TY - JOUR
T1 - Time-scale-chirp_rate operator for recovery of non-stationary signal components with crossover instantaneous frequency curves
AU - Chui, Charles K.
AU - Jiang, Qingtang
AU - Li, Lin
AU - Lu, Jian
N1 - Funding Information:
This work was partially supported by the ARO under Grant ♯ W911NF2110218, HKBU Grant ♯ RC-FNRA-IG/18-19/SCI/01, the Simons Foundation under Grant ♯ 353185, the National Natural Science Foundation of China under Grants ♯ 62071349, ♯ 61972265 and ♯ 11871348, and by National Natural Science Foundation of Guangdong Province of China under Grant ♯ 2020B1515310008.
Publisher Copyright:
© 2021 Elsevier Inc. All rights reserved.
PY - 2021/9
Y1 - 2021/9
N2 - The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly crossover instantaneous frequency (IF) curves from a multi-component blind-source signal. The main idea is to incorporate a chirp rate parameter with the time-scale continuous wavelet-like transformation, by considering the quadratic phase representation of the signal components. Hence-forth, even if two IF curves cross, the two corresponding signal components can still be separated and recovered, provided that their chirp rates are different. In other words, signal components with the same IF value at any time instant could still be recovered. To facilitate our presentation, we introduce the notion of time-scale-chirp_rate (TSC_R) recovery transform or TSC_R recovery operator to develop a TSC_R theory for the 3-dimensional space of time, scale, chirp rate. Our theoretical development is based on the approximation of the non-stationary signal components with linear chirps and applying the proposed adaptive TSC_R transform to the multi-component blind-source signal to obtain fairly accurate error bounds of IF estimations and signal components recovery. Several numerical experimental results are presented to demonstrate the out-performance of the proposed method over all existing time-frequency and time-scale approaches in the published literature, particularly for non-stationary source signals with crossover IFs.
AB - The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly crossover instantaneous frequency (IF) curves from a multi-component blind-source signal. The main idea is to incorporate a chirp rate parameter with the time-scale continuous wavelet-like transformation, by considering the quadratic phase representation of the signal components. Hence-forth, even if two IF curves cross, the two corresponding signal components can still be separated and recovered, provided that their chirp rates are different. In other words, signal components with the same IF value at any time instant could still be recovered. To facilitate our presentation, we introduce the notion of time-scale-chirp_rate (TSC_R) recovery transform or TSC_R recovery operator to develop a TSC_R theory for the 3-dimensional space of time, scale, chirp rate. Our theoretical development is based on the approximation of the non-stationary signal components with linear chirps and applying the proposed adaptive TSC_R transform to the multi-component blind-source signal to obtain fairly accurate error bounds of IF estimations and signal components recovery. Several numerical experimental results are presented to demonstrate the out-performance of the proposed method over all existing time-frequency and time-scale approaches in the published literature, particularly for non-stationary source signals with crossover IFs.
KW - 3D time-scale-chirp_rate space
KW - Instantaneous frequency estimation
KW - Mode retrieval
KW - Multi-component signals with crossover instantaneous frequencies
KW - Recovery of signal components
KW - Time-scale-chirp_rate transform
UR - http://www.scopus.com/inward/record.url?scp=85107980168&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2012.14010
DO - 10.48550/arXiv.2012.14010
M3 - Journal article
AN - SCOPUS:85107980168
SN - 1063-5203
VL - 54
SP - 323
EP - 344
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
ER -