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Power Spectral Density Calculation Using FFT in MATLAB


Power spectral density (PSD) tells us how the power of a signal is distributed across different frequency components, whereas Fourier Magnitude gives you the amplitude (or strength) of each frequency component in the signal.

Steps to calculate the PSD of a signal

  1. Firstly, calculate the first Fourier transform (FFT) of a signal
  2. Then, calculate the Fourier magnitude of the signal
  3. The power spectrum is the square of the Fourier magnitude
  4. To calculate power spectrum density (PSD), divide the power spectrum by the total number of samples and the frequency resolution. {Frequency resolution = (sampling frequency / total number of samples)}

MATLAB Script

% The code is written by SalimWireless.com
clear
close all
clc
fs = 40000; % sampling frequency
T = 1; % total recording time
L = T .* fs; % signal length
tt = (0:L-1)/fs; % time vector
ff = (0:L-1)*fs/L;
y = sin(2*pi*100 .* tt) .* sin(2*pi*1000 .* tt); y = y(:); % reference sinusoid


% Allow user to input SNR in dB
snr_db = input('Enter the SNR (in dB): '); % User input for SNR
snr_linear = 10^(snr_db / 10); % Convert SNR from dB to linear scale


% Calculate noise variance based on SNR
signal_power = mean(y.^2); % Calculate signal power
noise_variance = signal_power / snr_linear; % Calculate noise variance


x = noise_variance*randn(L,1) + y; x = x(:); % sinusoid with additive Gaussian noise




% Plot results
figure


% Manual Power Spectral Density plots
subplot(311)
plot(y, tt,'r')
title('Original Message signal')
legend('Original signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')


% Manual Power Spectral Density plots
subplot(312)
[psd_y, f_y] = manualPSD(y, fs); % PSD of the original signal
plot(f_y,10*log10(psd_y),'r')
title('Power Spectral Density')
legend('Original signal PSD')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')


% Manual Power Spectral Density plots
subplot(313)
[psd_x, f_x] = manualPSD(x, fs); % PSD of the noisy signal
plot(f_x,10*log10(psd_x),'k')
title('Power Spectral Density')
legend('Noisy signal PSD')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')




% Manual PSD calculation function
function [psd, f] = manualPSD(signal, fs)
N = length(signal); % Signal length
fft_signal = fft(signal); % FFT of the signal
fft_signal = fft_signal(1:N/2+1); % Take only the positive frequencies
psd = (1/(fs*N)) * abs(fft_signal).^2; % Compute the power spectral density
psd(2:end-1) = 2*psd(2:end-1); % Adjust the PSD for the one-sided spectrum
f = (0:(N/2))*fs/N; % Frequency vector
end

Output





Copy the MATLAB Code from here


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Admin & Author: Salim

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  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
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