FFT Analyzer Basic FAQ

A power spectrum is a graph obtained by analyzing the power of a time signal x (t) using FFT to determine the power for each frequency bandwidth (i.e., frequency resolution Δf), with frequency on the horizontal axis.

An FFT analyzer calculates it as follows: If X (f) is the Fourier spectrum of a signal x (t), then the power spectrum P (f) is:

(* represents complex conjugate)

（1）

This can be calculated as follows. From equation (1), we can see that the power spectrum has the following characteristics: [1] the phase information of the original signal x (t) is lost, and [2] it has dimensions equal to the square of the amplitude, that is, if the physical unit of the signal x (t) is EU(V), then it becomes ^EU² (^V²).

 

As a concrete example, if the input signal is x (t) in equation (2), the power spectrum will be A²^/ 2 (=(A / √2) ^², the square of the RMS value).

 

（2）

Furthermore, since the power spectrum is equivalent to the square of the amplitude, its square root is called the linear spectrum (or amplitude spectrum), and it represents the effective value in each frequency bandwidth. Similarly, the linear spectrum of equation (2) x (t) is 0.707 A (0.707 = 1/ √2).

Power spectrum (FFT analyzer basic terminology glossary)