Experiment4

alpha=1+mod(269,3);

Problem 1
%Set the reference parameters
duration=2;
frequency=15*alpha;
sampleRate=120;

%Generate the signal
time=0:1/sampleRate:duration-1/sampleRate;
signal = sin(2*pi*frequency*time);

%Generate the DFT of 120 samples of the signal
N1=120;
signal_dft=fft(signal(1:N1));
mag_1=abs(signal_dft);
norm_1=(mag_1-min(mag_1))/(max(mag_1)-min(mag_1));

%Plot the DFT
graph_frequency_1=(0:length(mag_1)-1)/N1;
plot(graph_frequency_1, norm_1, "LineWidth", 1.1);
grid on;
title("DFT Magnitude for 120 & 130 samples");
xlabel("Frequency (Hz)");
ylabel("Magnitude");

%Generate and plot DFT for 130 samples
hold on;
N2=130;
signal_dft_2=fft(signal(1:N2));
mag_2=abs(signal_dft_2);
norm_2=(mag_2-min(mag_2))/(max(mag_2)-min(mag_2));
graph_frequency_2=(0:length(mag_2)-1)/N2;
plot(graph_frequency_2, norm_2, 'r', LineWidth=1);
hold off;
legend('120 samps',"130 samps");

%Find another N3 such that 120-DFT matches with N3-DFT
N3=240;
mag_3=abs(fft(signal(1:N3)));
norm_3=mag_3/N3;
graph_frequency_3=(0:length(mag_3)-1)/N3;
plot(graph_frequency_3, norm_3, "LineWidth",1.1)
grid on;
title("Magnitude for 240 samples/sec");
xlabel("Frequency(Normalized)");
ylabel("Magnitude")

Problem 2
% Define the parameters
A = 160;
B = 166;
duration = 10;
sampling_rate=200;
sampling_cases=[215, 415, 1115, 1515, 1915];

%Generate signal
t1=0:1/sampling_rate:duration-1/sampling_rate;
x_t= 0.1*sin(A*pi*t1)+cos(B*pi*t1);
plot(t1, x_t)
grid on;
title("Original Signal");
xlabel("Time (s)");
ylabel("x(t)");

for j=1:length(sampling_cases)
    %Generate DFT for different cases
    signal_dft=fft(x_t(1:sampling_cases(j)));
    dft_mag=abs(signal_dft)/sampling_cases(j);

    %Plot the DFT graph
    freq=(0:sampling_cases(j)-1)/sampling_cases(j);
    subplot(length(sampling_cases),1,i)
    plot(freq, dft_mag);
    grid on;
    title(sprintf("%d samples/sec", sampling_cases(j)));
    xlabel("Frequency (Hz)");
    ylabel("Magnitude");
end


Problem 3
sampling_cases=[215, 415, 1115, 1515, 1915];
for i=1:length(sampling_cases)
    L=sampling_cases(i);
    %Generate blackmann window
    blackman_window=blackman(L);

    %Create windowed signal for new DFT
    windowed_signal=x_t(1:L).*(blackman_window)';
    windowed_dft=fft(windowed_signal);
    abs_windowed=abs(windowed_dft)/L;

    %Plot the original signal
    windowed_freq=(0:L-1)/L;
    figure;
    plot(freq, dft_mag, "LineStyle","--");
    grid on;
    xlabel("Frequency (Hz)");
    ylabel("Magnitude");

    %Plot the DFT signal on the same graph
    hold on;
    plot(windowed_freq, abs_windowed, "r");
    title(sprintf("DFT of Blackman: %d samples/sec", L));
    xlabel("Frequency (Hz)");
    ylabel("Magnitude");
    hold off;
end

Problem 4
%Load data from file
data=load("Exp4Data3.txt");
N=length(data);

%Create hamming windowed signal
hamming_window=hamming(N);
windowed_signal=data.*(hamming_window)';

%Add the extra 10,000 samples and normalize
hamming_fft=fft(windowed_signal, 1e4);

%Create frequency axis and normalize
freq_hamming=(0:(length(hamming_fft)-1))/1e4;

%Plot the DFT magnitude
figure;
subplot(2,1,1);
plot(freq_hamming, abs(hamming_fft)/1e4);
grid on;
title("DFT Magnitude with Hamming");
xlabel("Frequency (Hz)");
ylabel("Magnitude");

%Find the peak frequencies from both components
[max_amp_hamming, idx_max_hamming] = findpeaks(abs(hamming_fft)/1e4, "SortStr","descend");
peak_freq_hamming = freq_hamming(idx_max_hamming);

%Repeat the same for rectangular window
rectangular_window=rectwin(N);
rectangular_signal=data.*(rectangular_window)';

rectangular_fft=fft(rectangular_signal,1e4);

freq_rectangular=(0:length(rectangular_fft)-1)/1e4;

subplot(2,1,2);
plot(freq_rectangular, abs(rectangular_fft)/1e4);
grid on;
title("DFT Magnitude with Rectangular Window");
xlabel("Frequency (Hz)");
ylabel("Magnitude");

[amp_rectangular, id_max_rectangular]=findpeaks(abs(rectangular_fft)/1e4, SortStr="descend");
peak_freq_rectangular=freq_rectangular(id_max_rectangular);

fprintf("Frequency 1 for Hamming: (%.3f)*Fs Hz\n", peak_freq_hamming(1));
fprintf("Frequency 2 for Hamming: (%.3f)*Fs Hz\n", peak_freq_hamming(2));

fprintf("Frequency 1 for Rectangular: (%.3f)*Fs Hz\n", peak_freq_rectangular(1));
fprintf("Frequency 2 for Rectangular: (%.3f)*Fs Hz\n", peak_freq_rectangular(2));