Question

I am trying to do spectral analysis on a WAV file using the jTransforms library: Official Site

But I have problems on how to convert the WAV file into an acceptable input for FFT using jTransforms, and how can I display a frequency spectrum after FFT? I have searched around Google and found I need to somehow convert the WAV file into a double[] or Complex[], and afterwards how should I interpret the output?

Sorry I am very new to FFT so this question may sound extremely stupid. Many thanks!

Answer 1

I don’t know your library but i guess they have extensive documentation on how to apply the transforms.

Regarding the interpretation, if you use a complex transform you can interpret the real part as energy for the corresponding freuqncy bin and the imaginary as phase of the sinusoid.
The power spectral density (PSD) can be computed by

real(fftData)*conj(fftData) 

which is equal to

abs(fftData^2)

(so multiply the real parts by their complex conjugate).

One thing you might have to consider is rescaling your fft output. Some algorithms scale the output proportional to the fftSize. So you will have to multiply the output by 1/fftSize.

And the last thing in case you are not aware of, you only have to take half of the fft output since the spectrum is symmetric.
The middle bin (fftSize/2) is usually the mirrored fundamental frequency and is equal to fftData[0]. This marks the Nyquist frequency which is the highest frequency you can analyze with the given fftSize.
So if you want to display frequencies upto 22kHz make sure your fftSize is at least 44k.

There are many pitfalls with FFT, so be sure you read up on some parts and understand what you are doing there. The mathematics itself are not that important if you just want to use it, so you might skip them.

EDIT: There is even more. Consider to weight your input data with a tapered window (gaussian, hamming, hanning…) to avoid nasty edge effects if you don’t feed your whole wav file as input. Otherwise you will get artificial high frequencies into your fft output which are simply not present in the original.