FFT Size and "Bins"

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http://support.ircam.fr/docs/AudioSculpt/3.0/co/FFT%20Size.html

FFT Size

The window size influences the temporal or frequency resolution, or precision of the representation of the signal. The frequency resolution can be increased changing the FFT size, that is, the number of bins of the analysis window.

FFT Size and "Bins"[size=1.1em]Reminder : Bins

The FFT size defines the number of bins used for dividing the window into equal strips, or bins. Hence, a bin is a spectrum sample, and defines the frequency resolution of the window.

By default :

• N (Bins) = FFT Size/2
• FR = Fmax/N(Bins)
  
  

For a 44100 sampling rate, we have a 22050 Hz band. With a 1024 FFT size, we divide this band into 512 bins.

FR = 22050/1024 ≃ 21,53 Hz.

[size=1.1em]FFT Size

Basically, the FFT size can be defined independently from the window size. In AS, the FFT size can only be calcularted proportionnaly to the window size, in order to preserve a relevant relationship between both parameters.Also, it is not displayed as an absolute value, but is expressed as a number of bins.

By default, the FFT size is the first equal or superior power of 2 of the window size. This relationship can be modified proportionnaly with the oversampling factor.

[size=1.1em]Zero Padding

If the window size is smaller than the FFT size, the missing number of 0s is interpolated with the samples to get the closest power of two. The zero-padding doesn't increase the information of the input signal, but the number of calculated samples.

With a higher N number of samples, the frequency resolution of the analysis is increased : remember that FR = SR/N Bins.

[size=1.1em]Increasing the Frequency Resolution with the FFT Size

The number of bins of the windows can be increased via the Oversampling pop up menu FFT size zone in the dialogue window. By default, the FFT size is the first equal or superior power of 2, which corresponds to an oversampling factor of 1.

With the oversampling factor, this number of bins can be increased with a power of 2 factor (2 ; 4 ; 8...)

Interests of Increasing the FFT Size[size=1.1em]Analysis

The frequency resolution is improved. With an oversampling rate of 2, we have twice more bins in the window, and the frequency resolution is twice more precise.

[size=1.1em]Treatments

The results of treatments is also improved : artefacts are reduced.

[size=1.1em]Buffering Time

An increase of the FFT size slows the calculus time proportionnally.

Analysis Parameters and Calculus Time

• Time Buffer
  

Advised Oversampling Factor[size=1.1em]Analysis and Treatments

The oversampling factor can vary depending on the signal's characteristics and the goals of the analysis. In the case of Partial Tracking Analysis and Chord Sequence Analysis, a 4 oversampling factor is generally advised.

[size=1.1em]Sonogram Display

In AS, the FFT size can't be superior to 65 536, in order to display the sonogram, which corresponds to a 0.67 Hz frequency resolution – which is very high. A way to increase this frequency resolution would be decreasing the sampling rate.