BUTTERWORTH LOW / HIGH PASS FILTER :
Rp =input("enter th
e ripple at passband in db :")%1
Rs =input("enter the ripple at stopband in db :")%40
Wp = input("enter the passband frequency in radians:")%0.2000
Ws = input("enter the stopband frequency in radians:")%0.8000
[N,Wc] = buttord(Wp,Ws,Rp,Rs)
[b,a] = butter(N,Wc,"high"%low);
W = 0:0.1:pi;
h = freqz(b,a,W)
plot(W,abs(h))
title('Butterworth highpass Filter');xlabel('Frequency
(radians)');ylabel('Magnitude');
BUTTERWORTH BAND STOP / PASS FILTER :
Rp = input('Enter the ripple at passband in dB: ')%1
Rs = input('Enter the ripple at stopband in dB: ')%40
Wp = input('Enter the passband frequencies [Wp1, Wp2] in radians: ')%[0.3,0.7]
Ws = input('Enter the stopband frequencies [Ws1, Ws2] in radians: ')%[0.4,0.6]
[N, Wc] = buttord(Wp, Ws, Rp, Rs)
[b, a] = butter(N, Wc, 'stop');%bandpass
W = 0:0.01:pi;
h = freqz(b, a, W);
plot(W, abs(h));
title('Butterworth Bandstop Filter');xlabel('Frequency
(radians)');ylabel('Magnitude');
CHEBYSHEV 1 LPF / HPF :
Rp = input('Enter the ripple at passband in dB: ')%1
Rs = input('Enter the ripple at stopband in dB: ')%40
Wp = input('Enter the passband frequency in radians: ')%0.2000
Ws = input('Enter the stopband frequency in radians: ')%0.8000
[N, Wc] = cheb1ord(Wp, Ws, Rp, Rs)
[b, a] = cheby1(N, Rp, Wc, 'high');%high
W = 0:0.01:pi;
h = freqz(b, a, W);
plot(W, abs(h));
title('Chebyshev1 LPF');xlabel('Frequency (radians)');ylabel('Magnitude');
CHEBYSHEV 1 BPF / BSF :
Rp = input('Enter the ripple at passband in dB: ')%1
Rs = input('Enter the ripple at stopband in dB: ')%40
Wp = input('Enter the passband frequencies [Wp1, Wp2] in radians: ')%[0.3,0.7]
Ws = input('Enter the stopband frequencies [Ws1, Ws2] in radians: ')%[0.4,0.6]
[N, Wc] = cheb1ord(Wp, Ws, Rp, Rs)
[b, a] = cheby1(N, Rp, Wc, 'bandpass');%stop
W = 0:0.01:pi;
h = freqz(b, a, W);
figure;
plot(W, abs(h));
title('Chebyshev 1 Bandpass Filter');xlabel('Frequency(radians)');ylabel('Magnitude');
CHEBYSHEV 2 LPF / HPF :
Rp = input('Enter the ripple at passband in dB: ')%1
Rs = input('Enter the ripple at stopband in dB: ')%40
Wp = input('Enter the passband frequency in radians: ')%0.2000
Ws = input('Enter the stopband frequency in radians: ')%0.8000
[N, Wc] = cheb2ord(Wp, Ws, Rp, Rs)
[b, a] = cheby2(N, Rs, Wc, 'low');%high
W = 0:0.01:pi;
h = freqz(b, a, W);
plot(W, abs(h));
title('Chebyshev1 LPF');xlabel('Frequency (radians)');ylabel('Magnitude');
CHEBYSHEV 2 BPF / BSF :
Rp = input('Enter the ripple at passband in dB: ')%1
Rs = input('Enter the ripple at stopband in dB: ')%40
Wp = input('Enter the passband frequencies [Wp1, Wp2] in radians: ')%[0.3,0.7]
Ws = input('Enter the stopband frequencies [Ws1, Ws2] in radians: ')%[0.4,0.6]
[N, Wc] = cheb2ord(Wp, Ws, Rp, Rs)
[b, a] = cheby2(N, Rs, Wc, 'bandpass');%stop
W = 0:0.01:pi;
h = freqz(b, a, W);
figure;
plot(W, abs(h));
title('Chebyshev 1 Bandpass Filter');xlabel('Frequency
(radians)');ylabel('Magnitude');
Down Sampling :
#include <stdio.h>
int main() {
int N = 10, M = 3, x[10] = {0,1,2,3,4,5,6,7,8,9};
int y[10] = {0}, i, len = N / M;
for(i = 1; i <= len; i++) {
y[i] = x[M * i];
}
for(i = 0; i <= len; i++) {
printf("%d\t", y[i]);
}
return 0;
}
Up Sampling
#include <stdio.h>
int main() {
int Sr = 4, N = 10;
int x[10] = {0,1,2,3,4,5,6,7,8,9};
int y[50] = {0}, len = N * Sr;
int i, k = Sr - 1, pad = Sr - 1;
y[0] = x[0];
for(i = 1; i < len; i++) {
if(i % Sr == 0) {
y[i] = x[i - k];
k += pad;
} else {
y[i] = 0;
}
}
for(i = 0; i < len; i++) {
printf("%d ", y[i]);
}
return 0;
}
BUTTERWORTH LOW PASS FILTER USING IMPLUSE INVARIANT
Wp = 0.2 * pi; % Digital Passband edge (rad/sample)
Ws = 0.6 * pi; % Digital Stopband edge (rad/sample)
Rp = -20 * log10(0.8); % Passband ripple (dB)
Rs = -20 * log10(0.2); % Stopband attenuation (dB)
Wp_norm = Wp / pi;
Ws_norm = Ws / pi;
[N, Wn] = buttord(Wp_norm, Ws_norm, Rp, Rs);
disp(N);
cutoff_freq = Wp/ ((10^(Rp/10) - 1)^(1/(2*N)))
[bs, as] = butter(N, cutoff_freq, 's')
[bz, az] = impinvar(bs, as, 1)
[H] = freqz(bz, az, 1024, 'half', 1);
plot(abs(H), 'b', 'LineWidth', 1.5);
title('Butterworth Low-Pass Filter (Impulse Invariant Method)');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
BUTTERWORTH LOW PASS FILTER USING BILINEAR TRANSFORMATION:
Wp = 0.5 * pi; % Digital PRssband edge (rad/sample)
Ws = 0.75 * pi; % Digital Stopband edge (rad/sample)
Rp = -20 * log10(0.707); % Passband ripple (dB)
Rs = -20 * log10(0.2); % Stopband attenuation (dB)
Warped = (2) * tan(Wp/2);
Wp_norm = Wp / pi;
Ws_norm = Ws / pi;
[N, Wn] = buttord(Wp_norm, Ws_norm, Rp, Rs);
disp(N);
cutoff_freq = Warped / ((10^(Rp/10) - 1)^(1/(2*N)));
[bs,as] = butter(N, cutoff_freq, 's')
[bz, az] = bilinear(bs, as, 1)
H = freqz(bz, az, 1024, 'half', 1);
plot(abs(H), 'b', 'LineWidth', 1.5);
title('Butterworth Low-PRss Filter (Bilinear Transformation)');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
4.BAND PASS REJECT FILTER USING FOURIER SERIES:
% Input parameters
N = input('Enter the Length of the filter: ')
Wc1 = input('Enter the lower cutoff frequency (in radians): ')
Wc2 = input('Enter the upper cutoff frequency (in radians): ')
n = 0:N-1;
a = (N-1)/2;
c = 0.0001;
h = (sin(Wc1*(n-a+c)) + sin(pi*(n-a+c))-sin(Wc2*(n-a+c))) ./ (pi*(n-a+c))
w = 0:0.01:pi;
H = freqz(h, 1, w);
plot(w, abs(H))
title('Band-Reject FIR Filter Frequency Response');
xlabel('Frequency (rad/sample)');
ylabel('Magnitude');
5.FFT:
x = input("Input sequence:");
N = input("Number of points for DFT:");
L = length(x);
if N >= L
x = [x, zeros(1, N - L)];
z = fft(x)
stem(0:N-1, abs(z));
title('Magnitude Spectrum');
xlabel('Frequency Index');
ylabel('|X(k)|');
grid on;
else
error('Give proper input: N should be greater than or equal to the length of
the input sequence');
end
6.IFFT:
x = input("Input sequence:");
N = input("Number of points for IDFT:");
L = length(x);
if N >= L
x = [x, zeros(1, N - L)];
z =ifft(x)
abs(z)
figure;
stem(0:N-1, abs(z));
title('Magnitude Spectrum');
xlabel('TIME');
ylabel('|X(n)|');
grid on;
else
error('Give proper input: N should be greater than or equal to the length of
the input sequence');
end
UNIT STEP
t = linspace(-10, 10, 100); % time vector
unit_step = t >= 0; % function
subplot(2,1,1);
plot(t,unit_step);
title('Unit Step Signal');
subplot(2,1,2);
stem(t, unit_step);
title('Unit Step Signal');
xlabel('Time');
ylabel('Amplitude');
RAMP
time = 0:10
ramp_function = time .* (time >= 0);
subplot(2,1,1);
plot(time, ramp_function);
title('Ramp Signal');
subplot(2,1,2);
stem(time, ramp_function);
title('Ramp Signal');
xlabel('Time');
ylabel('Amplitude');
SIN
sine = sin(t);
subplot(2,1,1);
plot(t, sine);
title('Sine Signal');
subplot(2,1,2);
stem(t, sine);
title('Sine Signal');
xlabel('Time');
ylabel('Amplitude');
COS
cosine = cos(t);
subplot(2,1,1);
plot(t, cosine);
title('Cosine Signal');
subplot(2,1,2);
stem(t, cosine);
title('Cosine Signal');
xlabel('Time');
ylabel('Amplitude');
IEXPO
i_exp = exp(t);
subplot(2,1,1);
plot(t, i_exp);
title('Increasing Exponential Signal');
subplot(2,1,2);
stem(t, i_exp);
title('Increasing Exponential Signal');
xlabel('Time');
ylabel('Amplitude');
DEXPO
d_exp = exp(-t);
subplot(2,1,1);
plot(t, d_exp);
title('Decreasing Exponential Signal');
subplot(2,1,2);
stem(t, d_exp);
title('Decreasing Exponential Signal');
xlabel('Time');
ylabel('Amplitude');
SINC:
t = linspace(-10, 10, 100);
y = sinc(t);
figure;
x= sinc(t);
subplot(2,1,1);
plot(t, y, 'b', 'LineWidth', 1);
title('Sinc Signal');
subplot(2,1,2);
stem(t,x);
title('Sinc Signal');
xlabel('Time');
ylabel('Amplitude');
IMPLUSE
ts = -1000:1000;
impulse_function = (ts == 0);
subplot(2,1,1);
plot(ts, impulse_function);
title('Impulse Signal');
subplot(2,1,2);
stem(ts, impulse_function);
title('Impulse Signal');
xlabel('Time');
ylabel('Amplitude');
SIGNUM
signum = sign(t);
subplot(2,1,1);
plot(t, signum);
title('Signum Signal');
subplot(2,1,2);
stem(t, signum);
title('Signum Signal');
xlabel('Time');
ylabel('Amplitude');
