spectrum returned by FFT

[Ruiduan L]

FFT is a digital representation of the Fourier transform, in my view. SO the FFT should not yield a continuous spectrum, but a discrete spectrum (especially in the frequency domain). BUT why what we can get in WAVESURFER seems like a continuous spectrum?

[Simon]

You are correct: the Fast Fourier Transform (FFT) is simply a fast implementation of the Discrete Fourier Transform (DFT). Both are discrete: they take as input a digital signal (i.e., sampled) and produce as output a discrete (i.e., sampled) spectrum.

Wavesurfer is showing you a discrete spectrum – it’s just “joining up the dots” with a line, to make visualisation easier. That’s just the same as what happens in the waveform display.

The spectrum produced by the FFT is discrete in frequency: in other words, it is “sampled” at a set of evenly spaced frequencies between 0Hz and the Nyquist frequency.

The resolution (i.e., how closely spaced the samples are) depends directly on the analysis frame length.

If you zoom in far enough to either the spectrum or the waveform, you’ll see this discrete nature.

[Danielle O]

Hi I just stumbled upon this and would like to ask if this is the answer as to why this and this are essentially the same thing but appear different (because of Wavesurfer).

Thank you!

[Simon]

Yes, these are both the spectrum of a voiced speech sound. The upper one appears to be on a linear vertical scale, so we only see the very largest amplitudes and everything else appears to be zero. The lower plot is on a logarithmic vertical scale and therefore we can see both very large and very small magnitudes on the same plot. The lower plot is more informative.

[Author]

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