INPUT:
Enter the N value6
Enter the length of ramp sequence10
Enter the length of exponential sequence5
Enter the a value4
OUTPUT:
GENERATION OF FUNCTIONAL SEQUENCES;
clc;
clear all;
close all;
%program for the generation of unit impulse signal
t=-2:1:2; y=[zeros(1,2),ones(1,1),zeros(1,2)];
subplot(2,2,1);
stem(t,y);
ylabel('amplitude--.');
xlabel('(a)n--.');
%program for the generation of unit step sequence
[u(n)2u(n 2 N)] n=input('enter the N value');
t=0:1:n-1;
y1=ones(1,n);
subplot(2,2,2);
stem(t,y1);
ylabel('amplitude--.');
xlabel('(b)n--.');
%program for the generation of ramp sequence
n1=input('enter the length of ramp sequence');
t=0:n1;
subplot(2,2,3);
stem(t,t);
ylabel('amplitude--.');
xlabel('(c)n--.');
%program for the generation of exponential sequence
n2=input('enter the length of exponential sequence');
t=0:n2;
a=input('Enter the a value');
y2=exp(a*t);
subplot(2,2,4);
stem(t,y2);
ylabel('amplitude--.');
xlabel('(d)n--.');
%program for the generation of continuous exponential sequences
n3=input('enter the n value')'
t=0:2:n3-1;
a=input('enter the a value');
y3=exp(a*t); subplot(3,1,1);
plot(t,y3);
ylabel('amplitude--.');
xlabel('(a)n--.');
%program for the generation of sine sequence
t=0:.01:pi;
y=sin(2*pi*t);
subplot(3,1,2);
plot(t,y);
ylabel('amplitude--.');
xlabel('(a)n--.');
%program for the generation of cosine sequence
t=0:.01:pi;
y=cos(2*pi*t);
subplot(3,1,3);
plot(t,y);
ylabel('amplitude--.'); xlabel('(b)n--.');
INPUT:
Enter the n value6
Enter the a value0.2
OUTPUT:
OUTPUT:(RANDOM SEQUENCES)
RANDOM SEQUENCES
N=1024;
R1=randn(1,N);
R2=rand(1,N);
figure(1);
subplot(2,2,1);
plot(R1);
grid;
title('normal[gaussion]distributed random signal');
xlabel('sample number');
ylabel('amplitude');
subplot(2,2,2);
hist(R1);
grid;
title('histogram[pdf]of a normal random signal');
xlabel('sample number');
ylabel('total');
subplot(2,2,3);
plot(R2);
grid;
title('uniformly distributed random signal');
xlabel('sample number');
ylabel('amplitude');
subplot(2,2,4);
hist(R2);
grid;
title('histogram[pdf]of a uniformly random signal');
xlabel('sample number');
ylabel('Total');
RESULT
INPUT:
Enter the sequence[5 8 4] The
resultant signal is20 72 105 72 20
OUTPUT:
AUTO CORRELATION
Clc;
Clear all;
close all;
x=input('enter the sequence');
y=xcorr(x,x);
figure;
subplot(2,1,1);
stem(x);
ylabel('amplitude--.')
xlabel('(a)n--.');
subplot(2,1,2);
stem(fliplr(y));
ylabel('amplitude--.');
xlabel('(a)n--.');
disp('the resultant signal is');
fliplr(y
INPUT:
Enter the 1st sequence[5 8 4]
Enter the 2nd sequence[2 5 4]
The resultant signal is
ans =
8 36 66 57 20
OUTPUT:
CROSS CORRELATION
clc;
clear all;
close all;
x=input('enter the 1st sequence');
h=input('enter the 2nd sequence');
y=xcorr(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(fliplr(y));
ylabel('amplitude--.');
xlabel('(c)n--.');
disp('The resultant signal is ');
fliplr(y)
x=input('enter the sequence');
y=xcorr(x,x);
figure;
subplot(2,1,1);
stem(x);
ylabel('amplitude--.');
xlabel('(a)n--.');
subplot(2,1,2);
stem(fliplr(y));
ylabel('amplitude--.');
xlabel('(a)n--.');
disp('The resultant signal is');
fliplr(y),
RESULT
INPUT:
enter the input sequence:[3 4 7]
enter the impulse sequence:[2 6 7]
the resultant signal is
y =76 75 59
OUTPUT:
CIRCULARCONVOLUTION
clc;
close all;
clear all;
g=input('enter the input sequence:');
h=input('enter the impulse sequence:');
N1=length(g);
N2=length(h);
N=max(N1,N2);
N3=N1-N2;
if(N3>=0);
h=[h,zeros(1,N3)];
else
g=[g,zeros(1,N3)];
end
for n=1:N
y(n)=0;
for i=1:N
j=n-i+1;
if(j<=0)
j=N+j;
end
y(n)=y(n)+(g(i)*h(j));
end
end subplot(1,3,1);
stem(g);
xlabel('(g(n)...>');
ylabel('amplitude');
title('input sequence');
subplot(1,3,2); stem(h);
xlabel('h(n)');
ylabel('amplitude');
title('impulse sequence');
subplot(1,3,3);
stem(y);
xlabel('y(n)');
ylabel('amplitude');
title('convolution sequence');
disp('the resultant signal is');y
INPUT:
enter the length of input sequence4
enter the length of impulse sequence4
enter input sequence[2 5 38]
enter impulse sequence[7 5 2 9]
enter the sequence of y
y =14 45 50 99 91 43 72
OUTPUT
LINEAR CONVOLUTION
clc;
close;
clear all;
n=input('enter the length of input sequence');
n1=input('enter the length of impulse sequence');
x=input('enter input sequence');
h=input('enter impulse sequence');
y=conv(x,h);
subplot(1,3,1);
stem(x); xlabel('n ----->');
ylabel('amp ----->');
title('input sequence');
subplot(1,3,2); stem(h);
ylabel('amplitude ----->');
xlabel('n----->');
title ('impulse response');
subplot(1,3,3);
stem(y); ylabel('amplitude----->');
xlabel('n------>');
title('linear convolution');
disp('enter the sequence of y');y
RESULT
INPUT:
enter the pass band ripple0.04
enter the stopband ripple0.02
enter the passband freq1000
enter the stopband freq2000
enter the sampling freq8000
OUTPUT:
FINITE IMPULSE RESPONSE
RECTANGULAR WINDOW
clc;
clear all;
close all;
rp=input('enter the pass band ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passbandfreq');
fs=input('enter the stopbandfreq');
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=boxcar(n1);
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('LPF');
ylabel('gain in dB--.');
xlabel
'(a)normalisedfreq--.');
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('HPF');
ylabel('gain in dB--.');
xlabel('(b)normalisedfreq--.');
wn=[wp,ws];
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('BPF');
ylabel('gain in dB-->');
xlabel('(c)normalisedfreq-->');
wn=[wp,ws];
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('BSF');
ylabel('gain in dB-->');
xlabel('(d)normalisedfreq-->');
INPUT:
enter the pass band ripple0.04
enter the stopband ripple0.02
enter the passband freq1000
enter the stopband freq2000
enter the sampling freq8000
OUTPUT:
TRIANGULAR WINDOW
clc;
clear all;
close all;
rp=input('enter the pass band ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passbandfreq');
fs=input('enter the stopbandfreq');
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=triang(n1);
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('LPF'); ylabel('gain in dB--.');
xlabel('(a)normalisedfreq--.');
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('HPF'); ylabel('gain in dB--.');
xlabel('(b)normalisedfreq--.');
wn=[wp,ws];
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('BPF'); ylabel('gain in dB-->');
xlabel('(c)normalisedfreq-->');
wn=[wp,ws];
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('BSF'); ylabel('gain in dB-->');
xlabel('(d)normalisedfreq-->');
INPUT:
enter the pass band ripple0.04
enter the stopband ripple0.02
enter the passband freq1000
enter the stopband freq2000
enter the sampling freq8000
OUTPUT:
HAMMING WINDOW
clc;
clear all;
close all;
rp=input('enter the pass band ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passbandfreq');
fs=input('enter the stopbandfreq');
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);
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('LPF');
ylabel('gain in dB--.');
xlabel('(a)normalisedfreq--.');
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('HPF'); ylabel('gain in dB--.');
xlabel('(b)normalisedfreq--.');
wn=[wp,ws];
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('BPF'); ylabel('gain in dB-->');
xlabel('(c)normalisedfreq-->');
wn=[wp,ws];
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('BSF'); ylabel('gain in dB->');
xlabel('(d)normalisedfreq-->');
INPUT:
enter the pass band ripple0.04
enter the stopband ripple0.02
enter the passband freq1000
enter the stopband freq2000
enter the sampling freq8000
OUTPUT:
HANNING WINDOW
clc;
clear all;
close all;
rp=input('enter the pass band ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passbandfreq');
fs=input('enter the stopbandfreq');
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);
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('LPF'); ylabel('gain in dB--.');
xlabel('(a)normalisedfreq--.');
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('HPF'); ylabel('gain in dB--.');
xlabel('(b)normalisedfreq--.');
wn=[wp,ws];
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('BPF'); ylabel('gain in dB-->');
xlabel('(c)normalisedfreq-->');
wn=[wp,ws];
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('BSF'); ylabel('gain in dB-->');
xlabel('(d)normalisedfreq-->');
INPUT:
enter the pass band ripple0.04
enter the stopband ripple0.02
enter the passband freq1000
enter the stopband freq2000
enter the sampling freq8000
OUTPUT:
BLACKMAN WINDOW
clc;
clear all;
close all;
rp=input('enter the pass band ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passbandfreq');
fs=input('enter the stopbandfreq');
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=blackman(n1);
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('LPF');
ylabel('gain in dB--.');
xlabel('(a)normalisedfreq--.');
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('HPF');
ylabel('gain in dB--.');
xlabel('(b)normalisedfreq--.');
wn=[wp,ws];
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('BPF');
ylabel('gain in dB-->');
xlabel('(c)normalisedfreq-->');
wn=[wp,ws];
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('BSF');
ylabel('gain in dB-->');
xlabel('(d)normalisedfreq-->');
INPUT:
enter the pass band ripple0.04
enter the stopband ripple0.02
enter the passbandfreq1000
enter the stopbandfreq2000
enter the sampling freq8000
OUTPUT:
KAISER WINDOW
clc;
clear all;
close all;
rp=input('enter the pass band ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passbandfreq');
fs=input('enter the stopbandfreq');
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=kaiser(n1);
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('LPF');
ylabel('gain in dB--.');
xlabel('(a)normalisedfreq--.');
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('HPF');ylabel('gain in dB--.');
xlabel('(b)normalisedfreq--.');
wn=[wp,ws];
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('BPF');ylabel('gain in dB-->');
xlabel('(c)normalisedfreq-->');
wn=[wp,ws];
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('BSF');
ylabel('gain in dB-->');
xlabel('(d)normalisedfreq-->');
RESULT
INPUT:
enter the passband ripple0.6
enter the stop band ripple25
enter the passbandfreq1300
enter the stopbandfreq3000
enter the sampling freq8000
OUTPUT:
INFINITE IMPULSE RESPONSE BUTTERWORTH FILTER
clc;
close all;
clear all;
rp=input('enter the passband ripple');
rs=input('enter the stop band ripple');
wp=input('enter the psaabandfreq');
ws=input('enter the stopbandfreq');
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);
[h,w]=freqz(b,a,512);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,1);
plot(w,abs(h));
ylabel('gain');
xlabel('normalized frequency');
title('LPF');
[b,a]=butter(n,wn,'high');
[h,w]=freqz(b,a,512);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,2);
plot(w,abs(h));
ylabel('gain');
xlabel('normalized frequency');
title('HPF');
wn1=[w1 w2];
[b,a]=butter(n,wn1,'bandpass');
[h,w]=freqz(b,a,512);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,3);
plot(w,abs(h));
ylabel('gain');
xlabel('normalized frequency');
title('BPF');
wn2=[w1 w2];
[b,a]=butter(n,wn2,'stop');
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,4);
plot(w,abs(h));
ylabel('gain');
xlabel('normalized frequency');
title('BSF');
INPUT:
enter the passband ripple.25
enter the stop band ripple40
enter the psaaband freq2500
enter the stopband freq2750
enter the sampling freq7000
OUTPUT:
CHEBYSHEV -1 INFINITE IMPULSE RESPONSE FILTER
clc;
close all;
clear all;
format long
rp=input('enter the passband ripple');
rs=input('enter the stop band ripple');
wp=input('enter the psaabandfreq');
ws=input('enter the stopbandfreq');
fs=input('enter the sampling freq');
w1=2*wp/fs;
w2=2*ws/fs;
[n,wn]=cheb1ord(w1,w2,rp,rs);
[b,a]=cheby1(n,rp,wn);
w=0:.01:pi;
[h,om]=freqz(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,1);
plot(om/pi,m);
ylabel('gain');
xlabel('a');
[b,a]=cheby1(n,rp,wn,'high');
w=0:.01/pi:pi;
[h,om]=freqz(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,2);
plot(om/pi,m);
ylabel('gain');
xlabel('a');
wn=[w1 w2];
[b,a]=cheby1(n,rp,wn,'bandpass');
w=0:0.01:pi;
[h,om]=freqz(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,3);
plot(om/pi,m);
ylabel('gain');
xlabel('c');
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(2,2,4);
plot(om/pi,m);
ylabel('gain');
xlabel('d');
INPUT:
enter the passband ripple.3 enter
the stop band ripple46 enter the
psaaband freq1400 enter the
stopband freq2000 enter the
sampling freq8000
OUTPUT:
CHEBYSHEV -2 INFINITE IMPULSE RESPONSE FILTER
clc;
close all;
clear all;
format long
rp=input('enter the passband ripple');
rs=input('enter the stop band ripple');
wp=input('enter the psaabandfreq');
ws=input('enter the stopbandfreq');
fs=input('enter the sampling freq');
w1=2*wp/fs;
w2=2*ws/fs;
[n,wn]=cheb2ord(w1,w2,rp,rs);
[b,a]=cheby1(n,rp,wn);
w=0:.01:pi;
[h,om]=freqz(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,1);
plot(om/pi,m);
ylabel('gain');
xlabel('a');
[b,a]=cheby2(n,rs,wn,'high');
w=0:.01/pi:pi;
[h,om]=freqz(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,2);
plot(om/pi,m);
ylabel('gain');
xlabel('a');
wn=[w1 w2];
[b,a]=cheby2(n,rs,wn,'bandpass');
w=0:0.01:pi;
[h,om]=freqz(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,2,3);
plot(om/pi,m);
ylabel('gain');
xlabel('c');
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(2,2,4);
plot(om/pi,m);
ylabel('gain');
xlabel('d');
RESULT
OUTPUT:
MULTIRATE FILTERS
INTERPOLATION
clc;
close all;
clear all;
N=31;
Nord=N-1;
L=3; ro1=.2;
h1=firnyquist(Nord,L,ro1);
ro2=.4;
h2=firnyquist(Nord,L,ro2);
ro3=.6;
h3=firnyquist(Nord,L,ro3);
figure(1)
subplot(3,1,1);
stem(0:N-1,h1,'b');
axis([0,30,-.2,.5]);
ylabel('h1(n)');
title('figure 1');
legend('h1')
subplot(3,1,2);
stem(0:N-1,h2,'k');
axis([0,30,-.2,.5]);
ylabel('h2');
legend('h2')
subplot(3,1,3)
stem(0:N-1,h3,'r');
axis([0,30,-.2,.5]);
ylabel('h3(n)');
xlabel('n');
legend('h3')
[H1,f]=freqz(h1,1,256,2);
[H2,f]=freqz(h2,1,256,2);
[H3,f]=freqz(h3,1,256,2);
figure(2)
plot(f,abs(H1),'b',f,abs(H2),'k',f,abs(H3),'r'); grid
title('fig2');
axis([0,1,0,1.1]);
xlabel('\omega/\pi');
ylabel('mag');
legend('|H_1(e^j^\omega)|''|H_2(e^j^\omega)|''|H_3(e^j^\omega)|')
OUTPUT:
DECIMATOR
close all;
clear all;
% Computing the coefficients of the Lth-band decimation filter:
N =29;
% Filter length
Nord = N-1;
% Filter order
L = 4;
ro = 0.2;
% Roll-off factor
h = firnyquist(Nord,L,ro);
% Filter design
[H,f] = freqz(h,1,500,2);
% Computing the frequency response
figure (1)
subplot(2,1,1)
stem(0:N-1,h);
xlabel('n');
ylabel('h[n]');
title('Figure 1')
axis([0,N-1,-0.1,0.3])
subplot(2,1,2)
plot(f,20*log10(abs(H))),
xlabel('\omega/\pi'),
ylabel('Gain, dB')
axis([0,1,-60,2]), grid
% Polyphase components of the decimation filter h[n]
e0 = downsample(h,4,0);
e1 = downsample(h,4,1);
e2 = [0,0,0,0.25,0,0,0];
e3 = downsample(h,4,3);
% Generating the original signal x[n]
n = 0:255;x = cos(pi*0.15*n)+cos(pi*0.55*n);
[X,f] = freqz(x,1,500,2);
figure (2)
plot(f,abs(X))
xlabel('\omega/\pi');
ylabel('Amplitude')
title('Figure 2: Amplitude spectrum of the original signal, |X(e^j^\omega)|')
% Polyphasedownsampling of the original signal
x0 = [x(1:4:256),0]; x1 = [0,x(4:4:256)]; x2 =[0,x(3:4:256)]; x3 = [0,x(2:4:256)];
% Polyphase filtering
y0 = filter(e0,1,x0); y1
= filter(e1,1,x1);
y2 = 0.25*[0,0,0,x2(1:length(x2)-3)];
y3 = filter(e3,1,x3);
% Decimated signal y[n]
y = y0+y1+y2+y3;
[Y,fd] = freqz(y,1,500,2);
figure (3) ;
plot(fd,abs(Y))
xlabel('\omega/\pi');
ylabel('Amplitude');
title('Figure 3: Amplitude spectrum of the decimatedl signal, |Y(e^j^\omega)|')
OUTPUT :(RESAMPLING)
RESAMPLING
clear all, close all
% STEP 1
h = firhalfband(22,0.4);
% FIR filter design
% Generation of the input signal
F = [0,0.05,0.45,1]; A = [0,1,0.1,0.05];
x1 = fir2(256,F,A); x2 = sin(2*pi*(0:256)*0.4)/150;
x = x1 + x2;
[X,f] = freqz(x,1,512,2);
% Spectrum of the original signal
figure (2)
plot(f,abs(X(1:512))),;
xlabel('\omega/\pi';
ylabel('|X(e^{j\omega})|');
title('Figure 2: Spectrum of the original signal')
axis([0,1,0,1.1])
% Polyphase decomposition
e0 = h(1:2:(length(h)-1)/2);
% Setting the initial states
xk = zeros(size(1:(length(h)+1)/2)); %
Decimation
rot = 0; % Initial switch position y =
[];
for n=1:length(x) xn =
x(n);
if rot==0 ss=1; pro =
xn*e0;
xk = [pro+xk(1:length(xk)/2),fliplr(pro) + xk((length(xk)/2+1):length(xk))]; yn
= xk(length(xk));
y = [yn,y];
xk = [0,xk(1:length(xk)-1)]; else
end
if rot==1 ss=0;
xk(length(xk)/2+1) = 0.5*xn + xk(length(xk)/2+1);
else
end rot=ss;
end
Y = freqz(y,1,512,2); % Spectrum of the decimated signal figure (3)
plot(f,abs(Y(1:512))), xlabel('\omega/\pi'),ylabel('|Y(e^{j\omega})|')
title('Figure 3: Spectrum of the decimated signal')
axis([0,1,0,0.6])
% STEP 2
% Interpolation according to Figure 1
yi=[]; xk=zeros(size(1:(length(h)+1)/2));
rot=0;
k=1;
for
n=1:length(y)*2-1
xn=y(k);
if k==1, xk=[xn,xk(1:length(xk)-1)];
else
end
if rot==0 ss=1;
yn=2*sum((xk(1:length(xk)/2)+fliplr(xk(length(xk)/2+1:length(xk)))).*e0);
yi=[yi,yn];
OUTPUT:
elsee
nd
if rot==1 ss=0;
yi=[yi,xk(length(xk)/2)];
if k>1 xk=[xn,xk(1:length(xk)-1)];
else
end
k=k+1;
else
end
rot=ss;
end
[Yi,f]=freqz(yi,1,512,2); % Spectrum of the interpolated signal figure(4)
plot(f,abs(Yi));
title('Figure3: Spectrum of the interpolated signal')
xlabel('\omega/\pi');
ylabel('|(Y_i)|')
RESULT
OUTPUT:
EQUALIZATION
clc;
clear all;
close all;
M=3000;
T=2000;
L=20;
ChL=5;
(ChL+1) EqD=round((L+ChL)/2);
Ch=randn(1,ChL+1)+sqrt(1)*randn(1,ChL+1); Ch=Ch/norm(Ch);
TxS=round(rand(1,M))*2-1; TxS=TxS+sqrt(1)*(round(rand(1,M))*2-1);
x=filter(Ch,1,TxS);
n=randn(1,M); %+sqrt(-1)*randn(1,M);
e(i)=TxS(i+10+L-EqD)-c'*X(:,i+10);
c=c+mu*conj(e(i))*X(:,i+10);
endsb=c'
*X;
sb1=sb/norm(c);
sb1=sign(real(sb1))+sqrt(-1)*sign(imag(sb1));
start=7;
sb2=sb1-TxS(start+1:start+length(sb1)); SER=length(find(sb2~=0))/length(sb2);
disp(SER);
subplot(2,2,1), plot(TxS,'*');
grid;
title('Input symbols');
xlabel('real part'),
ylabel('imaginary part')
axis([-2 2 -2 2])
subplot(2,2,2),
plot(x,'o');
grid,
title('Received samples');
xlabel('real part'),
ylabel('imaginary part')
subplot(2,2,3),
plot(sb,'o');
grid, title('Equalized symbols'),
xlabel('real part'),
ylabel('imaginary part')
subplot(2,2,4),
plot(abs(e));
grid,
title('Convergence'),
xlabel('n'),
ylabel('error signal')
RESULT
OUTPUT
enter value for m4
enter value for n4
Enter values for i/p
1234
Enter Values for
n1234
The Value of output y[0]=1 The
Value of output y[1]=4 The
Value of output y[2]=10 The
Value of output y[3]=20 The
Value of output y[4]=25 The
Value of output y[5]=24 The
Value of output y[6]=16
LINEAR CONVOLUTION USING TMS320C5416
PROGRAM
#include<stdio.h>intx
[15],h[15],y[15];
main()
{
inti,j,m,n;
printf("\n enter value for m");
scanf("%d",&m);
printf("\n enter value for n");
scanf("%d",&n);
printf("Enter values for i/p
x(n):\n"); for(i=0;i<m;i++)
scanf("%d",&x[i]);
printf("Enter Values for i/p h(n) \n");
for(i=0;i<n; i++)
scanf("%d",&h[i]); / padding of zeros for(i=m;i<=m+n-1;i++);
for(i=n;i<=m+n-1;i++) h[i]=0;
/* convolution operation */
for(i=0;i<m+n-1;i++)
{
y[i]=0;
for(j=0;j<=i;j++)
{
y[i]=y[i]+(x[j]*h[i-j]);
}}
//displaying the o/p
for(i=0;i<m+n-1;i++)
printf("\n The Value of output y[%d]=%d",i,y[i]);
}
RESULT
OUTPUT:Enter the length of the first sequence 4
Enter the length of the second sequence 3
Enter the first sequence 1 2 3 4
Enter the second sequence 1 2 3
The circular convolution is 18 16 10 16
CIRCULAR CONVOLUTION USING TMS320C5416 PROGRAM
#include<stdio.h>
intm,n,x[30],h[30],y[30],i,j, k,x2[30],a[30];
void main()
{
printf(" Enter the length of the first
sequence\n"); scanf("%d",&m);
printf(" Enter the length of the second sequence\n");
scanf("%d",&n);
printf(" Enter the first
sequence\n"); for(i=0;i<m;i++)
scanf("%d",&x[i]);
printf(" Enter the second sequence\n");
for(j=0;j<n;j++)
scanf("%d",&h[j]); if(m-n!=0) /*If length of both sequences are not equal*/
{
if(m>n) /* Pad the smaller sequence with zero*/
{
for(i=n;i<m;i++)
h[i]=0;
n=m;
}
for(i=m;i<n;i++)
x[i]=0;
m=n;
}
y[0]=0;a[0]=h[0];for(j=1;j<n;j++) /*folding h(n) to h(-n)*/ a[j]=h[n-j];
/*Circular convolution*/
for(i=0;i<n;i++)
y[0]+=x[i]*a[i];for(k=1;k<n;k++
)
{
y[k]=0;
/*circular shift*/
for(j=1;j<n;j++)
x2[j]=a[j-1];x2[0]=a[n-1];for(i=0;i<n;i++)
{
a[i]=x2[i];y[k]+=x[i]*x2[i];
}
}
/*displaying the result*/
printf(" The circular convolution is\n");
for(i=0;i<n;i++)
printf("%d \t",y[i]);
}
RESULT
OUTPUT
FIR LOWPASS FILTER
FIR HIGH PASS FILTER
IMPLEMENTATION OF FIR FILTER USING TMS320C5416
PROGRAM
#include<stdio.h>
#include<math.h>
#define pi 3.1415
intn,N,c;
floatwr[64],wt[64];
void main()
{
printf("\n enter no. of samples,N= :");
scanf("%d",&N);
printf("\n enter choice of window function\n 1.rect \n 2. triang \n c= :");
scanf("%d",&c);
printf("\n elements of window function are:");
switch(c)
{
case 1: for(n=0;n<=N1;n++)
{
wr[n]=1;
printf(" \n wr[%d]=%f",n,wr[n]);
}
break;
case 2:
for(n=0;n<=N-1;n++)
{
wt[n]=1-(2*(float)n/(N-1));
printf("\n wt[%d]=%f",n,wt[n]);
}
break;
}}
RESULT
OUTPUT
IIR LOWPASS FILTER
IIR HIGH-PASS FILTER
IMPLEMENTATION OF IIR FILTER USING TMS320C6713
//iirfilters
#include<stdio.h>
#include<math.h>in
ti,w,wc,c,N; float
H[100];
floatmul(float, int);
void main()
{
printf("\n enter order of filter ");
scanf("%d",&N);
printf("\n enter the cutoff freq
"); scanf("%d",&wc);
printf("\n enter the choice for IIR filter 1. LPF 2.HPF ");
scanf("%d",&c);
switch(c)
{
case 1:
for(w=0;w<100;w++)
{
H[w]=1/sqrt(1+mul((w/(float)wc),2*N));
printf("H[%d]=%f\n",w,H[w]); }
break;
case 2:
for(w=0;w<=100;w++)
{
H[w]=1/sqrt(1+mul((float)wc/w,2*N));
printf("H[%d]=%f\n",w,H[w]);
}
break;
}}
floatmul(float a,int x)
{
for(i=0;i<x-1;i++) a*=a;
return(a);
}
RESULT
OUTPUT:
SINEWAVE:
COSINE WAVE:
GENERATION OF WAVEFORMS USING TMS320C6713 PROGRAM:
SINEWAVE:
#include<stdio.h>
#include<math.h>
float a[100]; main()
{
int i;
for(i=0;i<99;i++)
{
a[i]=sin(2*3.14*5*i/100);
printf("%f",a[i]);
}
}
COSINE WAVE
#include<stdio.h>
#include<math.h>
float a[100]; main()
{
int i;
for(i=0;i<99;i++)
{
a[i]=cos(2*3.14*5*i/100);
printf("%f",a[i]);
}
}
UNIT RAMP:
#include<stdio.h>
#include<math.h>in
ta[50];
main()
{
int i;
for(i=0;i<49;i++)
{
a[i]=i;
printf("%d",i);
}
}
UNIT RAMP:
UNIT STEP:
UNIT STEP:
#include<stdio.h>
#include<math.h>in
ta[10];
main()
{
int i=1,j;
for(j=0;j<9;j++)
{
a[j]=i;
printf("%d",i);
}
}
RESULT
FFT INPUT
FFT OUTPUT
IMPLEMENTATION OF FFT USING TMS320C5416
fft.c
#define PTS 64
typedefstruct{float real,imag;}COMPLEX;
extern COMPLEX w[PTS];
void FFT(COMPLEX*Y,int N)
{
COMPLEX
temp1,temp2; inti,j,k;
intupper_leg,lower_leg;
intleg_diff;
intnum_stages=0;
intindex,step; i=1;
do
{
num_stages+=1;
i=i*2;
}
while(i!=N); leg_diff=N/2;
step=(PTS*2)/N;
for(i=0;i<num_stages;i++)
{
index=0;
for(j=0;j<leg_diff;j++)
{
for(upper_leg=j;upper_leg<N;upper_leg+=(2*leg_diff))
{lower_leg=upper_leg+leg_diff;
temp1.real=(Y[upper_leg]).real+(Y[lower_leg]).real;
temp1.real=(Y[upper_leg]).imag+(Y[lower_leg]).imag;
temp2.real=(Y[upper_leg]).real+(Y[lower_leg]).real;
temp2.imag=(Y[upper_leg]).imag+(Y[lower_leg]).imag;
(Y[lower_leg]).real=temp2.real*(w[index]).real-temp2.imag*(w[index]).imag;
(Y[lower_leg]).imag=temp2.real*(w[index]).real+temp2.imag*(w[index]).imag;
(Y[upper_leg]).real=temp1.real;
(Y[upper_leg]).imag=temp1.imag;
}
index+=step;
}
leg_diff=leg_diff/2;
step*=2;
}
j=0; for(i=1;i<(N1);i++)
{
k=N/2;
while(k<=j)
{
j=j-k;
k=k/2;
}
j=j+k;
if(i<j)
temp1.real=(Y[j]).real;
temp1.imag=(Y[j]).imag;
(Y[j]).real=(Y[i]).real;
(Y[j]).imag=(Y[i]).imag;
(Y[i]).real=temp1.real;
(Y[j]).imag=temp1.imag;
}
}
return;
}
fft 256.c
#include<math.h>
#define PTS 64
#define PI 3.14159265358979
typedefstruct{float real,imag;}COMPLEX;
void FFT(COMPLEX*Y,int n);
floatiobuffer[PTS];
float x1[PTS]; short
i;
shortbuffercount=0;
short flag=0;
COMPLEX w[PTS];
COMPLEX
samples[PTS]; main()
{
for(i=0;i<PTS;i++)
{
w[i].real=cos(2*PI*i/(PTS*2.0));
w[i].imag=-sin(2*PI*i/(PTS*2.0));
}
for(i=0;i<PTS;i++)
{
iobuffer[i]=sin(2*PI*10*i/(PTS*2.0));
samples[i].real=0.0;
samples[i].imag=0.0;
}
for(i=0;i<PTS;i++)
{
samples[i].real=iobuffer[i];
}
for(i=0;i<PTS;i++)
samples[i].imag=0.0;
FFT(samples,PTS);
for(i=0;i<PTS;i++)
{
x1[i]=sqrt(samples[i].real*samples[i].real+samples[i].imag*samples[i].imag);
}
}
RESULT