Periodogram
Fast but high variance.
Take the raw time-domain signal x[n]x[n] of length NN.
Optionally apply a window (e.g., Hann, Hamming) to reduce spectral leakage.
Compute the DFT or FFT of the (optionally windowed) signal.
Estimate the power spectral density (PSD) from the squared magnitude of the FFT.
Welch’s Method
Averaged periodogram with reduced variance.
Divide the signal into overlapping segments.
Apply a window function to each segment.
Compute the FFT and PSD of each windowed segment.
Average the PSDs across all segments.
Correlogram
Estimate the autocorrelation function (ACF) of the full signal.
Apply a window if desired.
Compute the Fourier Transform of the autocorrelation to obtain the PSD.
Blackman–Tukey Method
Estimate the autocorrelation function (ACF) of the signal for a limited range of lags (typically from −M−M to +M+M, where M<NM<N).
Apply a window to the truncated ACF to smooth the estimate.
Compute the Fourier Transform of the windowed ACF to obtain the PSD.
Bartlett’s Method
Divide the signal into non-overlapping segments of equal length.
Optionally apply a window to each segment.
Compute the FFT and PSD for each segment.
Average the PSDs across all segments to reduce variance.