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
- 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
represents the continuous Fourier transform