Related papers: Is FFT Fast Enough for Beyond-5G Communications?
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is…
The Fast Fourier Transform (FFT) is the most efficiently known way to compute the Discrete Fourier Transform (DFT) of an arbitrary n-length signal, and has a computational complexity of O(n log n). If the DFT X of the signal x has only k…
We give algorithms with lower arithmetic operation counts for both the Walsh-Hadamard Transform (WHT) and the Discrete Fourier Transform (DFT) on inputs of power-of-2 size $N$. For the WHT, our new algorithm has an operation count of…
The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…
Most communications systems tend to achieve bandwidth, power and cost efficiencies to capable to describe modulation scheme. Hence for signal modulation, orthogonal frequency division multiplexing (OFDM) transceiver is introduced to cover…
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…
Edge devices are being deployed at increasing volumes to sense and act on information from the physical world. The discrete Fourier transform (DFT) is often necessary to make this sensed data suitable for further processing -- such as by…
Orthogonal frequency-division multiplexing (OFDM) has been selected as a baseline waveform for long-term evolution (LTE) and fifth-generation new radio (5G NR). Fast-convolution (FC)-based frequency-domain signal processing has been…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
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…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
We consider the problem of building numerically stable algorithms for computing Discrete Fourier Transform (DFT) of $N$- length signals with known frequency support of size $k$. A typical algorithm, in this case, would involve solving…
By viewing the nonuniform discrete Fourier transform (NUDFT) as a perturbed version of a uniform discrete Fourier transform, we propose a fast, stable, and simple algorithm for computing the NUDFT that costs $\mathcal{O}(N\log…
This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU$(2)$-nonlinear Fourier transform (NFT). The theoretical underpinnings of this generalization of the conventional…
This paper proposes an analog orthogonal frequency division multiplexing (OFDM) architecture based on the real-time Fourier transform (RTFT). The core enabling component is a linear-chirp phaser with engineered group velocity dispersion…
Nonlinear distortion experienced by signals during their propagation through optical fibers strongly limits the throughput of optical communication systems. Recently, a strong research focus has been dedicated to nonlinearity mitigation and…
The technologically-relevant task of feature extraction from data performed in deep-learning systems is routinely accomplished as repeated fast Fourier transforms (FFT) electronically in prevalent domain-specific architectures such as in…