Parseval's Theorem
Discover the relation between signal energy in the time and frequency domains.
We'll cover the following...
The energy of a length- discrete-time signal is defined as:
Parseval’s relation links the energy of a signal in the time domain to its energy in the frequency domain. In the equation form, it is expressed as:
In other words, the energy of a signal in the time domain is equal to its energy in the transform domain after scaling by .
Derivation
From the definition of the inverse discrete Fourier transform, we have:
...