Is resizing of frequency spectrum a valid method of resampling?

Signal Processing Asked on January 2, 2022

One method of resampling is to perform a Fourier Transform on a signal, resize the resulting frequency spectrum, and then return to the resampled version of the signal with an inverse fourier transform.

Is this a method used in practice?
Are there methods that perform better down/upsampling (it terms of interpolation error)?
Are there faster methods?

One Answer

Interpolation by zero padding and computing the IDFT is used in practice but is not optimum and will have greater error over other approaches with the same or less resources, for the same reason that filtering by zeroing frequency bins in a DFT is not recommended. This point is detailed at this post Why is it a bad idea to filter by zeroing out FFT bins?.

Methods that perform better in terms of efficiency and performance include polyphase resampling structures using filter coefficients based on least squares algorithm, and specifically for multiband fiters that concentrate rejection at the image locations associated with the spectral distortion.

For further details on such approaches see:

How to implement Polyphase filter?


Computational Complexity of Polyphase Resampling

When a Sinx/x droop can be tolerated (or easily compensated for, see how to make CIC compensation filter) cascade-integrator-comb (CIC) interpolators are highly attractive for their simplicity and efficiency (there are many posts here that detail the beautiful CIC (otherwise called the Hogenhauer filter after the original author) further, see:

CIC Cascaded Integrator-Comb spectrum

Puzzled by CIC filters

Interpolating/Decimating CIC Filter Group Delay

Answered by Dan Boschen on January 2, 2022

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