A nonlinear time-frequency analysis method

An alternative method of time-frequency signal analysis is introduced and is compared with the conventional discrete Fourier transfer (DFT)-based methods. The structure of the proposed algorithm and its mathematical properties are presented. The proposed algorithm has a nonlinear structure that provides a frequency-adaptivity feature. It can be implemented both in analog and in digital form and is particularly suitable for real-time applications where computational efficiency is important. A comparison is made with the DFT in terms of algorithm efficiency, sensitivity, and complexity. It is shown that compared with the DFT, the algorithm is more efficient for real-time applications and is less sensitive to noise and variations in the frequency and sampling rate while maintaining simplicity of the structure and computational efficiency. Slower convergence rate of the algorithm, compared with the DFT, constitutes its main shortcoming.

I. Introduction

The discrete Fourier transform (DFT) is by far the most popular signal analysis tool in science and engineering. It is a means of decomposition of a given signal into its individual frequency components. Study of the individual sinusoidal components of a signal provides useful information about the signal and is therefore a means of analysis of the signal [1], , [3]. In power engineering, for example, the DFT or its computationally efficient variant—the fast Fourier transform (FFT)—has been widely used as the standard method of harmonic detection and analysis [4], [5], [6] and phasor measurement [7], [8].