频域中的RMS值ISO 10816

频域中的RMS值ISO 10816-1(RMS value in frequency domain ISO 10816-1)

我需要在频域中计算Velocity RMS值。 在使用带通滤波器对信号进行滤波以接收10到1 kHz频率范围内的信号并使用FFT对频谱进行计数之后，我得到了：

我已经找到了一个函数的方程RMS：

1）

但我不知道如何在matlab中编写它。 Parseval定理等于上面的等式1）??

来自互联网的Parseval定理代码不确定是否正确：

rms = sqrt（sum（（abs（x）/ length（x））。^ 2））;

所以我找到了旧主题，并且s1写了等式来计算RMS，如下所示：

rms1 = sum（abs（FFTDATA /length（data））.^ 2）

rms2 = sum（abs（FFTDATA。^ 2）/ length（data））/（length（data））

RMS1 = RMS2

但

有效值= SQRT（RMS1）

不确定巫婆的rms命令是否等于---> 1）或其中任何一个

I need to count Velocity RMS value in frequency domain. After filtering signals with band-pass filter to receive signals in the frequency range between 10 and 1 kHz and use FFT to count spectrum, I got :

I have found equation RMS for a function over all time:

1)

but im not sure how to write it in matlab. Parseval's theorem is equal to equation 1) from above ??

Parseval's theorem code from internet not sure that is correct:

rms = sqrt(sum((abs(x)/length(x)).^2));

so i found on old topic and s1 wrote equation to count RMS like this:

rms1 = sum(abs(FFTDATA /length(data)).^2)

rms2 = sum(abs(FFTDATA .^2) / length(data)) / (length(data) )

rms1=rms2

but

rms=sqrt(rms1)

not sure witch rms comand from above is equal to --->1) or any of them

最满意答案

RMS代表均方根，因此您正在寻找在LaTeX中编写的公式，即sqrt(rms1) ， sqrt(rms2)或rms 。

请注意，除非您有复杂的值，否则abs()调用是无用的。

Parseval的定理说你可以使用你的变换的平方和（在频域中）来得到你的平方和（或积分），而不是未转换的速度（在时域中）。 因此，一旦过滤了ISO 10816中的频率，就不必转换回来。

请注意，Parseval的定理是关于平方的和（或积分），而不是完整的RMS（你仍然必须除以T并取平方根）。 这可以解释为什么各种来源有不同的代码。

简而言之：使用sqrt(rms1)的公式

rms = sqrt（（abs（FFTDATA）/ length（data））。^ 2）;

Well RMS stands for Root Mean Square, so you are looking for the formula you wrote in LaTeX, thus sqrt(rms1), sqrt(rms2), or rms.

Note that unless you have complex values, the abs() calls are useless.

Parseval's Theorem says that you may use the squared sum of your transform (in frequency domain) to get your sum (or integral) of squares, instead of that of the velocities untransformed (in time domain). So you don't have to transform back once you filtered the frequencies that are within the ISO 10816.

Note that Parseval's Theorem is about the sum (or integral) of squares, but not the complete RMS (you still have to divide by T and take the square root). Which might explain why various sources have different codes.

In short : use the formula with sqrt(rms1)

rms = sqrt((abs(FFTDATA)/length(data)).^2);