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Let's say I want to increase the sampling rate of my signal, $f_t$, from a sampling frequency $f_s$ to some multiple $Mf_s$. One way to do this is to add zeros between the samples of $f_t$. This increases $f_s$, but also adds unwanted high frequency content and because of this the modified signal has to be filtered with a low-pass filter so that its spectral content matches the original signal.

What is the difference between this method ( zero stuffing ) and Fourier interpolation ( zero padding )? Both can be used to upsample a signal by adding zeros in the time-domain. Is the difference in the method only?

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  • $\begingroup$ Can you explain how zero padding increases the sample rate? All zero-padding does is take [1,2,3,4] and make [1,2,3,4,0,0,0,0] which doesn't increase the sampling rate of the start data. $\endgroup$
    – Peter K.
    Oct 22, 2022 at 12:10
  • $\begingroup$ I might have confused Fourier interpolation with zero padding here $\endgroup$ Oct 22, 2022 at 13:07
  • $\begingroup$ Right! Hilmar's explanation is probably the best to see the relationship. $\endgroup$
    – Peter K.
    Oct 22, 2022 at 18:01

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Both can be used to upsample a signal by adding zeros in the time-domain.

Nope. Zero padding in time interpolates in frequency. If you want to interpolate in time, you need to zero pad in frequency, which you actually can do.

Both methods close cousins. Zero padding in the Fourier Domain is essentially the same as lowpass filtering with a rectangular filter. However it's not often used since the filter is an awkward one: it needs to be implemented as overlap add/save and the impulse response is a circular sinc which has some undesirable time domain properties.

Interpolating with zero stuffing gives you full control over the low pass filter and you can choose the one which fits your requirements best.

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  • $\begingroup$ Also, zero stuffing and low pass filtering can be done in time domain with a rather small window. $\endgroup$ Oct 23, 2022 at 1:29

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