DSP CODES

EXP 7- ALL FIR FILTERS
N = input("Enter the number of samples (Filter Length): ");
Wc = input("Enter the cutoff frequency (in radians, between 0 and pi): "); % Cutoff frequency in radians
n = 0:1:N-1;
alpha = (N-1)/2;
hd = (sin(Wc*(n-alpha))) ./ (pi*(n-alpha));
hd(alpha+1) = Wc / pi;
disp('Ideal Impulse Response hd(n):');
disp(hd);
Rec = ones(1, N);  % Rectangular window
han = 0.5*(1 - cos(2*pi*n/(N-1)));  % Hanning window
ham = 0.54 - 0.46*cos(2*pi*n/(N-1));  % Hamming window
bman = 0.42 - 0.5*cos(2*pi*n/(N-1)) + 0.08*cos(4*pi*n/(N-1));  % Blackman window
beta = 5;  % Kaiser window shape parameter, you can adjust this
kaiser_win = besseli(0, beta * sqrt(1 - ((2*n/(N-1)) - 1).^2)) / besseli(0, beta);
Hr = hd .* Rec;     % Rectangular windowed filter
Hhan = hd .* han;   % Hanning windowed filter
Hham = hd .* ham;   % Hamming windowed filter
Hbman = hd .* bman; % Blackman windowed filter
Hkais = hd .* kaiser_win; % Kaiser windowed filter
% Output the final impulse response h(n)
disp('Final Impulse Response h(n) with Rectangular Window:');
disp(Hr);
disp('Final Impulse Response h(n) with Hanning Window:');
disp(Hhan);
disp('Final Impulse Response h(n) with Hamming Window:');
disp(Hham);
disp('Final Impulse Response h(n) with Blackman Window:');
disp(Hbman);
disp('Final Impulse Response h(n) with Kaiser Window:');
disp(Hkais);
Nfft = 512;
Hr_fft = fft(Hr, Nfft);
Hhan_fft = fft(Hhan, Nfft);
Hham_fft = fft(Hham, Nfft);
Hbman_fft = fft(Hbman, Nfft);
Hkais_fft = fft(Hkais, Nfft);
freq_axis = linspace(-pi, pi, Nfft);
Hr_fft = fftshift(Hr_fft);
Hhan_fft = fftshift(Hhan_fft);
Hham_fft = fftshift(Hham_fft);
Hbman_fft = fftshift(Hbman_fft);
Hkais_fft = fftshift(Hkais_fft);
figure;
subplot(5,2,1);
plot(freq_axis/pi, abs(Hr_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Magnitude');
title('Magnitude Response: Rectangular Window');
subplot(5,2,3);
plot(freq_axis/pi, abs(Hhan_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Magnitude');
title('Magnitude Response: Hanning Window');
subplot(5,2,5);
plot(freq_axis/pi, abs(Hham_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Magnitude');
title('Magnitude Response: Hamming Window');
subplot(5,2,7);
plot(freq_axis/pi, abs(Hbman_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Magnitude');
title('Magnitude Response: Blackman Window');
subplot(5,2,9);
plot(freq_axis/pi, abs(Hkais_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Magnitude');
title('Magnitude Response: Kaiser Window');
subplot(5,2,2);
plot(freq_axis/pi, angle(Hr_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Phase');
title('Phase Response: Rectangular Window');
subplot(5,2,4);
plot(freq_axis/pi, angle(Hhan_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Phase');
title('Phase Response: Hanning Window');
subplot(5,2,6);
plot(freq_axis/pi, angle(Hham_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Phase');
title('Phase Response: Hamming Window');
subplot(5,2,8);
plot(freq_axis/pi, angle(Hbman_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Phase');
title('Phase Response: Blackman Window');
subplot(5,2,10);
plot(freq_axis/pi, angle(Hkais_fft));
xlabel('Normalized Frequency (\omega/\pi)');
ylabel('Phase');
title('Phase Response: Kaiser Window');

EXP 6- 4pt DFT AND FFT

signal = input('Enter unit signal ');
N = length(signal);
dft_signal = zeros(1, N);
idft_signal = zeros(1, N);
for k = 1:N
   for n = 1:N
       dft_signal(k) = dft_signal(k) + signal(n) * exp(-1i * 2 * pi * (k-1) * (n-1) / N);
   end
end
for n = 1:N
   for k = 1:N
       idft_signal(n) = idft_signal(n) + dft_signal(k) * exp(1i * 2 * pi * (k-1) * (n-1) / N);
   end
   idft_signal(n) = idft_signal(n) / N; % Scale by 1/N
end
fft_signal = fft(signal);
disp('DFT Signal:');
disp(dft_signal);
disp('IDFT Signal (Recovered Original Signal):');
disp(idft_signal);
disp('FFT Signal (Verification):');
disp(fft_signal);
frequencies = (0:N-1) / N;
figure;
subplot(2, 2, 1);
stem(frequencies, abs(dft_signal), 'b', 'LineWidth', 1.5);
xlabel('Frequency');
ylabel('Magnitude');
title('4-Point DFT Magnitude');
grid on;
subplot(2, 2, 2);
stem(frequencies, angle(dft_signal), 'r', 'LineWidth', 1.5);
xlabel('Frequency');
ylabel('Phase (radians)');
title('4-Point DFT Phase');
grid on;
subplot(2, 2, 3);
stem(0:N-1, signal, 'g', 'LineWidth', 1.5);
xlabel('Time Index');
ylabel('Amplitude');
title('Original Signal');
grid on;
subplot(2, 2, 4);
stem(0:N-1, real(idft_signal), 'm', 'LineWidth', 1.5);
xlabel('Time Index');
ylabel('Amplitude');
title('Recovered Signal from IDFT');
grid on;

EX 5- To plot mag response , freq response and pole zero filter
num=input("enter signal values of numerator: ");
den=input("enter signal values of denominator: ");
w=linspace(-pi,pi,1000);
tf= polyval(num,exp(1j*w))./ polyval(den,exp(1j*w));
freq=abs(tf);
phase=angle(tf);
zeroes=roots(numerator);
poles=roots(denominator);

subplot(3,1,1);
plot(w,freq);
xlabel("w");
ylabel("|h(w)");
title("Feq Response;");
subplot(3,1,2);
plot(w,phase);
xlabel("w");
ylabel("phi(w)");
title("phase Response;");
subplot(3,1,3);
plot(real(zeroes),imag(zeroes),'ob');
hold on;
plot(real(poles),imag(poles),'xr');
theta=linspace(-2*pi,2*pi,500);
plot(cos(theta),sin(theta));
xlabel("Real");
ylabel("Imaginary");
title("POLE ZERO FILTER");
grid on;
axis equal;
legend('Zeros', 'Poles', 'Unit Circle');

EXP 4- LINEAR AND CIRCULAR CONVOLUTION

x=input("Enter signal x[n]: ");
h=input("Enter signal h[n]: ");
i=input( "Enter 1 for circular and 0 for linear convolution: ");
if(i==0)
   lin=conv(x,h);
   disp(lin)
   figure;
   stem(lin,'LineWidth',3);
   xlabel('n index');
   ylabel('amplitude ')
   title('Linear Convolution')
   grid on;
end
if(i==1)
   T=input("Enter time period: ");
   x_pad=[x zeros(1,T-length(x))];
   h_pad=[h zeros(1,T-length(h))];
   cir=ifft(fft(x_pad).*fft(h_pad));
   figure;
   disp(cir)
   stem(cir);
   xlabel('n')
   ylabel('amplitude')
   title('Circular Convo: ')
   figure;
   grid on;
 end

EXP 3- EVEN AND ODD FNC

DT-
signal = [1,2,3 ,4];
origin = 3;
n = (1:length(signal)) - origin;
signal_even = 0.5 * (signal + flip(signal));
signal_odd = 0.5 * (signal - flip(signal));
figure;
subplot(3,1,1);
stem(n, signal, 'b');
title('Original Discrete Signal');
xlabel('Index (n)');
ylabel('Amplitude');
grid on;
% Plot the even part of the signal
subplot(3,1,2);
stem(n, signal_even, 'r');
title('Even Part of the Discrete Signal');
xlabel('Index (n)');
ylabel('Amplitude');
grid on;
% Plot the odd part of the signal
subplot(3,1,3);
stem(n, signal_odd, 'g');
title('Odd Part of the Discrete Signal');
xlabel('Index (n)');
ylabel('Amplitude');
grid on;

CT-
t=-10:0.01:10;
u=@(t) double(t>=0);
r=@(t)t.*u(t);
signal= 4*u(t + 2) - 2*r(t) + 2*r(t - 2) ;
n = (1:length(signal)) - origin;
signal_even = 0.5 * (signal + flip(signal));
signal_odd = 0.5 * (signal - flip(signal));
figure;
subplot(3,1,1);
plot(n, signal);
title('Original Discrete Signal');
xlabel('Index (n)');
ylabel('Amplitude');
grid on;
subplot(3,1,2);
plot(n, signal_even, 'r');
title('Even Part of the Discrete Signal');
xlabel('Index (n)');
ylabel('Amplitude');
grid on;
% Plot the odd part of the signal
subplot(3,1,3);
plot(n, signal_odd, 'g');
title('Odd Part of the Discrete Signal');
xlabel('Index (n)');
ylabel('Amplitude');
grid on;

EXP 2- Scaling and shifting
CT-
t = -5:0.01:5;
u = @(t) double(t >= 0);
r = @(t) t .* u(t);
input_str = input('Enter the function of t (use u(t) for unit step and r(t) for unit ramp): ', 's');
shift_str = input('Enter the time shift (e.g., 1 for shifting right by 1): ', 's');
scale_str = input('Enter the time scaling factor (e.g., 2 for compression by 2, 0.5 for stretching by 2): ', 's');
scale = str2double(scale_str);
shift = str2double(shift_str);
input_function = str2func(['@(t, u, r) ' input_str]);
t_transformed = scale * t - shift;
x = input_function(t_transformed, u, r);
figure;
plot(t, x, 'b', 'LineWidth', 2);
grid on;
xlabel('t');
ylabel('x(t)');
title('Continuous Signal with Time Scaling and Shifting');
axis([-3 3 -3 3]);
legend('x(t)', 'Location', 'Best');

DT-
numElements = input('Enter the number of elements in the signal: ');
sequence_input = input('Enter the signal values as a vector: ');
if length(sequence_input) ~= numElements
   error('The number of values provided does not match the specified number of elements.');
end
origin = input('Enter the origin index: ');
if origin < 1 || origin > numElements
   error('Origin index must be within the range of the number of elements.');
end
start_x = -1 * (origin - 1);
end_x = numElements - origin;
x_coordinates = start_x:end_x;
a = input('Enter the scaling factor a: ');
b = input('Enter the shifting factor b: ');
x_new = (x_coordinates - b) / a;
int_flag = mod(x_new, 1) == 0;
x_new = x_new(int_flag);
seq_input_new = sequence_input(int_flag);
seq_str = sprintf('%d, ', sequence_input);
n = length(seq_str);
seq_str = seq_str(1:n-2);
switch(mod(origin, 10))
   case 1
       if mod(origin, 100) == 11
           ordinal = 'th';
       else
           ordinal = 'st';
       end
   case 2
       if mod(origin, 100) == 12
           ordinal = 'th';
       else
           ordinal = 'nd';
       end
   case 3
       if mod(origin, 100) == 13
           ordinal = 'th';
       else
           ordinal = 'rd';
       end
   otherwise
       ordinal = 'th';
end
% Generating Graphs:
fig = figure;
subplot(2,1,1)
stem(x_coordinates, sequence_input, 'filled')
grid on
hold on
plot([0 0], ylim, 'Color', [0 0 0])
title("Original Signal: x(n)", sprintf("x(n) = [%s]\n%d%s term at Origin", seq_str, origin, ordinal));
xlabel("Discrete Time (n)");
ylabel("Amplitude");
subplot(2,1,2)
stem(x_new, seq_input_new, 'filled')
grid on
hold on
plot([0 0], ylim, 'Color', [0 0 0])
title(sprintf("Altered Signal: x(%.2fn%+.2f)", a, b))
xlabel("Discrete Time (n)");
ylabel("Amplitude");
figure(fig);

EXP 1: CUSTOM

t=-2:0.01:2;
u=@(t) double(t>=0);
r=@(t) t.*u(t);
inp_string=input("enter string","s");
inp_func=str2func(['@(t,u,r)' inp_string]);
y=inp_func(t,u,r);
figure;
plot(t,y,LineWidth=3);
xlabel('time');
ylabel('x(t)');
title('Custom Singal: ')
grid on;
axis([-5.5,5.5,-5.5,5.5]);