Multiplications of time domain vectors of two signals is equivalent to convolutions in frequency domain and also use circular convolutions for when FIR filter design using window method in frequency. if working Discrete Fractional Fourier transform (DFRFT) i.e. on bins between time and frequency domain then which is proper operation (multiplication, convolution or any other operational treatment) gives same effect for FIR filter design using window when DFRFT of window function and FFT of Ideal filter is taken? Please explain with example if possible.

  • $\begingroup$ what do you mean?? do you mean using the FFT (or DFT) and then multiplying by $e^{-j 2 \pi k \tau /N}$ will delay by $\tau$ samples (and $\tau$ can be fractional)? circular convolution is what the DFT does. fractional-delay filters can be done in the time domain with linear convolution. $\endgroup$ – robert bristow-johnson May 11 '14 at 4:13

The question is very unclear. Whether convolution is circular or not depends only on what flavor Fourier Transform you use. It has nothing to do with filter design. It has also nothing to do with whether signal are "on bins" or not.

  • $\begingroup$ Please check edited question. $\endgroup$ – Jatinder Singh Brar May 12 '14 at 2:15
  • $\begingroup$ it's even less clear now. how is the FFT related to the "DFRFT"? (what does the "R" stand for?) $\endgroup$ – robert bristow-johnson May 12 '14 at 2:56
  • $\begingroup$ I believe he is referring to the Discrete Fractional Fourier Transform - so the "FR" refers to Fractional. It's the discrete equivalent of the Fractional Fourier transform. $\endgroup$ – David May 12 '14 at 12:19
  • $\begingroup$ should be "DFrFT" then. i admit i was being sorta "pedantic". $\endgroup$ – robert bristow-johnson May 12 '14 at 18:41

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