Help obtaining the variance of a signal from a power spectrum?

1. How do you find the variance of a signal?
2. How do you calculate power spectral density?
3. How do you calculate the power spectrum of a signal?
4. How DFT and FFT are helpful in power spectral estimation?

How do you find the variance of a signal?

Variance of a signal is the difference between the normalized squared sum of instantaneous values with the mean value.

How do you calculate power spectral density?

A signal consisting of many similar subcarriers will have a constant power spectral density (PSD) over its bandwidth and the total signal power can then be found as P = PSD · BW.

How do you calculate the power spectrum of a signal?

Power spectrum (PS) of biological time series (of an electroencephalogram recording, for instance) often shows a relationship of decreasing power as a function of frequency (f) according to the general equation: PS(f) = ψ × f^-α (Norena et al., 2010).

How DFT and FFT are helpful in power spectral estimation?

The discrete Fourier transform (DFT) or fast Fourier transform (FFT) of a real signal is a complex number, having a real and an imaginary part. You can obtain the power in each frequency component represented by the DFT or FFT by squaring the magnitude of that frequency component.