STFT With Adaptive Window Width Based on the Chirp Rate

Abstract

Abstract-An adaptive time-frequency representation (TFR) with higher energy concentration usually requires higher complexity. Recently, a low-complexity adaptive short-time Fourier transform (ASTFT) based on the chirp rate has been proposed. To enhance the performance, this method is substantially modified in this paper: i) because the wavelet transform used for instantaneous frequency (IF) estimation is not signal-dependent, a low-complexity ASTFT based on a novel concentration measure is addressed; ii) in order to increase robustness to IF estimation error, the principal component analysis (PCA) replaces the difference operator for calculating the chirp rate; and iii) a more robust Gaussian kernel with time-frequency-varying window width is proposed. Simulation results show that our method has higher energy concentration than the other ASTFTs, especially for multicomponent signals and nonlinear FM signals. Also, for IF estimation, our method is superior to many other adaptive TFRs in low signal-to-noise ratio (SNR) environments.

Selection of optimal window length using STFT for quantitative SNR analysis of LFM signal

“…In the existing methods to select the window width for ASTFT, there are mainly two strategies: (i) define a limited window set, and use some concentration measures to select a correct value from the window set [25,27]; (ii) define a window width T w as the benchmark, and adjust it according to some concentration measures to add or subtract a constant Δl every time [18,21,26]. These methods have the same problems: (i) they cannot obtain the required window width quickly, or even cannot converge to the optimal width; (ii) they are computationally expensive and sensitive to noise; (iii) there are many parameters, but there are no instructions about how to determine the optimal value for each parameter.…”

“…Because no prior knowledge about LFM signals, most of the existing methods based on ASTFT only select window width from a limited window set [21,25,27]. It results in the high computational complexity and no accurate window width.…”

“…Recently, some researches about the selection of the window width were proposed in literature such as adaptive STFT (ASTFT) [17][18][19][20][21][22][23][24][25][26][27]. However, these methods have two drawbacks: (i) only selecting the window width from a limited window set; (ii) high computational complexity in the optimization process.…”

An Efficient Adaptive Window Size Selection Method for Improving Spectrogram Visualization

“…As such, two consecutive sinusoids with frequency difference Δ f can then be separated by setting the window size as$\begin{array}{c}T1W=\frac{B_s{F}_s}{\mathrm{\Delta }f},\end{array}$where W is the window size (number of samples), B s is the used window's main lobe size, and F s is the sampling frequency. If no prior information is available regarding an input signal, then most of the existing methods follow the adaptive STFT that selects a window length from a pool of window sets [40–43]. This approach involves a high computation cost and the limited pool of window sets also reduces the chances of getting an accurate window length.…”

Contribution to the Fault Diagnosis of a Doubly Fed Induction Generator for a Closed-loop Controlled Wind Turbine System Associated with a Two-level Energy Storage System

“…A variety of recent non-stationary techniques have been proposed in the literature, including the adaptive short-time Fourier transform (STFT) [13], adaptive S-transformer [14], and adaptive smoothed pseudo Wigner-Ville distribution (WVD) [15]. However, the main disadvantage of these approaches is the very high computational complexity [16]. In this article, depending on the rate of change of the instantaneous frequency (IF), an optimal window length can be deduced for the spectrogram [17].…”