chap 2. signals and spectra: energy signal, power signal and spectrum

energy spectrum density (ESD)

• the ESD is defined for energy waveforms by

where

 (FT pairs).

 has units of joules per hertz.

power spectrum (power spectrum density, PSD)

(FYI) chap 2. signals and spectra: useful wave characteristic, wave의 power에 대해 정리한 내용 참고. 

• the PSD for a deterministic power waveform is

where

 (FT paris).
and

 has units of watts per hertz.

• Wiener-Khintchine theorm. PSD and autocorrelation function of certain physical waveform are Fourier transform pairs relation; that is