% Constants and Signal Definition
Fs = 1000; % Sampling frequency in Hz
duracion = 1; % Duration in seconds
N = Fs * duracion; % Total number of samples
delta = zeros(1, N); % Initialize delta function
delta(round(N/2)) = sqrt(N); % Impulse in the center
% FFT-based PSD
X = fft(delta);
Pxx1_delta = 2*abs(X(1:N/2)).^2/(N*Fs); % PSD computation
frecuencias = linspace(0, Fs/2, N/2); % Frequency vector for FFT
% CWT-based PSD
delta_time = 1/Fs;
scales = 1:16; % Define scales
freqs = scal2frq(scales, 'db6', delta_time); % Convert scales to frequencies
coefs_base = cwt(delta, scales, 'db6'); % CWT
pow_base = (abs(coefs_base)).^2; % Power spectrum from CWT coefficients
bias_corr_pow_base = pow_base ./ scales'; % Correcting for scale bias
time_avg_pow_base_spec = mean(bias_corr_pow_base, 2); % Global Wavelet Spectrum
% Interpolate Wavelet Spectrum to match FFT frequencies
interp_wavelet_spectrum = interp1(freqs, time_avg_pow_base_spec, frecuencias, 'linear', 'extrap');
% Plotting
figure;
loglog(frecuencias, interp_wavelet_spectrum, 'LineWidth', 2, 'DisplayName', 'Interpolated Wavelet PSD');
hold on;
loglog(frecuencias, Pxx1_delta, 'LineWidth', 2, 'DisplayName', 'FFT PSD');
xlabel('Frequency (Hz)');
ylabel('Power');
title('Comparison of FFT and Interpolated Wavelet-Based PSD');
legend('show');
grid on;
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