Parseval's Theorem states that the total energy computed in the time domain must equal the total energy computed in the frequency domain. It is a statement of conservation of energy. Parseval's relationship in its continuous form is given by
You can express the discrete version of Parseval's relationship as
,
where is a discrete FFT pair, and n is the number of elements in the sequence.
You can implement Parseval's relationship using the Real FFT VI to compute the FFT of a real input sequence, as shown in the following illustration.
The upper branch in the block diagram evaluates the left side of Parseval's relationship. The lower branch evaluates the right side.
Applying Parseval's relationship to the time signal and the corresponding FFT, the total computed energy in the time domain signal is the same total computed energy in the frequency domain, as shown in the following illustration.