Related papers: Fractional Fourier Sound Synthesis
As an old and widely used tool, it is still possible to find new insights and applications from Fast Fourier Transform (FFT)-based analyses. The FFT is frequently used to generate the Power Spectral Density (PSD) function, by squaring the…
Many audio synthesizers can produce the same signal given different parameter configurations, meaning the inversion from sound to parameters is an inherently ill-posed problem. We show that this is largely due to intrinsic symmetries of the…
For most of the state-of-the-art speech enhancement techniques, a spectrogram is usually preferred than the respective time-domain raw data since it reveals more compact presentation together with conspicuous temporal information over a…
The Short-Time Fourier Transform (STFT) has been a staple of signal processing, often being the first step for many audio tasks. A very familiar process when using the STFT is the search for the best STFT parameters, as they often have…
In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if $u$ and…
In this paper, we reduce the computational complexities of partial and dual partial cyclotomic FFTs (CFFTs), which are discrete Fourier transforms where spectral and temporal components are constrained, based on their properties as well as…
This paper proposes an efficient parameterization of the Room Transfer Function (RTF). Typically, the RTF rapidly varies with varying source and receiver positions, hence requires an impractical number of point to point measurements to…
We present a neural network for rendering binaural speech from given monaural audio, position, and orientation of the source. Most of the previous works have focused on synthesizing binaural speeches by conditioning the positions and…
The Discrete Fourier Transform (DFT) is a fundamental computational primitive, and the fastest known algorithm for computing the DFT is the FFT (Fast Fourier Transform) algorithm. One remarkable feature of FFT is the fact that its runtime…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…
The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…
Mechanical metamaterials are increasingly attracting interest in engineering applications due to their unique mechanical properties and lightweight nature. This study develops a novel sound-based representation to characterize the…
Controlling waves by actively changing the material parameters of a medium enables the development of new acoustic and electrical devices. Modulating the material breaks classical properties like reciprocity and the conservation of energy,…
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…
One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…
Fourier synthesis is one of the foundations of physical optics. Spatial Fourier optics is a basis for understanding optical imaging, microscopy, and holography. In conventional Fourier optics, the complex spatial field distribution in the…
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and…