This file concludes some codes related to some topics of DIGITAL SIGNAL PROCESSING as Butterworth filter, Chebyshev filter and many others.............

1. ROORKEE COLLEGE OF
ENGINEERING, ROORKEE
UNDER THE GUIDANCE OF:
 Miss. RUCHITA SINGH
(Asst. Professor, EEE Dept.)
ROORKEE COLLEGE OF
ENGINEERING, ROOORKEE
BY – PRASHANT SRIVASTAV
ROLL NO. - 661020108001
B.Tech.- EEE (Vth
sem.)

2. INDEX
SR.NO. NAME OF PROGRAM DATE TEACHERS’REMARK
1 WAVE FORM
GENERATION
2 LINEAR CONVOLUTION
3 DESIGN OF
BUTTERWORTH FILTER:
(I) ANALOG LOW PASS FILTER
(II) DIGITAL BANDPASS
FILTER
4 AUTOCORRELATION
5 DESIGN OF CHEBYSHEV
DIGITAL FILTER
(I) TYPE – I BANDPASS
(II) TYPE – II BANDPASS
(III) TYPE –II BANDSTOP
6 FFT & IFFT WITHOUT
USING FUNCTION
7 DESIGN OF FIR FILTER BY
USING HANNING
WINDOW
8 DESIGN OF FIR FILTER BY
USING CHEBYSHEV
WINDOW

3. 1.WAVE FORM GENERATION
COSINE WAVE
 t=0:.01:pi;
 y=cos(2*pi*t);
 subplot(2,1,1);plot (t,y);ylabel('amplitude -->');
 xlabel('(b) n -->');
GENERATION OF EXPONENTIAL SIGNAL
1. n=input('enter the length of the exponential sequence');
2. t=0:n;
3. a=input('enter the a value');
4. y2=exp(a*t);
5. subplot(2,2,4);
6. stem(t,y2);
7. ylabel('Amplitude -->');
8. xlabel('(d) n -->');
Enter the length of the exponential sequence'
Enter the a value'

4. GENERATION OF UNIT IMPULSE
1. t=-2:1:2;
2. y=[zeros(1,2),ones(1,1),zeros(1,2)];
3. subplot(2,2,1);
4. stem(t,y);
5. ylabel('amplitude_ _>');
6. xlabel('(a)n_ _>');
GENERATION OF UNIT STEP SEQUENCE
1. n=input('enter the N value');
2. t=0:1:n-1;
3. y1=ones(1,n);
4. subplot(2,2,2);
5. stem(t,y1);
6. ylabel('amplitude_ _>');
7. xlabel('(b)n_ _>');
enter the “n” values.

5. GENERATION OF RAMP SEQUENCE
1. n=input('enter the length of the ramp sequence');
2. t=0:n;
3. subplot(2,2,3);
4. stem(t,t);
5. ylabel('amplitude -->');
6. xlabel('(c) n -->');
„Enter the length of the ramp sequence'
SINE WAVE
 t=0:.01:pi;
 y=sin(2*pi*t);figure(2);
 subplot(2,1,1);plot (t,y);ylabel('amplitude -->');
 xlabel('(a) n -->');

6. 2.LINEAR CONVOLUTION
 clc;
 clear all;
 close all;
 x=input('enter the 1st sequence');
 h=input('enter the 2nd sequence');
 y=conv(x,h);
 figure;subplot(3,1,1);
 stem(x);
 ylabel('amplitude -->');
 xlabel('(a) n -->');
 subplot(3,1,2);
 stem(h);ylabel('amplitude -->');
 xlabel('(b) n -->');
 subplot(3,1,3);
 stem(y);ylabel('amplitude -->');
 xlabel('(c) n -->');
 disp('the resultant signal is ');y
example,
1st
sequence – [1, 2]
2nd
sequence – [1, 2, 4]

7. 3.DESIGN OF BUTTERWORTH FILTER
ANALOG LOW PASS FILTER
1. clc;
2. close all;
3. clear all;
4. format long
5. rp=input('enter the passband ripple');
6. rs=input('enter the stopband ripple');
7. wp=input('enter the passband freq');
8. ws=input('enter the stopband freq');
9. fs=input('enter the sampling freq');
10.w1=2*wp/fs;w2=2*ws/fs;
11.[n,wn]=buttord(w1,w2,rp,rs,'s');
12.[z,p,k]=butter(n,wn);
13.[b,a]=zp2tf(z,p,k);
14.[b,a]=butter(n,wn,'s');
15.w=0:.01:pi;
16.[h,om]=freqs(b,a,w);
17.m=20*log10(abs(h));
18.an=angle(h);
19.subplot(2,1,1);
20.plot(om/pi,m);
21.ylabel('Gain in dB --.');
22.xlabel('(a) Normalised frequency --.');
23.subplot(2,1,2);
24.plot(om/pi,an);
25.xlabel('(b) Normalised frequency --.');
26.ylabel('Phase in radians --.');
Example:
 enter the passband ripple 0.15
 enter the stopband ripple 60
 enter the passband freq 1500
 enter the stopband freq 3000
 enter the stopband freq 7000

8. DIGITAL BANDPASS FILTER
 clc;
 clear all;
 rp = input('Enter the passband ripple = ');
 rs = input('Enter the stopband ripple = ');
 wp = input('Enter the passband frequency = ');
 ws = input('Enter the stopband frequency = ');
 fs = input('Enter the sampling frequency = ');
 w1 = 2*wp/fs;
 w2 = 2*ws/fs;
 [n] = buttord(w1,w2,rp,rs);
 wn = [w1 w2];
 [b,a] = butter(n,wn,'bandpass');
 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);
 subplot(2,1,1);
 plot(om/pi,m);
 title('Magnitude Response');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 subplot(2,1,2);
 plot(om/pi,an);
 title('Phase Response');
 xlabel('Normalised Frequency ---->');
 ylabel('Phase in radians ---->');
 grid on;
 Enter the passband ripple = 0.2
 Enter the stopband ripple = 40
 Enter the passband frequency = 1500
 Enter the stopband frequency = 2000
 Enter the sampling frequency = 9000

9. 4.AUTO-CORRELATION
Algorithm:
1. Get the signal x(n)of length N in matrix form
2. The correlated signal is denoted as y(n)
3. y(n)is given by the formula
y(n) 5 [ ( ) ( )] x k x k n k − =−∞ ∞ ∑ where n52(N 2 1) to (N 2 1)

10. 5.DESIGN OF CHEBYSHEV
DIGITAL FILTER
TYPE-I BAND PASS FILTER
 clc;
 clear all;
 rp = input('Enter the passband ripple = ');
 rs = input('Enter the stopband ripple = ');
 wp = input('Enter the passband frequency = ');
 ws = input('Enter the stopband frequency = ');
 fs = input('Enter the sampling frequency = ');
 w1 = 2*wp/fs;
 w2 = 2*ws/fs;
 [n] = cheb1ord(w1,w2,rp,rs,'s');
 wn = [w1 w2];
 [b,a] = cheby1(n,rp,wn,'bandpass','s');
 w = 0:0.01:pi;
 [h,om] = freqs(b,a,w);
 m = 20*log10(abs(h));
 an = angle(h);
 subplot(2,1,1);
 plot(om/pi,m);
 subplot(2,1,1);
 plot(om/pi,m);
 title('Magnitude Response');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 subplot(2,1,2);
 plot(om/pi,an);
 title('Phase Response');
 xlabel('Normalised Frequency ---->');
 ylabel('Phase in radians ---->');
 grid on;
 Enter the passband ripple = 0.3
 Enter the stopband ripple = 40
 Enter the passband frequency = 1400
 Enter the stopband frequency = 2000
 Enter the sampling frequency = 5000

11. CHEBYSHEV TYPE-2 BANDSTOP FILTER
 clc;
 clear all;
 rp = input('Enter the passband ripple = ');
 rs = input('Enter the stopband ripple = ');
 wp = input('Enter the passband frequency = ');
 ws = input('Enter the stopband frequency = ');
 fs = input('Enter the sampling frequency = ');
 w1 = 2*wp/fs;
 w2 = 2*ws/fs;
 [n] = cheb2ord(w1,w2,rp,rs);
 wn = [w1 w2];
 [b,a] = cheby2(n,rs,wn,'stop');
 w = 0:0.1/pi:pi;
 [h,om] = freqz(b,a,w);
 m = 20*log10(abs(h));
 an = angle(h);
 subplot(2,1,1);
 plot(om/pi,m);
 subplot(2,1,1);
 plot(om/pi,m);
 title('Magnitude Response');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 subplot(2,1,2);
 plot(om/pi,an);
 title('Phase Response');
 xlabel('Normalised Frequency ---->');
 ylabel('Phase in radians ---->');
 grid on;
 Enter the passband ripple = 0.3
 Enter the stopband ripple = 46
 Enter the passband frequency = 1400
 Enter the stopband frequency = 2000
 Enter the sampling frequency = 8000

12. CHEBYSHEV TYPE-I BANDSTOP FILTER
 clc;
 clear all;
 rp = input('Enter the passband ripple = ');
 rs = input('Enter the stopband ripple = ');
 wp = input('Enter the passband frequency = ');
 ws = input('Enter the stopband frequency = ');
 fs = input('Enter the sampling frequency = ');
 w1 = 2*wp/fs;
 w2 = 2*ws/fs;
 [n] = cheb1ord(w1,w2,rp,rs);
 wn = [w1 w2];
 [b,a] = cheby1(n,rp,wn,'stop');
 w = 0:0.1/pi:pi;
 [h,om] = freqz(b,a,w);
 m = 20*log10(abs(h));
 an = angle(h);
 subplot(2,1,1);
 plot(om/pi,m);
 subplot(2,1,1);
 plot(om/pi,m);
 title('Magnitude Response');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 subplot(2,1,2);
 plot(om/pi,an);
 title('Phase Response');
 xlabel('Normalised Frequency ---->');
 ylabel('Phase in radians ---->');
 grid on;
 Enter the passband ripple = 0.25
 Enter the stopband ripple = 40
 Enter the passband frequency = 2500
 Enter the stopband frequency = 2750
 Enter the sampling frequency = 7000
>>

13. 6.FFT & IFFT WITHOUT USING
FUNCTION
 clc;
 clear all;
 x = input('Enter the input sequence = ');
 N = length(x);
 for k = 1:N
 y(k) = 0;
 for n = 1:N
 y(k) = y(k)+x(n)*exp(-1i*2*pi*(k-1)*(n-1)/N);
 end
 end
 %code block to plot the input sequence
 t = 0:N-1;
 subplot(2,2,1);
 stem(t,x);
 ylabel('Amplitude ---->');
 xlabel('n ---->');
 title('Input Sequence');
 grid on;
 magnitude = abs(y); % Find the magnitudes of individual FFT points
 disp('FFT Sequence = ');
 disp(magnitude);
 %code block to plot the FFT sequence
 t = 0:N-1;
 subplot(2,2,2);
 stem(t,magnitude);
 ylabel('Amplitude ---->');
 xlabel('K ---->');
 title('FFT Sequence');
 grid on;
 R = length(y);
 for n = 1:R
 x1(n) = 0;
 for k = 1:R
 x1(n) = x1(n)+(1/R)*y(k)*exp(1i*2*pi*(k-1)*(n-1)/R);
 end
 end
 %code block to plot the IFFT sequence

14.  t = 0:R-1;
 subplot(2,2,3);
 stem(t,x1);
 disp('IFFT Sequence = ');
 disp(x1);
 ylabel('Amplitude ---->');
 xlabel('n ---->');
 title('IFFT sequence');
 grid on;
Enter the input sequence = [1 4 2 5 2]
FFT Sequence =
14.0000 2.8124 4.3692 4.3692 2.8124
IFFT Sequence =
Columns 1 through 4
1.0000 - 0.0000i 4.0000 - 0.0000i 2.0000 - 0.0000i 5.0000 + 0.0000i
Column 5
2.0000 + 0.0000i

15. 7.FIR USING HANNING WINDOW
 clc;
 clear all;
 rp = input('Enter the passband ripple = ');
 rs = input('Enter the stopband ripple = ');
 fp = input('Enter the passband frequency = ');
 fs = input('Enter the stopband frequency = ');
 f = input('Enter the sampling frequency = ');
 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);
 % low-pass filter
 b = fir1(n,wp,y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,1);
 plot(o/pi,m);
 title('Magnitude Response of LPF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 % high-pass filter
 b = fir1(n,wp,'high',y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,2);
 plot(o/pi,m);
 title('Magnitude Response of HPF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 % band pass filter
 wn = [wp ws];

16.  b = fir1(n,wn,y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,3);
 plot(o/pi,m);
 title('Magnitude Response of BPF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 % band stop filter
 b = fir1(n,wn,'stop',y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,4);
 plot(o/pi,m);
 title('Magnitude Response of BSF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 OUTPUT:
 Enter the passband ripple = 0.03
 Enter the stopband ripple = 0.01
 Enter the passband frequency = 1400
 Enter the stopband frequency = 2000
 Enter the sampling frequency = 8000

17. 8. FIR FILTER USING
CHEBYSHEV WINDOW
 clc;
 clear all;
 rp = input('Enter the passband ripple = ');
 rs = input('Enter the stopband ripple = ');
 fp = input('Enter the passband frequency = ');
 fs = input('Enter the stopband frequency = ');
 f = input('Enter the sampling frequency = ');
 r = input('Enter the ripple value(in dBs) = ');
 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);
 if(rem(n,2)==0)
 n = n+1;
 end
 y = chebwin(n,r);
 % low-pass filter
 b = fir1(n-1,wp,y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,1);
 plot(o/pi,m);
 title('Magnitude Response of LPF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 % high-pass filter
 b = fir1(n-1,wp,'high',y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,2);
 plot(o/pi,m);
 title('Magnitude Response of HPF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 % band pass filter
 wn = [wp ws];

18.  b = fir1(n-1,wn,y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,3);
 plot(o/pi,m);
 title('Magnitude Response of BPF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 % band stop filter
 b = fir1(n-1,wn,'stop',y);
 [h,o] = freqz(b,1,256);
 m = 20*log10(abs(h));
 subplot(2,2,4);
 plot(o/pi,m);
 title('Magnitude Response of BSF');
 ylabel('Gain in dB ---->');
 xlabel('Normalised Frequency ---->');
 grid on;
 OUTPUT:
 Enter the passband ripple = 0.03
 Enter the stopband ripple = 0.02
 Enter the passband frequency = 1800
 Enter the stopband frequency = 2400
 Enter the sampling frequency = 10000
 Enter the ripple value(in dBs) = 40