Related papers: Fractional Fourier Sound Synthesis
Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms…
A recently published method for audio style transfer has shown how to extend the process of image style transfer to audio. This method synthesizes audio "content" and "style" independently using the magnitudes of a short time Fourier…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
The fractional Fourier transform (FRFT) naturally exists in the strongly nonlocal nonlinear (SNN) media and the propagation of optical beams in SNN media can be simply regarded as a self-induced FRFT. Through FRFT technic the evolution of…
The Fourier Transform (FT) is a fundamental tool that permeates modern science and technology. While chemistry undergraduates encounter the FT as early as second year, their courses often only mention it in passing because computers…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
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…
A method is proposed which enables one to produce musical compositions by using transposition in place of harmonic progression. A transposition scale is introduced to provide a set of intervals commensurate with the musical scale, such as…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application. However, the high-performance DSP processor is the important method of electrical harmonic analysis. Hence, in this research…
In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…
In audio processing applications, phase retrieval (PR) is often performed from the magnitude of short-time Fourier transform (STFT) coefficients. Although PR performance has been observed to depend on the considered STFT parameters and…
Fast Fourier Transform (FFT) relies on the HRV frequency-domain analysis techniques. It requires re-sampling of the inherently unevenly sampled heartbeat time-series (RR tachogram) to produce an evenly sampled time series of the heartbeat.…
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…