DSP interview question: use of the identity in development of a significant transform 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?
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.