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I have read that people often use a zero-padded DFT with Hann-windowing to get the amplitude+phase information at one frequency (where the Hann window is used to reduce the effect of a small/finite sample size). Does it make sense to use this kind of windowing if I just do a DTFT at the frequency of interest? I want to use a DTFT because it doesn't do unnecessary computations for frequencies that I am not interested in.

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  • $\begingroup$ Why do you need a continuous-frequency result (which is what the DTFT gives you)? The Goertzel algorithm and this answer might be of particular interest to you. $\endgroup$
    – Jdip
    Nov 18, 2022 at 13:23
  • $\begingroup$ I stated this in the description. The DFT calculates information about other frequencies as well, which I am not interested in. I am using the DTFT for efficient computation and less memory usage. $\endgroup$
    – Chillpadde
    Nov 18, 2022 at 13:29

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Yes and no.

Windows are typically used to manage truncation or periodic discontinuities. In theory, the DTFT doesn't have these problems since you are summing from $-\infty$ to $+\infty$ so you have infinite frequency resolution.

However, in practice you can't calculate an infinite sum though. If your input signal has infinite support, than you need to truncate it somehow (in which case a window could be helpful). If it has finite support, than it has infinite bandwidth and you can's sample it without aliasing. Pick your poison.

The only exceptions are signal that have infinite support and are periodic. That's exactly what the DFT is all about.

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  • $\begingroup$ Any signal I will work with is a sampled (finite-length) time series. In my case the underlying measurand is periodic. Will Hann-windowing when calculated a DTFT in this case bias the phase information in the signal? $\endgroup$
    – Chillpadde
    Nov 18, 2022 at 14:57
  • $\begingroup$ Of course different windows are different. So they will affect the DTFT result differently. But I would say, off hand, that there is no reason why a Hann window or any other decent, even-symmetry window centered at $x[0]$ should affect the phase of your sinusoid adversely. $\endgroup$ Nov 18, 2022 at 16:50

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