dsp practicals
TRANSCRIPT
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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
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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.
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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
The given sample input for this program is:
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
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Conclusion
Thus we had obtained the convoluted signal output of the two sample input sequences.
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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
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ylabel('Amplitude');
grid ON;
Input
The given sample input for this program is:
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.
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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
The given sample input for this program is:
Signal sequence whose DFT to be calculated x(n): [1 3 5 7]
Output
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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.
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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);
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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):
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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
-->
(a) Normalized frequency-->
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-->
(a) Normalized frequency-->
Band Reject Filter (BR):
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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-->
(a) Normalized frequency-->
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.
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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('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 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);
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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--hamming window
a) Passband ripple=0.04
b) Stopband ripple=0.02
c) Passband frequency=1500
d) Stopband frequency=2000e) Sampling frequency=8000
Output
Low pass filter (LP):
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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-
->
(a) Normalized frequency-->
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-->
(a) Normalized frequency-->
Band reject filter (BR):
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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-->
(a) Normalized frequency-->
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.
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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');
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;end
y=hanning(n1);
switch(choice)
case 1
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b=fir1(n,wp,y);
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--hanning window
a) Passband ripple=0.03
b) Stopband ripple=0.01
c) Passband frequency=1400d) Stopband frequency=2000
e) Sampling frequency=8000
Output
Low pass filter (LP):
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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-->
(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-->
(a) Normalized frequency-->
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-->
(a) Normalized frequency-->
Band reject filter (BR):
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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-->
(a) Normalized frequency-->
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.
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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');
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=');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;
switch(choice)case 1
[n,wn]=buttord(w1,w2,rp,rs);[b,a]=butter(n,wn);
case 2
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[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);
ylabel('Gain in db-->');
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):
a) Passband ripple=0.5
b) Stopband ripple=50
c) Passband frequency=1200d) Stopband frequency=2400
e) Sampling frequency=10000
2) Butterworth band pass filter (BP):
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a) Passband ripple=0.3
b) Stopband ripple=40c) Passband frequency=1500
d) Stopband frequency=2000
e) Sampling frequency=9000
3) Butterworth band reject filter (BR):
a) Passband ripple=0.4
b) Stopband ripple=46
c) Passband frequency=1100
d) Stopband frequency=2200e) Sampling frequency=6000
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-->
(a) Normalized 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) Normalized frequency-->
phaseinradians-->
2) Butterworth high pass filter (HP):
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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-->
(a) Normalized 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) Normalized frequency-->
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--
>
(a) Normalized 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) Normalized frequency-->
phaseinradia
ns-->
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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-->
(a) Normalized 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) Normalized frequency-->
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.
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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('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 ripple=');
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;
switch(choice)
case 1
[n,wn]=cheb1ord(w1,w2,rp,rs);
[b,a]=cheby1(n,rp,wn);
case 2
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[n,wn]=cheb1ord(w1,w2,rp,rs);
[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);
ylabel('Gain in db-->');
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) Chebyshev Type-I Low Pass filter (LP):
a) Passband ripple=0.2
b) Stopband ripple=45c) Passband frequency=1300
d) Stopband frequency=1500
e) Sampling frequency=10000
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2) Chebyshev Type-I High Pass filter (HP):
a) Passband ripple=0.3b) Stopband ripple=60
c) Passband frequency=1500
d) Stopband frequency=2000e) Sampling frequency=9000
3) Chebyshev Type-I Band Pass filter (BP):
a) Passband ripple=0.4
b) Stopband ripple=35
c) Passband frequency=2000d) Stopband frequency=2500
e) Sampling frequency=10000
4) Chebyshev Type-I Band Reject filter (BR):
a) Passband ripple=0.25b) Stopband ripple=40
c) Passband frequency=2500
d) Stopband frequency=2750
e) Sampling frequency=7000
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-->
(a) Normalized 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) Normalized frequency-->
phaseinradians-->
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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-->
(a) Normalized 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) Normalized frequency-->
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-->
(a) Normalized 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) Normalized frequency-->
phaseinradians-->
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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-->
(a) Normalized 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) Normalized frequency-->
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.
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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');
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=');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;
switch(choice)case 1
[n,wn]=cheb2ord(w1,w2,rp,rs);[b,a]=cheby2(n,rs,wn);
case 2
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[n,wn]=cheb2ord(w1,w2,rp,rs);
[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-->');
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) Chebyshev Type-II Low Pass filter (LP):
a) Passband ripple=0.35
b) Stopband ripple=35
c) Passband frequency=1500d) Stopband frequency=2000
e) Sampling frequency=8000
2) Chebyshev Type-II High Pass filter (HP):
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a) Passband ripple=0.25
b) Stopband ripple=40
c) Passband frequency=1400d) Stopband frequency=1800
e) Sampling frequency=7000
3) Chebyshev Type-II Band Pass filter (BP):
a) Passband ripple=0.4b) Stopband ripple=40
c) Passband frequency=1400
d) Stopband frequency=2000
e) Sampling frequency=9000
4) Chebyshev Type-II Band Reject filter (BR):
a) Passband ripple=0.3b) Stopband ripple=46
c) Passband frequency=1400d) Stopband frequency=2000
e) Sampling frequency=8000
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-->
(a) Normalized 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) Normalized frequency-->
phaseinradians
-->
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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-->
(a) Normalized 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) Normalized frequency-->
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-->
(a) Normalized 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) Normalized frequency-->
phaseinradian
s-->
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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-->
(a) Normalized 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) Normalized frequency-->
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.