对信号进行频谱分析时的傅立叶变换(FFT)单位 [英] Units of a Fourier Transform (FFT) when doing Spectral Analysis of a Signal

问题描述

我的问题与对信号进行频谱分析或将信号放入FFT并解释使用合适的数值包得出的结果的物理意义有关，

My question has to do with the physical meaning of the results of doing a spectral analysis of a signal, or of throwing the signal into an FFT and interpreting what comes out using a suitable numerical package,

特别是:

• 获取信号，例如时变电压v(t)
• 将其放入FFT(您会得到一个复数序列)
• 现在取模数(abs)并平方结果，即| fft(v)| ^ 2.

所以您现在在y轴上有实数-我可以将这些光谱系数称为吗?

So you now have real numbers on the y axis -- shall I call these spectral coefficients?

• 使用采样分辨率，遵循食谱食谱，并将频谱系数与频率相关联.
• 在这个点上，您有一个频谱g(w)，其频率在x轴上，但是在y轴上有什么物理单位?

我的理解是，该频谱显示了电压信号中存在多少个各种频率-从某种意义上说，它们是频谱系数，它们是重构频率所需的各种频率的正弦和余弦系数.原始信号.

My understanding is that this frequency spectrum shows how much of the various frequencies are present in the voltage signal -- they are spectral coefficients in the sense that they are the coefficients of the sines and cosines of the various frequencies required to reconstitute the original signal.

第一个问题是，这些光谱系数的单位是什么?

这很重要的原因是频谱系数可能很小而且很大，因此我想使用dB标度来表示它们.

The reason this matters is that spectral coefficients can be tiny and enormous, so I want to use a dB scale to represent them.

但是要做到这一点，我必须做出选择:

But to do that, I have to make a choice:

• 我要么使用20log10 dB转换，要么对应于像电压这样的现场测量.
• 或者我使用10log10 dB转换，这与能量测量(例如功率)相对应.

我使用哪种缩放比例取决于单位.

任何对此的了解将不胜感激！

Any light shed on this would be greatly appreciated!

推荐答案

获取信号，随时间变化的电压v(t)

take a signal, a time-varying voltage v(t)

单位是 V ，值是实数.

将其放入FFT中-好的，您会得到一个复数序列

throw it into an FFT -- ok, you get back a sequence of complex numbers

单位仍然是 V ，值很复杂(不是 V/Hz -直流信号的FFT变成直流电平的点，而不是狄拉克三角函数的缩放转到无穷大)

units are still V, values are complex ( not V/Hz - the FFT a DC signal becomes a point at the DC level, not an dirac delta function zooming off to infinity )

现在取模数(abs)

now take the modulus (abs)

单位仍然是 V ，值是实数-信号分量的大小

units are still V, values are real - magnitude of signal components

对结果求平方，即| fft(v)| ^ 2

and square the result, i.e. |fft(v)|^2

单位现在是 V ² ，值是实数-信号分量的大小的平方

units are now V², values are real - square of magnitudes of signal components

我叫这些光谱系数吗?

shall I call these spectral coefficients?

它更接近功率密度，而不是通常使用的频谱系数.如果您的接收器是一个完美的电阻器，那将是功率，但是如果您的接收器是频率相关的，则它是输入电压FFT幅度的平方".

It's closer to an power density rather than usual use of spectral coefficient. If your sink is a perfect resistor, it will be power, but if your sink is frequency dependent it's "the square of the magnitude of the FFT of the input voltage".

在这个点上，您有一个频谱g(w):x轴上的频率，并且... y轴上的物理单位是什么?

AT THIS POINT, you have a frequency spectrum g(w): frequency on the x axis, and... WHAT PHYSICAL UNITS on the y axis?

单位是 V ²

单位很重要的另一个原因是频谱系数可能很小而且很大，所以我想用dB标度来表示它们.但是要做到这一点，我必须做出选择:我是否使用20log10 dB的转换(对应于像电压这样的现场测量)?还是我使用10log10 dB转换(对应于能量测量，例如功率)?

The other reason the units matter is that the spectral coefficients can be tiny and enormous, so I want to use a dB scale to represent them. But to do that, I have to make a choice: do I use the 20log10 dB conversion (corresponding to a field measurement, like voltage)? Or do I use the 10log10 dB conversion (corresponding to an energy measurement, like power)?

您已经对电压值进行平方，将等效功率提供给一个理想的1欧姆电阻，因此请使用10log10.

You've already squared the voltage values, giving equivalent power into a perfect 1 Ohm resistor, so use 10log10.

log(x ² )是 2 log(x)，因此 20log10 | fft(v)| = 10log10(| fft(v)| ² )，因此，如果您不对值取平方，则可以使用20log10.

log(x²) is 2 log(x), so 20log10 |fft(v)| = 10log10 ( |fft(v)|²), so alternatively if you did not square the values you could use 20log10.

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