Adaptive synchrosqueezing based on a quilted short-time Fourier transform

2017/07/11 by Alexander Berrian, Berrian, Alexander, Naoki Saito +1 · 7 citations
Computer Science · Engineering · #94A12 #FOS: Computer and information sciences #FOS: Mathematics #Machine Fault Diagnosis Techniques #Music and Audio Processing #Numerical Analysis (math.NA) #Sound (cs.SD) #Structural Health Monitoring Techniques

paper · pdf · doi:10.48550/arxiv.1707.03138

openalex publication_date 2017/07/11 · openalex created_date 2017/07/21 · openalex updated_date 2026/07/28

Abstract

In recent years, the synchrosqueezing transform (SST) has gained popularity as a method for the analysis of signals that can be broken down into multiple components determined by instantaneous amplitudes and phases. One such version of SST, based on the short-time Fourier transform (STFT), enables the sharpening of instantaneous frequency (IF) information derived from the STFT, as well as the separation of amplitude-phase components corresponding to distinct IF curves. However, this SST is limited by the time-frequency resolution of the underlying window function, and may not resolve signals exhibiting diverse time-frequency behaviors with sufficient accuracy. In this work, we develop a framework for an SST based on a "quilted" short-time Fourier transform (SST-QSTFT), which allows adaptation to signal behavior in separate time-frequency regions through the use of multiple windows. This motivates us to introduce a discrete reassignment frequency formula based on a finite difference of the phase spectrum, ensuring computational accuracy for a wider variety of windows. We develop a theoretical framework for the SST-QSTFT in both the continuous and the discrete settings, and describe an algorithm for the automatic selection of optimal windows depending on the region of interest. Using synthetic data, we demonstrate the superior numerical performance of SST-QSTFT relative to other SST methods in a noisy context. Finally, we apply SST-QSTFT to audio recordings of animal calls to demonstrate the potential of our method for the analysis of real bioacoustic signals.

Cited by

• Time-reassigned synchrosqueezing frequency-domain chirplet transform for multicomponent signals with intersecting group delay curves
• Synchrosqueezed X-Ray Wavelet-Chirplet Transform for Accurate Chirp Rate Estimation and Retrieval of Modes from Multicomponent Signals with Crossover Instantaneous Frequencies
• Analysis of an Adaptive Short-Time Fourier Transform-Based Multicomponent Signal Separation Method Derived from Linear Chirp Local Approximation
• Adaptive Synchrosqueezing Transform with a Time-Varying Parameter for Non-stationary Signal Separation
• Analysis of Adaptive Short-time Fourier Transform-based Synchrosqueezing Transform
• Signal Separation Based on Adaptive Continuous Wavelet Transform and Analysis
• Analysis of Adaptive Synchrosqueezing Transform with a Time-varying Parameter

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