Related papers: Frequency-Undersampled Short-Time Fourier Transfor…
In this work, we propose an algorithm for a filter based on the Fast Fourier Transform (FFT), which, due to its characteristics, allows for an efficient computational implementation, ease of use, and minimizes amplitude variation in the…
Hyperspectral imaging enables fine-grained recognition of materials by capturing rich spectral signatures, but learning robust classifiers is challenging due to high dimensionality, spectral redundancy, limited labeled data, and strong…
Cross-domain few-shot learning (CD-FSL) requires models to generalize from limited labeled samples under significant distribution shifts. While recent methods enhance adaptability through lightweight task-specific modules, they operate…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
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…
The inverse short-time Fourier transform network (iSTFTNet) has garnered attention owing to its fast, lightweight, and high-fidelity speech synthesis. It obtains these characteristics using a fast and lightweight 1D CNN as the backbone and…
In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion valued functions of two variables. We call it the quaternion quadratic phase Fourier transform (QQPFT). Based on the…
Using his formulation of the potential theoretic notion of balayage and his deep results about this idea, Beurling gave sufficient conditions for Fourier frames in terms of balayage. The analysis makes use of spectral synthesis, due to…
The standing waves existed in radio telescope data are primarily due to reflections among the instruments, which significantly impact the spectrum quality of the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Eliminating…
Time-frequency representation (TFR) allowing for mode reconstruction plays a significant role in interpreting and analyzing the nonstationary signal constituted of various modes. However, it is difficult for most previous methods to handle…
The fundamentals of Fourier Transform are presented, with analytical solutions derived for Continuous Fourier Transform (CFT) of truncated signals, to benchmark against Fast Fourier Transform (FFT). Certain artifacts from FFT were…
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…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…
Amplitude encoding of real-world data on quantum computers is often the workflow bottleneck: direct amplitude encoding scales poorly with input size and can offset any speedups in subsequent processing. Fourier-based sparse amplitude…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
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…
In this paper phase of a signal has been viewed from a different angle. According to this view a signal can have countably infinitely many phases, one associated with each Fourier component. In other words each frequency has a phase…