# Why are FFT numbers so high?

My input numbers are close to 10, here is a sample of some:

9.259992,9.253408,9.322236,9.375503,9.406026,9.507771,9.509567,9.403034,9.397048,9.36054,9.265977,9.262985,9.216302,9.228272,9.338395,9.430565


I am using this PHP library thinkingmik/FastFourierTransformation

My peak numbers in response are about 500. A control which was done using another tool is 1-1.5

FFT is well over my head, so I am trying to read this library to get a bit of an idea, but can't figure this out. The interesting thing is the client says the chart seems to be correct, just numerical values are wrong.

• Have you looked at the formula for the DFT? (The FFT is an algorithm that computes the DFT efficiently...so I would start with that and the answer should be very clear to you). And for your client just divide the answer by N where N is the length of the FFT and things should be as you expect. This is equivalent to averaging without doing the final divide. Same thing. – Dan Boschen Feb 7 '20 at 14:49

$$X[k]=\sum_{n=0}^{N-1}x[n]e^{-j2\pi kn/N}\tag{1}$$
where $$x[n]$$ is the input sequence and $$N$$ is the DFT length. So bin zero, i.e., $$X[0]$$, is just the average value of your input sequence multiplied by the DFT length. The maximum value of $$|X[k]|$$ can be as large as the maximum value of $$|x[n]|$$ multiplied by the DFT length.