Finite Synchrosqueezing Transform Based On The STFT

TL;DR

This paper introduces a finite Synchrosqueezing transform based on the Short-Time Fourier Transform (STFT) for analyzing finite signals, emphasizing its sparsity, invertibility, and computational efficiency.

Contribution

It defines the finite STFT Synchrosqueezing transform, explores its properties, and compares it with the standard finite STFT for improved time-frequency analysis.

Findings

Finite STFT Synchrosqueezing transform provides a sparse, invertible representation.

The transform offers an efficient matrix-based implementation.

Comparison shows advantages over traditional finite STFT in signal decomposition.

Abstract

The finite STFT Synchrosqueezing transform is a time-frequency analysis method that can decompose finite complex signals into time-varying oscillatory components. This representation is sparse and invertible, allowing recovery of the original signal. The STFT Synchrosqueezing transform on finite dimensional signals has the advantage of an efficient matrix representation. This article defines the finite STFT Synchrosqueezing transform and describes some properties of this transform. We compare the finite STFT and the finite STFT Synchrosqueezing transform by applying these transform to a set of signals.