amplitude of fft harmonics

[gio1]

Hello

I'm having a small problem in handling the results from a simple fft analysis of a signal (I don't do them everyday)

I am interested in finding the actual amplitude value of some harmonics. I managed to plot the spectrum: if I remember well I need to drop the first value (as this is the constant mean of the signal) and then consider only the first half of the fft result vector (the other half being a perfect mirror).

The major harmonics are actually where I was expecting (which means I hopefully managed to scale the X axis of the spectrum correctly in relation to the fundamental period). However, the values on the Y axis are way too high to be actual amplitudes.

If each k-th harmonic has the form

ak COS(kt) + bk SIN(kt)

Then the relationship between ak, bk and the k-th fft coefficient calculated by Matlab should be:

ak = (2/N) REAL(c(k+1))
bk = (-2/N) IMAG(c(k+1))

(where c=fft(x))

The quantity abs(c)=sqrt(real(c)^2+imag(c)^2) which I have plotted (and whose values are too high to make sense)strictly speaking is NOT the amplitude of the harmomics, as the amplitude should infact (am I right?) be

Amplitude=MAX( ak COS(kt) + bk SIN(kt) )

The above maximum turns out to be (after some calcs):

MAX( ak cos(kt) + bk sin(kt) )= ak COS(ATAN(bk/ak)) + bk SIN(ATAN(bk/ak))

But some of these values are negative, which doesn't make sense either...

So, back to the original question: How to calculate the actual amplitude of each harmonics?

Thanks

Gio1

 

[JockeK]

Here are two good guides

http://www.mathworks.com/support/tech-notes/1700/1703.html

http://www.mathworks.com/support/tech-notes/1700/1702.shtml

 

[IRstuff]

You should be calculating the magnitude of the complex amplitudes, not the maximum.

TTFN