I understand it is your objective to divide a large signal of size 7,000,000 into 4000 parts of length 1 hour containing 1750 samples each and compute the amplitude spectrum averaged across all the parts. You can refer to the steps mentioned below to do so:
1. First, since you have 1750 samples for each hour (which is 3600 seconds), the sampling frequency can be computed using the below MATLAB code snippet:
Fs = 1750 / 3600; % Sampling frequency in Hz
You can initialize an array "avg_spectrum" to store the average amplitude spectrum and use a for loop to compute the amplitude spectrum and store the scaled amplitude spectrum corresponding to the each segment. You can refer to the below mentioned MATLAB code snippet to do so:
daily_signal = your_signal; % Replace with your 1x7000000 signal vector
L = 1750; % Samples per segment
N_parts = 4000; % Number of parts
Fn = Fs / 2; % Nyquist frequency
Fv = linspace(-Fn, Fn, L); % Frequency vector
avg_spectrum = zeros(1, L); % Initialize average spectrum accumulator
for i = 1:N_parts
idx_start = (i - 1)*L + 1;
idx_end = i * L;
segment = daily_signal(idx_start:idx_end);
Fc = fft(segment) / L;
amp = abs(fftshift(Fc)); % Centered amplitude spectrum
avg_spectrum = avg_spectrum + amp./N_parts;
end
2. The average amplitude spectrum can then be visualized as a function of frequency ranging from "-Fs/2" to "Fs/2" using the below MATLAB code snippet:
figure;
plot(Fv, avg_spectrum);
xlabel('Frequency (Hz)');
ylabel('Average Amplitude');
title('Average Amplitude Spectrum Over 4000 Segments');
For more information, you can refer to the MathWorks documentation below:
- fft: https://www.mathworks.com/help/matlab/ref/fft.html
- fftshift: https://www.mathworks.com/help/matlab/ref/fftshift.html
- abs: https://www.mathworks.com/help/matlab/ref/double.abs.html
- linspace: https://www.mathworks.com/help/matlab/ref/double.linspace.html
I hope this is helpful!
