP, HP, BP and BR.


31/35

10. AimWrite a program to design digital Chebyshev Type-II filters [ LP, HP, BP,

BR] for the following specifications

a) Pass band ripple

b) Pass band frequency

c) Stop band ripple

d) Stop band frequencye) Sampling frequency

Use cheb2ord, cheby2 and freqz functions. Plot the amplitude and phase response.

Program

clear;clc;

choice = 0;

while(choice ~= 5)

clc;disp('**************MAIN MENU***************');

disp('-----Chebyshev type-II Filter--------');disp('1: Low pass filter');




choice = input('Your Choice :');


end

format long;


rs=input('enter the stopband riple=');wp=input('enter the passband freq=');


fs=input('enter the sampling freq=');

w1=2*wp/fs;w2=2*ws/fs;


[n,wn]=cheb2ord(w1,w2,rp,rs);[b,a]=cheby2(n,rs,wn);

case 2


32/35


[b,a]=cheby2(n,rs,wn,'high');

case 3

[n]=cheb2ord(w1,w2,rp,rs);wn=[w1 w2];

[b,a]=cheby2(n,rs,wn,'bandpass');

case 4

[n]=cheb2ord(w1,w2,rp,rs);

wn=[w1 w2];[b,a]=cheby2(n,rs,wn,'stop');

end

w=0:.01/pi:pi;

[h,om]=freqz(b,a,w);m=20*log10(abs(h));

an=angle(h);

subplot(2,1,1);

plot(om/pi,m);ylabel('Gain in db-->');


subplot(2,1,2);plot(om/pi,an);

xlabel('(b) Normalized frequency-->');

ylabel('phase in radians-->');

end

Input


1) Chebyshev Type-II Low Pass filter (LP):





2) Chebyshev Type-II High Pass filter (HP):


33/35





3) Chebyshev Type-II Band Pass filter (BP):





4) Chebyshev Type-II Band Reject filter (BR):




Output

1) Chebyshev Type-II Low Pass Filter (LP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradians

-->


34/35

2) Chebyshev Type-II High Pass filter (HP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

Gainind

b-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradians-->

3) Chebyshev Type-II Band pass filter (BP):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-400

-200

0

200

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradian

s-->


35/35

4) Chebyshev Type-II Band Reject filter (BR):

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100

-50

0

50

Gainindb-->


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4


phaseinradian

s-->

Conclusion

Thus we have obtained the filter design method for Chebyshev Type-II filter for all types

of filters viz. LP, HP, BP and BR.

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