Related papers: Adaptive synchrosqueezing based on a quilted short…

Algorithms for processing data in short-time batches are critical for both online and offline processing of streamed and large data respectively due to the quadratic relation between signal length and computational cost of convolution-based…

Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. There are mainly two stages in the sFFT: frequency bucketization and spectrum reconstruction. Frequency…

Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…

Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…

This paper introduces a new tool for time-series analysis: the Sliding Window Discrete Fourier Transform (SWDFT). The SWDFT is especially useful for time-series with local- in-time periodic components. We define a 5-parameter model for…

This paper proposes a new loss using short-time Fourier transform (STFT) spectra for the aim of training a high-performance neural speech waveform model that predicts raw continuous speech waveform samples directly. Not only amplitude…

For audio source separation applications, it is common to estimate the magnitude of the short-time Fourier transform (STFT) of each source. In order to further synthesizing time-domain signals, it is necessary to recover the phase of the…

The dependability of power electronics systems, such as three-phase inverters, is critical in a variety of applications. Different types of failures that occur in an inverter circuit might affect system operation and raise the entire cost…

This study puts forward a generalization of the short-time Fourier-based Synchrosqueezing Transform using a new local estimate of instantaneous frequency. Such a technique enables not only to achieve a highly concentrated time-frequency…

Recently, we proposed short-time Fourier transform (STFT)-based loss functions for training a neural speech waveform model. In this paper, we generalize the above framework and propose a training scheme for such models based on spectral…

The data analysis of space-based gravitational wave detectors like Taiji faces significant challenges from non-stationary noise, which compromises the efficacy of traditional frequency-domain analysis. This work proposes a unified framework…

A non-iterative method for the construction of the Short-Time Fourier Transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of…

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…

We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…

Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies. These methods utilize Fourier transformations to shift signals…

We provide the foundations of a Hilbert space theory for the short-time Fourier transform (STFT) where the flat tori \begin{equation*} \mathbb{T}_{N}^2=\mathbb{R}^2/(\mathbb{Z}\times N\mathbb{Z})=[0,1]\times \lbrack 0,N] \end{equation*} act…

A joint frame and carrier frequency synchronization algorithm for coherent optical systems, based on the digital computation of the fractional Fourier transform (FRFT), is proposed. The algorithm utilizes the characteristics of energy…

Short-time Fourier transform (STFT) is used as the front end of many popular successful monaural speech separation methods, such as deep clustering (DPCL), permutation invariant training (PIT) and their various variants. Since the frequency…

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…

Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier…