Time-Scale-Chirp_rate Operator for Recovery of Non-stationary Signal Components with Crossover Instantaneous Frequency Curves

by   Charles K. Chui, et al.

The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly cross-over 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.


page 18

page 20

page 22


A Signal Separation Method Based on Adaptive Continuous Wavelet Transform and its Analysis

Recently the synchrosqueezing transform (SST) was developed as an empiri...

Parametric Modeling of EEG by Mono-Component Non-Stationary Signal

In this paper, we propose a novel approach for parametric modeling of el...

Support Recovery for Sparse Signals with Non-stationary Modulation

The problem of estimating a sparse signal from low dimensional noisy obs...

Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data

This paper is concerned with the inverse problem of recovering the unkno...

Representation and Characterization of Non-Stationary Processes by Dilation Operators and Induced Shape Space Manifolds

We have introduce a new vision of stochastic processes through the geome...

RRCNN: A novel signal decomposition approach based on recurrent residue convolutional neural network

The decomposition of non-stationary signals is an important and challeng...

Please sign up or login with your details

Forgot password? Click here to reset