## FFT bin meaning

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Reply #1 –

I often see DFT bin in some DFT/stft literature,What does the term "bin" mean exactly?

Does it refer to a specific single frequency or a frequency range?

If we do N points DFT,then have N DFT bins, where do the 0-bin and N-1 bin refer to?

If N = 256,then where does 112.5 bin refer to?

In a sense, it's like a histogram, where the bin contains a range of frequencies between upper and lower bounds.

If the original time-domain chunk contained N=256 samples, that's 256 real values and 256 imaginary values (usually, the Imaginary part of each complex number is zero when we're considering Real data, such as audio waveforms).

The transform-domain chunk will also contain N=256 samples, meaning 256 real paired with 256 imaginary values, or combined, they could be considered 256 complex numbers. If you think about it, you'd be losing Information if you didn't have N=256 complex numbers, so you couldn't reconstruct the time-domain signal by performing the inverse DFT.

With certain kinds of symmetry in the original signal chunk it is possible to prove that the imaginary part must be zero, which can save some computation (e.g. even symmetry, IIRC, which you obtain when performing the autocorrelation function, whose transform is the power spectrum of the original signal - Wiener-Khinchin Theorem).

Anyhow, these N=256 complex numbers represent the full range of positive and negative frequencies. Negative frequencies do mean something in reconstructing the waveform, but in general analysis they tend to be ignored. So you have half the number of frequency bins.

The book Fourier Optics is quite an accessible academic text which I think covered much of this, and I have it in a box somewhere.