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Fast Algorithms for Polynomial Time-Frequency Transforms of Real-Valued Sequences

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3 Author(s)
Guoan Bi ; Nanyang Technol. Univ., Singapore ; Yingtuo Ju ; Xiumei Li

This paper presents fast algorithms for computing the polynomial time-frequency transform that deals with a real-valued sequence of length-apb, where a, b and p are positive integers. In particular, it shows that the polynomial time-frequency transform has a conjugate symmetric property, similar to that of the discrete Fourier transform, if the input sequence is real-valued. The computational complexities needed by these proposed algorithms are analyzed in terms of the numbers of real additions and real multiplications. When a=3,4, and 8, comparisons show that the computational complexities required by the proposed algorithms are less than 60% of those needed by the fast algorithms for complex-valued sequences.

Published in:

IEEE Transactions on Signal Processing  (Volume:56 ,  Issue: 5 )