Which is the correct way to scale the FFT?

Which is the correct way to scale the FFT?

Fs being the sampling frequency, df the step of the frequency vector. the matlab fft outputs 2 pics of amplitude A*Npoints/2 and so the correct way of scaling the spectrum is multiplying the fft by dt = 1/Fs. Dividing by Npoints highlights A but is not the correct factor to approximate the spectrum of the continuous signal.

What happens when the FFT is multiplied by DT?

And, if the fft is multiplied by dt, the energy of the input signal equals the energy of the spectrum. the relation is satisfied if the fft is multiplied dt and df is correctly defined.

How to calculate RMS level from FFT spectrum?

Equations (2) and (3) can be used to calculate rms level from the FFT Spectrum and PSD, where each summation is applied over the FFT bins spanning the frequency range of interest.

When is scaling a frequency spectrum unimportant?

You are right about scaling being unimportant if only the shape of the spectrum is desired. However, if it is necessary that the amplitudes in the frequency spectrum be correct, then there is only one option for scaling – your option #1.

How is the FFT computed with MATLAB and the IFFT?

How is it possible that the fft computed with matlab (no particular scaling!) and the FFT obtained by utilizing Xilinx module for SystemGenerator, have a 2000x factor scaling difference? i.e. Xilinx one is 2000 times lower amplitude? (I thought this topic was spot-on regarding amplitude issues, sorry for gravedigging!)

Which is the correct way to multiply the output of the FFT?

Multiplying the output from Matlab’s FFT function with “dt” is the only way to approximate the correct amplitudes (if you care about having physically meaningful amplitudes) AND allow for Parseval’s theorem to be satisfied.

Why does MATLAB Ifft expect that we have not scaled by already?

X_f = fft (x, n_sample, 1) / n_sample; % fft must be normalized by the number of samples in the data. % This convention was set by the software developer (Mathworks). Is this correct? If so, why does the MATLAB ifft function expect that we have not scaled by already?

Is the FFT the same as the power spectrum?

The FFT returns a two-sided spectrum in complex form (real and imaginary parts), which you must scale and convert to polar form to obtain magnitude and phase. The frequency axis is identical to that of the two-sided power spectrum.

How to get a PSD estimate using FFT?

This example shows how to obtain nonparametric power spectral density (PSD) estimates equivalent to the periodogram using fft. The examples show you how to properly scale the output of fft for even-length inputs, for normalized frequency and hertz, and for one- and two-sided PSD estimates.

What are the basic functions of the FFT?

The basic functions for FFT-based signal analysis are the FFT, the Power Spectrum, and the Cross Power Spectrum. Using these functions as building blocks, you can create additional measurement functions such as frequency response, impulse response, coherence, amplitude spectrum, and phase spectrum.

How is the amplitude of the FFT related to its magnitude?

The FFT returns a two-sided spectrum in complex form (real and imaginary parts), which you must scale and convert to polar form to obtain magnitude and phase. The frequency axis is identical to that of the two-sided power spectrum. The amplitude of the FFT is related to the number of points in the time-domain signal.

What should the length of the FFT function be?

The FFT function computes -point complex DFT. The length of the transformation should cover the signal of interest otherwise we will some loose valuable information in the conversion process to frequency domain. However, we can choose a reasonable length if we know about the nature of the signal.