CIRCULAR CONVOLUTION MATLAB PROGRAM

CIRCULAR CONVOLUTION

 

function f=circonv(a,b)

a=input('enter the first sequence=')

b=input('enter the second sequence=')

N1=length(a)

N2=length(b)

N=max(N1,N2)

a=[a zeros(1,N-N1)]

b=[b zeros(1,N-N2)]

for n=0:N-1

f(n+1)=0

for i=0:N-1

j=mod(n-i,N)

f(n+1)=f(n+1)+a(i+1)*b(j+1)

end

end

subplot(2,2,1)

stem(a)

xlabel('time index')

ylabel('amplitude')

subplot(2,2,2)

stem(b)

xlabel('time index')

ylabel('amplitude')

subplot(2,1,2)

stem(f)

xlabel('time index')

ylabel('amplitude')

title('circular convolution of two sequence')

 

 

 

 

OBSERVATION:

 

>> circonv(a,b)

enter the first sequence=[1,2,3]

a = 1 2 3

enter the second sequence=[1,2,3,4]

b = 1 2 3 4

N1 = 3

N2 = 4

N = 4

a = 1 2 3 0

b = 1 2 3 4

f = 0

j = 0

f = 1

j = 3

f = 9

j = 2

f = 18

j = 1

f = 18

f = 18 0

j = 1

f = 18 2

j = 0

f = 18 4

j = 3

f = 18 16

j = 2

f = 18 16

f = 18 16 0

j = 2

f = 18 16 3

j = 1

f = 18 16 7

j = 0

f = 18 16 10

j = 3

f = 18 16 10

f = 18 16 10 0

j = 3

f = 18 16 10 4

j = 2

f = 18 16 10 10

j = 1

f = 18 16 10 16

j = 0

f = 18 16 10 16

ans = 18 16 10 16

GENERATION OF FM SIGNAL DSP MATLAB PROGRAM

GENERATION OF FM SIGNAL

 

 

Fc=input('Enter the carrier frequency in Hz, Fc=');

Fm=input('Enter the modulating frequency in Hz, Fm=');

mf=input('Enter the modulation index, m=');

t=0:0.0001:1;

M=sin(2*pi*Fm*t);

Y=sin((2*pi*Fc*t)-(mf*M));

subplot(3,1,1);

plot(t,M);

axis([0 1 -1.5 1.5]);

title('Frequency modulation');

xlabel('Time');

ylabel('Modulation signal');

subplot(3,1,2);

plot(t,C);

axis([0 1 -1.5 1.5]);

xlabel('Time');

ylabel('Carrier signal');

subplot(3,1,3);

plot(t,Y);

axis([0 1 -1.5 1.5]);

xlabel('Time');

ylabel('FM signal');

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Observation:

 

Enter the carrier frequency in Hz, Fc=50

Enter the modulating frequency in Hz, Fm=10

Enter the modulation index, mf=2

 

 

FIR FILTER USING DIFFERENT WINDOW MATLAB PROGRAM

FIR FILTER USING DIFFERENT WINDOW

 

 

f=input('Samplin rate in Hz, f=');

fp=input('pass band edge frequency in Hz=');

fs=input('stop band edge frequency in Hz=');

rp=input('pass band ripple in dB=');

rs=input('minimum stop band attenuation in dB=');

wp=2*fp/f;

ws=2*fs/f;

[N,wn]=cheb1ord(wp,ws,rp,rs);

 

%Hann window

 

Hw=hann(N+1);

B=fir1(N,wn,Hw);

[H,omega]=freqz(B,1,256);

gain=20*log(abs(H));

subplot(2,2,1);

plot(omega/pi,gain);

grid;

xlabel('omega/pi');

ylabel('Gain in dB');

title('FIR LPF using HANN window');

 

%Hamming window

 

Hw=hamming(N+1);

B=fir1(N,wn,Hw);

[H,omega]=freqz(B,1,256);

gain=20*log(abs(H));

subplot(2,2,2);

plot(omega/pi,gain);

grid;

xlabel('omega/pi');

ylabel('Gain in dB');

title('FIR LPF using HAMMING window');

 

%Rectangular window

 

Hw=rectwin(N+1);

B=fir1(N,wn,Hw);

[H,omega]=freqz(B,1,256);

gain=20*log(abs(H));

subplot(2,2,3);

plot(omega/pi,gain);

grid;

xlabel('omega/pi');

ylabel('Gain in dB');

title('FIR LPF using RECTANGULAR window');

 

%Triangular window

 

Hw=triang(N+1);

B=fir1(N,wn,Hw);

[H,omega]=freqz(B,1,256);

gain=20*log(abs(H));

subplot(2,2,4);

plot(omega/pi,gain);

grid;

xlabel('omega/pi');

ylabel('Gain in dB');

title('FIR LPF using TRIANGULAR window');

 

 

 

 

 

 

 

 

Observation:

 

Samplin rate in Hz,f=2000

pass band edge frequency in Hz=200

stop band edge frequency in Hz=300

pass band ripple in dB=6

minimum stop band attenuation in dB=30

 

 

 

 

MOVING AVERAGE FILTER MATLAB PROGRAMS

MOVING AVERAGE FILTER

 

 

t=0:.01:1;

f=5;

y=sin(2*pi*f*t);

%Generation of random signal

g=0.5*randn(size(t));

z=g+y;

N=10; %order required

b=1/N*(ones(1,N));

x=filter(b,1,z); %filters noice

subplot(3,1,1);

plot(t,y);

ylabel('pure signal');

subplot(3,1,2);

plot(t,z);

ylabel('noise buried');

subplot(3,1,3);

plot(t,x);

ylabel('filtered signal');

xlabel('Time in seconds');

 

 

 

 

 

 

 

 

 

 

 

CHEBYSHEV TYPE 1 BAND PASS FILTER MATLAB PROGRAM

CHEBYSHEV TYPE 1 BAND PASS FILTER

 

 

alphap=input('pass band attenuation in dB=');

alphas=input('stop band attenuation in dB=');

fp1=input('pass band frequency fp1 in Hz=');

fp2=input('pass band frequency fp2 in Hz=');

fs1=input('stop band frequency fs1 in Hz=');

fs2=input('stop band frequency fs2 in Hz=');

f=input('Sampling frequency in Hz=');

wp1=2*fp1/f;ws1=2*fs1/f;

wp2=2*fp2/f;ws2=2*fs2/f;

wp=[wp1,wp2];

ws=[ws1,ws2];

%To find cutoff frequency and order of the filter

[n,wn]=cheb1ord(wp,ws,alphap,alphas);

%system function of the filter

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

w=0:.01:pi;

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

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

an=angle(h);

subplot(2,1,1);

plot(ph/pi,m);

grid;

ylabel('Gain in dB');

xlabel('Normalised frequency');

subplot(2,1,2);

plot(ph/pi,an);

grid;

ylabel('Phase in radians');

xlabel('Normalised frequency');

 

 

 

 

Observation:

 

pass band attenuation in dB=2

stop band attenuation in dB=20

pass band frequency fp1 in Hz=100

pass band frequency fp2 in Hz=500

stop band frequency fs1 in Hz=200

stop band frequency fs2 in Hz=400

Sampling frequency in Hz=2000

 

 

CHEBYSHEV TYPE 1 LOW PASS FILTER MATLAB PROGRAM

CHEBYSHEV TYPE 1 LOW PASS FILTER

 

 

alphap=input('pass band attenuation in dB=');

alphas=input('stop band attenuation in dB=');

fp=input('pass band frequency in Hz=');

fs=input('stop band frequency in Hz=');

f=input('Sampling frequency in Hz=');

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

%To find cutoff frequency and order of the filter

[n,wn]=cheb1ord(wp,ws,alphap,alphas);

%system function of the filter

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

w=0:.01:pi;

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

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

an=angle(h);

subplot(2,1,1);

plot(ph/pi,m);

grid;

ylabel('Gain in dB');

xlabel('Normalised frequency');

subplot(2,1,2);

plot(ph/pi,an);

grid;

ylabel('Phase in radians');

xlabel('Normalised frequency');

 

 

 

 

 

 

 

 

 

 

Observation:

 

pass band attenuation in dB=1

stop band attenuation in dB=30

pass band frequency in Hz=200

stop band frequency in Hz=600

Sampling frequency in Hz=2000

 

 

 

 

BUTTERWORTH BAND REJECT FILTER MATLAB PROGRAM

BUTTERWORTH BAND REJECT FILTER

 

 

alphap=2;    %Passband attenuation in dB

alphas=20;    %stopband attenuation in dB

ws=[.2,.4];    %stopband frequency in radians

wp=[.1,.5];    %Passband frequency in radians

%To find cutoff frequency and order of the filter

[n,wn]=buttord(wp,ws,alphap,alphas);

%system function of filter

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

w=0:.01:pi;

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

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

an=angle(h);

subplot(2,1,1);

plot(ph/pi,m);

grid;

ylabel('Gain in dB');

xlabel('Normalised frequency');

subplot(2,1,2);

plot(ph/pi,an);

grid;

ylabel('Phase in radians');

xlabel('Normalised frequency');

 

 

 

BUTTERWORTH HIGH PASS FILTER MATLAB PROGRAM

BUTTERWORTH HIGH PASS FILTER

 

 

alphap=.4;    %Passband attenuation in db

alphas=30;    %stopband attenuation in db

fs=400;    %stopband frequency in hz

fp=800;    %passband frequency in hz

F=2000;

omp=2*fp/F;oms=2*fs/F;

%To find cutoff frequency and order of the filter

[n,wn]=buttord(omp,oms,alphap,alphas);

%system function of the filter

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

w=0:.01:pi;

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

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

an=angle(h);

subplot(2,1,1);

plot(om/pi,m);

grid;

ylabel('Gain in db');

xlabel('Normalised frequency');

subplot(2,1,2);

plot(om/pi,an);

grid;

ylabel('Phase in radians');

xlabel('Normalised frequency');

BUTTERWORTH BAND PASS FILTER MATLAB PROGRAM

BUTTERWORTH BAND PASS FILTER

 

 

alphap=2;    %Passband attenuation in dB

alphas=20;    %stopband attenuatio in dB

wp=[.2*pi,.4*pi];    %Passband frequency in radians

ws=[.1*pi,.5*pi];    %Stopband frequency in radians

%To find cutoff frequency and order of the filter

[n,wn]=buttord(wp/pi,ws/pi,alphap,alphas);

%system function of the filter

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

w=0:.01:pi;

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

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

an=angle(h);

subplot(2,1,1);

plot((ph/pi),m);

grid;

ylabel('Gain in dB');

xlabel('Normalised frequency');

subplot(2,1,2);

plot((ph/pi),an);

grid;

ylabel('phase in radians');

xlabel('Normalised frequency');

 

BUTTERWORTH LOW PASS FILTER MATLAB PROGRAM

 

BUTTERWORTH LOW PASS FILTER

 

 

alphap=4;    %Passband attenuation in db

alphas=30;    %Stopband attenuation in db

fp=400;    %Passband frequency in hz

fs=800;    %Stopband frequency in hz

F=2000;    %Sampling frequency in hz

omp=2*fp/F;oms=2*fs/F;

%To find cutoff frequency and order of the filter

[n,wn]=buttord(omp,oms,alphap,alphas);

%system function of the filter

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

w=0:.01:pi;

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

m=abs(h);

an=angle(h);

subplot(2,1,1);

plot(om/pi,20*log(m));    

grid;

ylabel('Gain in db');

xlabel('Normalised frequency');

subplot(2,1,2);

plot(om/pi,an);

grid;

ylabel('phase in redians');

xlabel('Normalised frequency');

Dsp matlab program to Generate AM signal

GENERATION OF AM SIGNAL

 

 

Fc=input('Enter the carrier frequency in Hz, Fc=');

Fm=input('Enter the modulating frequency in Hz, Fm=');

m=input('Enter the modulation index, m=');

t=0:0.0001:1;

C=sin(2*pi*Fc*t);

M=sin(2*pi*Fm*t);

Y=(1+m*M).*C;

subplot(3,1,1);

plot(t,M);

axis([0 1 -1.5 1.5]);

title('Amplitude modulation');

xlabel('Time');

ylabel('Modulation signal');

subplot(3,1,2);

plot(t,C);

axis([0 1 -1.5 1.5]);

xlabel('Time');

ylabel('Carrier signal');

subplot(3,1,3);

plot(t,Y);

axis([0 1 -1.5 1.5]);

xlabel('Time');

ylabel('AM signal');

 

 

 

Observation:

 

Enter the carrier frequency in Hz, Fc=50

Enter the modulating frequency in Hz, Fm=5

Enter the modulation index, m=0.6