Table of Contents
Power spectral density (PSD) is a measure of signal power distributed over frequency. Calculating PSD using Fast Fourier Transform (FFT) is a common method in signal processing. This guide provides a step-by-step process to perform this calculation accurately.
Preparing the Signal Data
Start by collecting your time-domain signal data. Ensure the data is sampled at a consistent rate, known as the sampling frequency. Remove any DC offset or trends to focus on the frequency components of interest.
Applying the FFT
Compute the FFT of the prepared signal. Most programming environments provide built-in FFT functions. The FFT converts the time-domain data into the frequency domain, revealing the amplitude of different frequency components.
Normalize the FFT output by dividing by the number of points in the FFT to obtain the correct amplitude scaling.
Calculating Power Spectral Density
Calculate the power spectrum by squaring the magnitude of the FFT results. For real signals, consider only the positive frequencies due to symmetry.
To obtain the PSD, divide the power spectrum by the bandwidth of each frequency bin, which is the sampling frequency divided by the number of FFT points. This normalization accounts for the distribution of power across frequencies.
Optional: Plotting the PSD
Plot the PSD against frequency to visualize the distribution of power. Use logarithmic scales if needed for better clarity of a wide range of power levels.