The chirp transform of a vector a = (a 0 , a 1 , . . .

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The chirp transform of a vector a = (a0, a1, . . . ,an-1) is the vector y= (y0, y1, . . . ,yn-1), where yk = Σn-1j=0?aj zkj and z is any complex number. The DFT is therefore a special case of the chirp transform, obtained by taking z = ωn. Show how to evaluate the chirp transform in time?O(nlgn)?for any complex number?. Use the equation

image


to view the chirp transform as a convolution.

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Introduction to Algorithms

ISBN: 978-0262033848

3rd edition

Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest

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