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Is it possible to perform Frequency Down-Mixing (sometimes referred to as Down-Conversion) by simply rotating the DFT sequence? If so what are the Advantages and Disadvantages of this method?

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  • $\begingroup$ Hi! Please clearly specify, using unambiguous standard DSP mathematical notation, what do you mean by rotating the DFT sequence and what do you also mean by Signal Up / Down conversion... $\endgroup$ – Fat32 Mar 11 at 11:41
  • $\begingroup$ Hi. By rotation I mean circularly shifting the DFT indices to perform down-conversion which is usually done in time domain by multiplication with NCO $\endgroup$ – malik12 Mar 11 at 12:00
  • $\begingroup$ Ok, good. A more standard term (if not necessarily better) for Down-Conversion is frequency down-mixing, or frequency shifting or even mere demodulation (depending on the perspective you prefer to have). However, quite a large number of dsp novice experts ! prefer using the term down-conversion in place of down sampling (sample rate conversion). So you better add frequency down-mixing into your context. $\endgroup$ – Fat32 Mar 11 at 12:21
  • $\begingroup$ I have updated the question as per your suggestion. $\endgroup$ – malik12 Mar 11 at 12:23
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Is it possible to perform Frequency Down-Mixing ... by simply rotating the DFT sequence?

Yes.

If so what are the Advantages and Disadvantages of this method?

As compared to the standard method of just multiplying with a cosine or complex exponential, there are no advantages (hence, no one really does it). There are lot of disadvantages: it requires framing including overlap management and potentially windowing, it's computational expensive and calculates a lot of stuff that you actually don't need.

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  • $\begingroup$ Thanks for your response. I have an application in which I am already computing a sufficient resolution FFT and afterwards I need to extract portion of frequencies and down-convert them and was thinking that It may be easier to do this by DFT rotation . Can you kindly elaborate the framing and overlap management? $\endgroup$ – malik12 Mar 12 at 5:59
  • $\begingroup$ The FFT always assumes that the signal is periodic in time with the FFT length. Most signals are not so you need to manage this discrepancies. That's typically done by chopping the time domain signal into FFT-length long frames with or without overlap and with our without windowing. It also tends to create discontinuities at frame boundaries that you need to manage. For example: band pass filtering using an FFT is generally not a good idea. See for example: dsp.stackexchange.com/questions/6220/… $\endgroup$ – Hilmar Mar 13 at 12:36
  • $\begingroup$ By framing and overlap method do you mean the use of Overlap Add/Overlap Save? $\endgroup$ – malik12 Mar 15 at 5:21
  • $\begingroup$ There multiple ways to deal with this. Overlap add/save is one of them. $\endgroup$ – Hilmar Mar 15 at 14:50

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