# STFT with Adaptive Window Width Based on the Chirp Rate

## TL;DR

This paper introduces an improved adaptive short-time Fourier transform that uses a novel concentration measure, PCA for chirp rate estimation, and a Gaussian kernel with variable window width, achieving higher energy concentration and robustness especially in noisy, multicomponent, and nonlinear FM signals.

## Contribution

The paper proposes a new low-complexity ASTFT with a signal-dependent concentration measure, PCA-based chirp rate estimation, and a time-frequency-varying Gaussian window, enhancing performance over existing methods.

## Key findings

- Higher energy concentration for multicomponent signals.
- Superior performance in low SNR environments.
- Improved robustness to instantaneous frequency estimation errors.

## 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.

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Source: https://tomesphere.com/paper/1705.08795