function [f,power] = frequencySpectrum(signal,freq_sampling,plt)
%{
function [f,power] = frequencySpectrum(signal,freq_sampling,plt)
ex: [f,power] = frequencySpectrum(x, 40, 1)

Task: to generate the power spectrm of a signal

Inputs:
    -signal: the signal that we want to get FFT
    -freq_sampling: how many samples we want per second 

Outputs:
    -f: vector of frequency 
    -power: power spectrum of the input signal 

Author: Tikea TE 
Date: 11/04/2025
%}

n = length(signal);  % this is our number of samples  

% generate the frequency vector
f = (0:n-1)*(freq_sampling/n); % fs/n is the frequency resolution, it tells how many hz are between each bin

% generate the power vector
y = fft(signal,n); % compute DFT of the signal with the same length
power = abs(y).^2/n; % compute the power(spectrum) of the DFT of the signal

% find the max value of the power and its index 
[val,ind] = max(power); 

% plotting the figure 
if (plt)
    figure;
    subplot(1,3,1) % time plot 
	t=0:1/freq_sampling:(n-1)/freq_sampling; % time range
	plot(t, signal)
	xticks(0:0.1*freq_sampling:n);
	xticklabels(0:0.1:n/freq_sampling);
	xlabel('Time (s)');
	ylabel('Amplitude (a.u.)');

    subplot(1,3,2) % linear frequency plot
	plot(f,power, 'b*'); hold on;
	plot(f,power, 'r');
	xlabel('Frequency (Hz)')
	ylabel('Power (a.u.)')

	subplot(1,3,3) % log frequency plot
	plot(f,10*log10(power/power(ind)));
	xlabel('Frequency (Hz)')
	ylabel('Power (dB)')
end