RMS in frequency domain using Plancherel theorem

1. How do you find RMS in frequency domain?
2. How to compute RMS from FFT?
3. What is the RMS value of FFT?

How do you find RMS in frequency domain?

As such, it can be seen as a function which associates to a frequency f the squared of the absolute value of the Fourier transform of x evaluated at f . In other words, in terms of your notation, the periodogram of x = x(t) goes as P(f) = |X|^2(f) . RMS = sqrt(sum(P))/N.

How to compute RMS from FFT?

This means that if we sum the squares of each component within a half-range FFT, multiply by 2 and form the square root we can obtain an estimate of the RMS of the original time history.

What is the RMS value of FFT?

Here we see that the calculated RMS value from the FFT spectrum is 1.1592 which agrees with the RMS calculation from the generated signal, hence proving Parseval's theorem.