I want to ask for a good textbook or online material which explains in detail:

-the time and frequency domain mathematics behind upsampling and downsampling.
-easy to follow

Note: Oppenheim's discrete-time signal processing book is hard to follow.

  • $\begingroup$ hm, could you be more specific about what you need to understand about this? Because, in all honesty, while your question isn't specific enough to preclude you actually need a book about multirate systems and complex polyphase resamplers, it does sound like you're just confused about the basics of aliasing and imaging, as that is really all you need to explain upsampling and downsampling. If that's the case, any resource would be hard to follow, because you're missing the basics... $\endgroup$ Commented Dec 13, 2020 at 11:58
  • $\begingroup$ I tried to learn upsampling and downsampling from Oppenheim's discrete-time signal processing book but it was hard to follow. As I said, I need the time and frequency domain mathematics behind upsampling and downsampling. $\endgroup$ Commented Dec 13, 2020 at 12:46
  • $\begingroup$ yes, and as I said, the whole math behind that is just "aliasing" and "imaging": make sure you understand these; you're really not being any more specific... $\endgroup$ Commented Dec 13, 2020 at 12:48
  • $\begingroup$ my question was clear and easy: any other alternative material for the same basic topics? $\endgroup$ Commented Dec 13, 2020 at 13:31
  • $\begingroup$ Yes, plenty. Literally every other book on discrete-time signal processing will tell you the same about aliasing and imaging as Oppenheim-Schaefer; it's the standard book for a reason, the math really doesn't change. It's really hard to recommend a single book from a library of choices if you can't even narrow down what you found hard to follow, and just insist it was hard. $\endgroup$ Commented Dec 13, 2020 at 13:34

2 Answers 2


The answer to my question is:

Essentials of Digital Signal Processing 1st Edition by B. P. Lathi


where in Section 6.6 you can find detailed discussions and good examples.

  • 1
    $\begingroup$ Lathi is definetely a recommended book. Nevertheless, sampling is harder to understand than some other DSP topics, as there's manipulations of functions through their Fourier transforms, and a mixture of continuous & discrete time signals can make it a little bit confusing at first. Try writing your own Octave/Matlab codes for gaining better insight. Or better come gere and ask specific questions, incuding those from Opp book too. $\endgroup$
    – Fat32
    Commented Dec 13, 2020 at 15:17

chapter 2 of the following book is in fact the best source:



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