Classical Sampling Series of Band Limited Functions: Oversampling and Non-existence

2016 ◽  
Vol 15 (1) ◽  
pp. 131-138
Author(s):  
B. A. Bailey ◽  
W. R. Madych
Keyword(s):  
Sampling Series ◽  
Band Limited

scholarly journals A generalization of the exponential sampling series and its approximation properties

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Carlo Bardaro ◽  
Loris Faina ◽  
Ilaria Mantellini
Keyword(s):  
Uniform Convergence ◽  
Convergence Theorem ◽  
Approximation Properties ◽  
Quantitative Form ◽  
Sampling Series ◽  
Band Limited

AbstractHere we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin band-limited functions using both classical and generalized exponential sampling series.

Method of estimation of hidden correlation of narrowband noise signals

2019 ◽  
pp. 34-39 ◽  
Author(s):  
E.I. Chernov ◽  
N.E. Sobolev ◽  
A.A. Bondarchuk ◽  
L.E. Aristarhova
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
New Technology ◽  
Digital Signal ◽  
Measuring Instruments ◽  
Central Frequency ◽  
Pearson Criterion ◽  
Useful Signal ◽  
Band Limited ◽  
Narrowband Noise

The concept of hidden correlation of noise signals is introduced. The existence of a hidden correlation between narrowband noise signals isolated simultaneously from broadband band-limited noise is theoretically proved. A method for estimating the latent correlation of narrowband noise signals has been developed and experimentally investigated. As a result of the experiment, where a time frag ent of band-limited noise, the basis of which is shot noise, is used as the studied signal, it is established: when applying the Pearson criterion, there is practically no correlation between the signal at the Central frequency and the sum of signals at mirror frequencies; when applying the proposed method for the analysis of the same signals, a strong hidden correlation is found. The proposed method is useful for researchers, engineers and metrologists engaged in digital signal processing, as well as developers of measuring instruments using a new technology for isolating a useful signal from noise – the method of mirror noise images.

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Sign in / Sign up

Export Citation Format

Share Document