In Signal Processing

In signal processing, the Parseval’s theorem is often written as equivalence of computing the energy or power of a signal in the time domain and frequency domain. It can apply to both periodic and aperiodic signals.

For periodic signal: The Parseval’s theorem states that given the the Fourier series of the periodic signal with period :

  • where is the angular frequency the the average power of the signal is equal to the sum of the powers of its Fourier components:

For aperiodic signals: The Parseval’s theorem relates the energy of the signal in the time domain to its energy in the frequency domain:

where