Compressive Chirp Transform for Estimation of Chirp Parameters

This paper develops a new algorithm for estimating the parameters of multiple chirp signals in noise. The proposed method uses Compressive Sensing (CS) formulation of the Discrete Chirp Fourier Transform (DCFT) basis to achieve superior estimator performance. Unlike Fourier or time-frequency based approaches, DCFT incorporates the underlying chirp signal model parameters in formulating the transform [1] –[4]. In this work a CS formulation exploits the parametric DCFT basis for fast recovery to achieve highly accurate parameter estimation results in polynomial time using Orthogonal Matching Pursuit (OMP). The performance of the proposed algorithm has been compared with existing methods via simulations.

[1]  Xiang-Gen Xia,et al.  A modified discrete chirp-Fourier transform scheme , 2000, WCC 2000 - ICSP 2000. 2000 5th International Conference on Signal Processing Proceedings. 16th World Computer Congress 2000.

[2]  Israel Cohen,et al.  Parameter estimation of harmonic linear chirps , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[3]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[4]  R. Calderbank,et al.  Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery , 2009 .

[5]  Petar M. Djuric,et al.  Parameter estimation of chirp signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[6]  Jianyu Yang,et al.  Signal reconstructing least-squares algorithm for chirp signal parameters estimation , 2006, 2006 8th international Conference on Signal Processing.

[7]  Osama A S Alkishriwo.  The Discrete Linear Chirp Transform and its Applications , 2013 .

[8]  A. Shaw.  A novel cyclic algorithm for maximum likelihood frequency estimation , 1991, IEEE 1991 International Conference on Systems Engineering.

[10]  Xiang-Gen Xia,et al.  Discrete chirp-Fourier transform and its application to chirp rate estimation , 2000, IEEE Trans. Signal Process..

[11]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[13]  Xiaojun Yang,et al.  Parameter Estimation of Multicomponent Chirp Signals via Sparse Representation , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[14]  SHISHIR B SAHAY,et al.  Parameter estimation of linear and quadratic chirps by employing the fractional fourier transform and a generalized time frequency transform , 2015 .

[15]  Andreas Jakobsson,et al.  Sparse Semi-Parametric Estimation of Harmonic Chirp Signals , 2016, IEEE Transactions on Signal Processing.

[16]  K. S. Arun,et al.  Parameter estimation for superimposed chirp signals , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[17]  Wenyan He,et al.  A novel method for chirp signal detection based on fractional Fourier transform , 2008, International Symposium on Instrumentation and Control Technology.

[18]  Prasun Mahanti,et al.  Image reconstruction by deterministic compressed sensing with chirp matrices , 2009, International Symposium on Multispectral Image Processing and Pattern Recognition.

[19]  LJubisa Stankovic,et al.  Estimation of FM signal parameters in impulse noise environments , 2005, Signal Process..

[20]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[21]  E.J. Candes.  Compressive Sampling , 2022 .

[22]  Irena Orovic,et al.  Polynomial Fourier domain as a domain of signal sparsity , 2014, Signal Process..

[23]  Xin Guo,et al.  Comments on discrete chirp-Fourier transform and its application to chirp rate estimation [and reply] , 2002, IEEE Trans. Signal Process..

[24]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[25]  Luis F. Chaparro,et al.  A discrete linear chirp transform (DLCT) for data compression , 2012, 2012 11th International Conference on Information Science, Signal Processing and their Applications (ISSPA).

[26]  A.B. Gershman,et al.  High-resolution sensor array processing in the presence of multiple wideband chirp signals , 2000, Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154).