I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform?

How the simple identity

$$xy=\frac{1}{2}x^2 + \frac{1}{2}y^2 - \frac{1}{2}(x - y)^2$$

was used in developing a significant transform in digital signal processing?

  • 3
    $\begingroup$ "How? With a great deal of ingenuity, of course!" :-) $\endgroup$ Oct 29, 2014 at 13:11
  • $\begingroup$ Hi did you find the answers? $\endgroup$
    – gmotree
    Jun 8, 2015 at 15:22

1 Answer 1


This is related to Chirp Z-transform (CZT) (refer to the Bluestein's algorithm). Using this identity, the CZT can be expressed in terms of a convolution. Hence, it can be efficiently implemented using FFT.

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    $\begingroup$ Why the downvote? This answer is a bit terse, but it's correct, and following the link will reveal how this identity is used in the derivation of the CZT. $\endgroup$
    – Matt L.
    Sep 14, 2016 at 17:58
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    $\begingroup$ I guess one of the reasons is that answer points to wikipedia, which could be avoided by providing full explanation. $\endgroup$
    – jojeck
    Sep 14, 2016 at 21:44
  • $\begingroup$ @jojek I don't agree. I think it is even better to provide a link since there would be direct access to any further information that might be interesting. Also I realized my answer to dsp.stackexchange.com/questions/34220/fir-to-linear-phase-fir/… was converted to a comment. It does not fit the criteria explained for doing so. $\endgroup$
    – msm
    Sep 14, 2016 at 21:53
  • $\begingroup$ @msm: I can only guess, I don't know what is the true reason. I agree with you that literature is a valuable extension of every answer. $\endgroup$
    – jojeck
    Sep 14, 2016 at 21:58

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