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

This paper presents fast algorithms for computing the polynomial time-frequency transform that deals with a real-valued sequence of length-a^pb, 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.