I'm sure this is a silly question but reading a bit about the PSD vs ESD for continuous signals, I'm a bit confused how that applies to discrete signals.

Usually people seem to be using the PSD when analysing real world signals, why not the ESD, I would assume a discrete real world signal is never infinite and thus never encounters the problem of infinite energy?


Energy spectral density is mostly applied to time-limited signals. In such cases, energy is finite, and average power (throughout all time) is zero. These signals are not stationary.

Normally you work with (or model your signals as) stationary signals. These have constant power (and infinite energy). Power spectral density applies to stationary signals, and is defined as the Fourier transform of the autocorrelation function.

  • $\begingroup$ Thank you for the answer, however I'm still not sure as to why it is often assumed that a process is stationary (what are the benefits?), because many places where spectral power density is being used in the real world the signal is not stationary (ECG, stock market, temperature and other non-linear dynamic systems). Basically it seems to me that the energy spectral density should be much better suited for many real world signals. $\endgroup$ – meow Jul 13 at 14:34

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