Fast algorithms for polynomial time frequency transform

The computation of polynomial time frequency transform (PTFT) is required for the maximum likelihood method to estimate the phase parameters of the polynomial-phase signals (PPSs). The transform can be computed by directly using the 1D fast Fourier transforms (FFT), which requires a prohibitive comp...

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Bibliographic Details
Published in:Signal processing 2007-05, Vol.87 (5), p.789-798
Main Authors: Wei, Yongmei, Bi, Guoan
Format: Article
Language:English
Subjects:
Applied sciences
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
FFT
Information, signal and communications theory
Miscellaneous
Polynomial time frequency transform
Polynomial-phase signals
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
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Summary:The computation of polynomial time frequency transform (PTFT) is required for the maximum likelihood method to estimate the phase parameters of the polynomial-phase signals (PPSs). The transform can be computed by directly using the 1D fast Fourier transforms (FFT), which requires a prohibitive computational load for higher-order PPSs. By exploiting two properties of the PTFT, this paper presents a decimation-in-time fast algorithm to significantly reduce the computational complexity compared with that by only using 1D FFT. For example, the numbers of both complex multiplications and additions are reduced by a factor of 2 M log 2 N for N-point ( M + 1 ) th-order PTFTs.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2006.07.010