Fast algorithms for polynomial time frequency transform

Authors:
Yongmei Wei;Guoan Bi
Affiliations:
Block S1, School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore;Block S1, School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
Venue:
Signal Processing
Year:
2007

Citing 8
Cited 2

The fast Fourier transform and its applications

The fast Fourier transform and its applications
Transforms and Fast Algorithms for Signal Analysis and Representations

Transforms and Fast Algorithms for Signal Analysis and Representations
Fast parameter estimation algorithms for linear FM signals

ICASSP '94 Proceedings of the Acoustics, Speech, and Signal Processing,1994. on IEEE International Conference - Volume 04
Discrete chirp-Fourier transform and its application to chirp rateestimation

IEEE Transactions on Signal Processing
Instantaneous frequency estimation of polynomial FM signals usingthe peak of the PWVD: statistical performance in the presence ofadditive gaussian noise

IEEE Transactions on Signal Processing
Product high-order ambiguity function for multicomponentpolynomial-phase signal modeling

IEEE Transactions on Signal Processing
Parameter estimation for random amplitude chirp signals

IEEE Transactions on Signal Processing
Estimation and classification of polynomial-phase signals

IEEE Transactions on Information Theory

Local polynomial Fourier transform: A review on recent developments and applications

Signal Processing
The higher-order reassigned local polynomial periodogram and its properties

Signal Processing

Quantified Score

Hi-index	0.08

Visualization

Abstract

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^Mlog"2N for N-point (M+1)th-order PTFTs.