FFT后x轴上的单位 [英] units on x axis after FFT

问题描述

我的信号是由线性光电二极管阵列检测到的静态一维图案，具有N个像素和间距p.

My signal is a static 1D pattern detected by the linear photodiode array with N pixels and pitch p.

FFT频谱后，我将沿X轴获得什么单位?

What units will I get along the X-axis after FFT to spectrum?

推荐答案

如果信号f(x)的单位为U，取决于变量x的单位为V，则

If you have a signal f(x) with unit U depending on variable x with unit V. Then

f的连续傅立叶变换具有单位UV且取决于单位为V的变量.
• 示例1:f(x)是一个x，它是时间的电压.那么傅立叶变换的单位为Vs(或V/Hz)与变量1/s(或Hz).
• 示例2:f(x)是一个x为空格的幂.然后，FT的单位为Wm，x轴(即波数)的单位为1/m(这可能是您的情况).
• the continuous Fourier transform of f has unit UV and depends on a variable with unit 1/V.
  • Example 1: f(x) is a Voltage with x being time. then the Fourier transform has unit Vs (or V/Hz) versus variable 1/s (or Hz).
  • Example 2: f(x) is a power with x being space. Then the FT has unit Wm and the x axis (which is then a wavenumber) unit 1/m (this is probably your case).

  因此，FFT的X轴的单位为1(因为它是一个计数器).

  So the units of the X-Axis of a FFT are 1 (because it is a counter).

  我包括了连续傅里叶变换，因为我怀疑您只是将FFT(顺便说一句，它只是离散傅里叶变换的算法名称)与普通(连续)傅里叶变换相混淆.

  I included the continuous Fourier transform, because I suspect that you just confused the FFT (which is just the name of an algorithm for the discrete Fourier transform by the way) with the ordinary (continuous) Fourier transform.

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