digital signal processing matlab programs

MATLAB DIGITAL SIGNAL PROCESSING LAB BY: CHHAVI TRIVEDI , ROLL NO : 07213502709, B.TECH(CSE), VI SEMESTER

2012

IGIT KASHMERE GATE

1/1/2012

Q1. Plot u(n)

CODE:

>> clear all;

>> t=0:1:6;

>> y=ones(1,7);

>> plot(t,y);xlabel('n-->');ylabel('Amplitude');title('plot of u(n)')

FIGURE:

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

n-->

Am

plit

ude

plot of u(n)

Q2. Plot nu(n)

CODE:

>> t=0:1:6;

>> n=input('enter value of n ');

enter value of n 4

>> y=ones(1,7);

>> y1=y*n;

>> plot(t,y1);xlabel('n-->');ylabel('Amplitude');title('plot of 4u(n)')

FIGURE:

0 1 2 3 4 5 63

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

n-->

Am

plit

ude

plot of 4u(n)

Q3. Plot u(-n)

CODE:

t=-6:1:0;

>> y=ones(1,7);

>> plot(t,y);xlabel('n-->');ylabel('Amplitude');title('plot of u(-n)')

FIGURE:

-6 -5 -4 -3 -2 -1 00

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

n-->

Am

plitu

de

plot of u(-n)

Q4. Plot u(n)-u(N-1)

CODE:

>> n=input('enter the N value ');

enter the N value 1

>> t=0:1:n-1;

>> y1=ones(1,n);

>> stem(t,y1);ylabel('Amplitude');xlabel('n-->');title('plot of u(n)-u(N-1)')

FIGURE:

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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Am

plit

ude

n-->

plot of u(n)-u(N-1)

Q5. Plot the linear convolution of sequences of length 4.

CODE:

x=input('enter the 1st sequence ');

enter the 1st sequence

>> x=input('enter the 1st sequence ');

enter the 1st sequence [2 1 0 0.5]

>> h=input('enter the 2nd sequence ');

enter the 2nd sequence [2 2 1 1]

y=conv(x,h);

m=length(y)-1;

>> n=0:1:m;

subplot(2,1,1);stem(x);xlabel('n-->');ylabel('Amplitude');subplot(2,1,2);stem(h);xlabel('n--

>');ylabel('Amplitude')

stem(n,y);xlabel('n-->');ylabel('Amplitude')

FIGURE:

1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

n--

Am

plit

ude

x(n)

1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

n-->

Am

plit

ude

h(n)

0 1 2 3 4 5 60

1

2

3

4

5

6

n-->

Am

plit

ude

Q6. Plot the circular convolution of Q5.

CODE:

y=cconv(x,h);

>> m=length(y)-1;

>> n=0:1:m;

>> disp('output sequence is =');disp(y)

output sequence is =

4.0000 6.0000 4.0000 4.0000 2.0000 0.5000 0.5000

stem(n,y);xlabel('n-->');ylabel('Amplitude')

FIGURE:

0 1 2 3 4 5 60

1

2

3

4

5

6

n-->

Am

plit

ude

Q7. Plot the cross-correlation of sequences of length 4.

CODE:

x=input('enter the 1st sequence ');

enter the 1st sequence [1 2 3 4]

>> h=input('enter the 2nd sequence ');

enter the 2nd sequence [4 3 2 1]

>> y=xcorr(x,h);

subplot(3,1,3);stem(fliplr(y));xlabel('n-->');ylabel('Amplitude');title('cross-

correlation');subplot(3,1,1);stem(x);xlabel('n--

>');ylabel('Amplitude');title('x(n)');;subplot(3,1,2);stem(h);xlabel('n-->');ylabel('Amplitude');title('y(n)')

FIGURE:

1 2 3 4 5 6 70

20

40

n-->

Am

plit

ude

cross-correlation

1 1.5 2 2.5 3 3.5 40

2

4

n-->

Am

plit

ude

x(n)

1 1.5 2 2.5 3 3.5 40

2

4

n-->

Am

plit

ude

y(n)

Q8. Plot zeros and poles of u(n).

CODE:

num=[1 0];

>> den=[1 -1];

>> zplane(num,den)

>> [z p k]=tf2zp(num,den);

>> m=abs(p);

>> disp('zeros are at ');disp(z);

zeros are at

0

>> disp('poles are at ');disp(p);

poles are at

1

disp('Gain constant ');disp(k);

Gain constant

1

>> disp('Radius of poles ' );disp(m);

Radius of poles

1

FIGURE:

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Real Part

Imagin

ary

Part

Q9. Compute the z-transform of anu(n) and plot its zeros and poles.

CODE:

syms a n;

>> g=a^n;

>> ztrans(g)

ans =

-z/(a - z)

a=input('Enter the value of a ');

Enter the value of a 2

>> num=[1 0];

>> den=[1 -a];

>> zplane(num,den)


>> m=abs(p);


zeros are at

0


poles are at

2


Gain constant

1


Radius of poles

2

FIGURE:

-1 -0.5 0 0.5 1 1.5 2

-1

-0.5

0

0.5

1

Real Part

Imagin

ary

Part

Q10. Plot u(n)coswon z-transform with its poles and zeros.

CODE:

w=input('enter the value of Wo ');

enter the value of Wo 1

num=[0 1 -cos(w)];

den=[1 -2*cos(w) 1];

>> zplane(num,den)


>> m=abs(p);


zeros are at

0.5403


poles are at

0.5403 + 0.8415i

0.5403 - 0.8415i


Gain constant

1


Radius of poles

1

1

FIGURE:

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Real Part

Imagin

ary

Part

Q11. Find and plot the dft of [1,2,3,4] and hence by the idft of the result obtained.

CODE(I):

x=input('enter the sequene ')

enter the sequene [1 2 3 4]

x =

1 2 3 4

>> n=input('enter the length of sequence ');

enter the length of sequence 4

y=fft(x,n);

stem(y);ylabel('Imaginary Axis --> ');xlabel('Real axis -->')

y =

10.0000 -2.0000 + 2.0000i -2.0000 -2.0000 - 2.0000i

FIGURE(I):

1 1.5 2 2.5 3 3.5 4-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Imagin

ary

Axis

-->

Real axis -->

CODE(II):

x=input('enter the sequene ')

enter the sequene [1 2 3 4]

x =

1 2 3 4

>> y=fft(x,4);

>> n=input('enter the length of idft ');

enter the length of idft 4

>> k=ifft(y,n)

k =

1 2 3 4

stem(k);xlabel('n --> ');ylabel('Amplitude --> ')

FIGURE(II):

1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

n -->

Am

plit

ude -

->

Q12. Perform dft of sequence of length 7 using overlap add method.

CODE:

b=input('Enter input signal (of length 7) ');

Enter input signal (of length 7) [1 2 3 4 5 6 7]

>> x=input('Enter impulse signal ');

Enter impulse signal [1 2 5 6 2 3 9]

>> n=input('Enter block size ');

Enter block size 3

>> y=fftfilt(x,b,n)

y =

1 4 12 26 42 61 89

>> stem(y)

FIGURE:

1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

Q13. Design low pass butterworth filter.

CODE:

format long;

>> rp=input('Enter the passband ripple ');

Enter the passband ripple 0.5

>> rs=input('Enter the stopband ripple ');

Enter the stopband ripple 50

>> wp=input('Enter the passband freq ');

Enter the passband freq 1200

>> ws=input('Enter the stopband freq ');

Enter the stopband freq 2400

>> fs=input('Enter the sampling freq ');

Enter the sampling freq 10000

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

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

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

>> w=0:0.01:pi;

>> [h om]=freqz(b,a,w);

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

an=angle(h);

subplot(2,1,1);plot(om/pi,m);ylabel('Gain in db --> ');xlabel('(a) Normalised frequency --

>');subplot(2,1,2);plot(om/pi,an);xlabel(' (b) Normalised frequency-->');ylabel('Phase in radians -->')

FIGURE:

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

Gain

in d

b -

->

(a) Normalised frequency -->

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) Normalised frequency-->

Phase in r

adia

ns -

->

Q14. Design low pass chebychev filter.

CODE:

format long;




Enter the stopband ripple


Enter the stopband ripple 45








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

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

>> w=0:0.01:pi;

>> [h om]=freqz(b,a,w);

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

an=angle(h);

>> subplot(2,1,1);plot(om/pi,m);ylabel('Gain in db --> ');xlabel('(a) Normalised frequency --

>');subplot(2,1,2);plot(om/pi,an);xlabel(' (b) Normalised frequency-->');ylabel('Phase in radians -->')

FIGURE:

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

-400

-200

0

200

Gain

in d

b -

->

(a) Normalised frequency -->

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) Normalised frequency-->

Phase in r

adia

ns -

->

Q15. Design low pass filter using rectangular window.

CODE:

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



Enter the stopband ripple 0.04








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

>> den=14.6*(ws-wp)/fs;

>> n=ceil(num/den);

n1=n+1;

>> if(rem(n,2)~=0)

n1=n;

n=n-1;

end

>> y=boxcar(n1);

>> b=fir1(n,w1,y);

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

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

subplot;plot(o/pi,m);ylabel('Gain in db --> ');xlabel('Normalised frequency -->')

FIGURE:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-80

-70

-60

-50

-40

-30

-20

-10

0

10

Gain

in d

b -

->

Normalised frequency -->

Q16. Design low pass filter using hamming window.

CODE:

clear all;





>> 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;


>> den=14.6*(fs-fp)/f;

>> n=ceil(num/den);

>> n1=n+1;

>> if(rem(n,2)~=0)

n1=n;

n=n-1;

end;

>> y=hamming(n1);

>> b=fir1(n,wp,y);

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

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

>> subplot;plot(o/pi,m);ylabel('Gain in db --> ');xlabel('Normalised frequency -->')

FIGURE:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-120

-100

-80

-60

-40

-20

0

20

Gain

in d

b -

->


Q17. Design low pass filter using hanning window.

CODE:

>> clear all;













>> den=14.6*(fs-fp)/f;

>> n=ceil(num/den);

>> n1=n+1;

>> if(rem(n,2)~=0)

n1=n;

n=n-1;

end;

y=hanning(n1);

>> b=fir1(n,wp,y);

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

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


FIGURE:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-140

-120

-100

-80

-60

-40

-20

0

20

Gain

in d

b -

->


Q18.Design low pass filter using Bartlett window.

CODE:

>> clear all;













>> den=14.6*(fs-fp)/f;

>> n=ceil(num/den);

>> n1=n+1;

>> if(rem(n,2)~=0)

n1=n;

n=n-1;

end;

y=bartlett(n1);

>> b=fir1(n,wp,y);

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

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


FIGURE:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Gain

in d

b -

->


Q19. Design an all pass filter and locate its poles and zeros.

CODE:

c=[1.5 0.7];

>> hd=dfilt.allpass(c)

hd =

FilterStructure: 'Minimum-Multiplier Allpass'

AllpassCoefficients: [1.5 0.7]

PersistentMemory: false

>> zplane(hd)

FIGURES:

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Real Part

Imagin

ary

Part

Pole/Zero Plot

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

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Normalized Frequency ( rad/sample)

Magnitu

de (

dB

)

Magnitude Response (dB)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-6

-5

-4

-3

-2

-1

0


Phase (

radia

ns)

Phase Response

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

2

4

6

8

10

12


Gro

up d

ela

y (

in s

am

ple

s)

Group Delay

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


Phase D

ela

y (

sam

ple

s)

Phase Delay

0 5 10 15 20 25 30 35 40 45 50

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Samples

Impulse Response

Am

plit

ude

Q20. Design a minimum phase filter and locate its poles and zeros.

CODE:

Fs = 96000;

Fn = Fs/2;

f = [0 17000 20000 28000 31000 Fn]/Fn;

a = [0 0 1 1 0 0];

w = [5 1 5];

b = firgr(44, f, a, w, 'minphase');

legend(fvtool(b),'Min Phase')

FIGURES:

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Real Part

Imagin

ary

Part

44

Pole/Zero Plot

Min Phase: Zero

Min Phase: Pole

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

6

8

10

12

14

16

18

20


Gro

up d

ela

y (

in s

am

ple

s)

Group Delay

Min Phase

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-40

-35

-30

-25

-20

-15

-10

-5

0


Magnitu

de (

dB

)

Magnitude Response (dB)

Min Phase

0 5 10 15 20 25 30 35 40

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Samples

Impulse Response

Am

plit

ude

Min Phase

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-6

-4

-2

0

2

4

6


Phase (

radia

ns)

Phase Response

Min Phase

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

16.5

17

17.5

18

18.5

19

19.5

20

20.5

21


Phase D

ela

y (

sam

ple

s)

Phase Delay

Min Phase

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