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I have an audio signal sampled at 44100Hz. I want to delay this signal by 1 microsecond (and maybe even less) for a steganographic purpose. Now if I delay it one sample, the corresponding time delay will be $\frac{1}{44100} = 2.2 \times 10^{-5}\,\text{s}$. But the delay I need is even lesser than that. How to achieve it?

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It's called a "fractional delay".

A really comprehensive analysis on how to do this can be found here: https://ieeexplore.ieee.org/document/482137/ and the design tools are still available here http://legacy.spa.aalto.fi/software/fdtools/

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    $\begingroup$ Interesting question/answer! Can you give the gist of it in the answer? $\endgroup$
    – Basj
    Jul 23, 2018 at 20:20
  • $\begingroup$ @Basj: The gist? "it's a complicated problem with no one-size-fits-all solution, the best design method depends on your specific application requirements and constraints". If you google enough, you can probably find a non-pay version of the article but I didn't want to post this here, since I don't know whether these are fully legal. $\endgroup$
    – Hilmar
    Jul 24, 2018 at 13:12

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