# Amplitude calculation of the original signal from its FFT

I have a signal whose FFT has a one prominent harmonic ($f_1$) and few other harmonics with a lower amplitude. In order to calculate the amplitude of the original signal I can use a well known theorem: a value of $f_1$ divided by half number of data points in the original signal.

But what if I have harmonics $f_2, f_3, \ldots$? Should I take their amplitudes into account for such calculation?

• Where are your harmonics come from? – MimSaad Aug 17 '16 at 14:33
• To get the accurate amplitude measurement, you must take into account all frequencies and their phases. Taking the amplitude of a single frequency, or even all of them is not enough. Think of the interference of all the waves - phase is crucial. – jojek Aug 17 '16 at 14:42

Whoa, clarification is needed. The peak amplitude ($A_p$) of an $N$-length $f_1$ input sinusoid can only be found using
$A_p = 2M/N$
(where $M$ is the the magnitude of the $f_1$ spectral component) if $N$ samples of that $f_1$ input sinusoid represent an exact integer number of cycles.
If that condition holds then you can measure $A_p$ for the $f_1$ sinusoid as well as the peak amplitudes of the harmonics. But those peak amplitude values apply only to the individual sinusoids that comprise your FFT input signal. You CANNOT use the individual measured peak amplitudes to measure the peak amplitude of your nonsinusoidal FFT input. That was the point made in jojek's comment.