Related papers: Quantization optimized with respect to the Haar ba…
The estimation of the parameters of a dynamic signal, such as a sine wave, based on quantized data is customarily performed using the least-square estimator (LSE), such as the sine fit. However, the characteristics of the experiments and…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
In this paper, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This…
Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
This letter presents a novel \textit{quantum algorithm} for signal denoising, which performs a thresholding in the frequency domain through amplitude amplification and using an adaptive threshold determined by local mean values. The…
Several analog-to-digital conversion methods for bandlimited signals used in applications, such as Sigma Delta quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued…
Recent work in time-frequency analysis proposed to switch the focus from the maxima of the spectrogram toward its zeros, which, for signals corrupted by Gaussian noise, form a random point pattern with a very stable structure leveraged by…
Quantization for deep neural networks have afforded models for edge devices that use less on-board memory and enable efficient low-power inference. In this paper, we present a comparison of model-parameter driven quantization approaches…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
Analog signals processed in digital hardware are quantized into a discrete bit-constrained representation. Quantization is typically carried out using analog-to-digital converters (ADCs), operating in a serial scalar manner. In some…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. For bandlimited signals, the distortion due to additive independent Gaussian…
We investigate the limits of communication over the discrete-time Additive White Gaussian Noise (AWGN) channel, when the channel output is quantized using a small number of bits. We first provide a proof of our recent conjecture on the…
Noise-shaping quantization techniques are widely used for converting bandlimited signals from the analog to the digital domain. They work by ``shaping" the quantization noise so that it falls close to the reconstruction operator's null…
In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampled-data H-infinity control. We formulate the discretization problem as minimization of the H-infinity norm of the error system…
We derive ultimate precision bounds for estimating parameters encoded in \emph{time-dependent} Hamiltonians in the presence of general Markovian noise, allowing for arbitrary adaptive protocols with fast controls and noiseless ancillas.…
We study the problem of estimating the best B term Fourier representation for a given frequency-sparse signal (i.e., vector) $\textbf{A}$ of length $N \gg B$. More explicitly, we investigate how to deterministically identify B of the…
We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…