Related papers: Zero-free regions of radar ambiguity functions and…
In this article, various results will be demonstrated that enable the delimitation of a zero-free region for holomorphic functions on a set $K$, studying the behavior of their imaginary or real part on the boundary of $K$. These findings…
The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its…
We study the possibility to reconstruct the primordial function for some periodic function. The procedure includes an analytical continuation of a discrete function for Fourier coefficients computation, that introduces an ambiguity. To…
In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to…
Some zero-free regions were known on the right half of the complex plane in the form of vertical strips for fractional hypergeometric zeta functions. In this paper, we describe and demonstrate zero free regions on the left half of the…
In this paper, we derive an ambiguity function (AF) for the transmit beamspace (TB)-based multipleinput multiple-output (MIMO) radar for the case of far-field targets and narrow-band waveforms. The effects of transmit coherent processing…
The ambiguity function (AF) is a critical tool in radar waveform design, representing the two-dimensional correlation between a transmitted signal and its time-delayed, frequency-shifted version. Obtaining a radar signal to match a…
We provide for a wide class of zero-free regions an upper bound for the error term in the Prime Number Theorem, refining works of Pintz (1980), Johnston (2024), and R\'ev\'esz (2024). Our method does not only apply to the Riemann zeta…
In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some…
This short note contributes a new zero-free region of the zeta function. This zero-free region has the form {s : Re(s) > a}, where a = 21/40.
This paper investigates the range ambiguity function of near-field systems where bandwidth and near-field beamfocusing jointly determine the resolution. First, the general matched filter ambiguity function is derived and the near-field…
In this paper we study how zeros of the Fourier transform of a function $f: \mathbb{Z}_p^d \to \mathbb{C}$ are related to the structure of the function itself. In particular, we introduce a notion of bandwidth of such functions and discuss…
Transition from Fourier series to Fourier integrals is considered and error introduced by ordinary substitution of integration for summing is estimated. Ambiguity caused by transition from discrete function to continuous one is examined and…
This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different…
The ambiguity function of a spatial signal in the "signal spatial frequency displacement vs antenna linear displacement" coordinates is considered in this paper; in case of a monochromatic signal with known carrier frequency, spatial signal…
It is shown that in asymptotic transition from Fourier series to integrals an error and ambiguity may arise. Ambiguity reduces to a possibility of addition of some distribution to the result. Properties of such distributions are studied and…
An accurate delay and Doppler estimation method for a radar system using time and frequency-shifted pulses with pseudo-random numbers is proposed. The ambiguity function of the transmitted signal has a strong peak at the origin and is close…
The ambiguity function is fundamental to radar waveform design, characterizing range and Doppler resolution capabilities. However, its traditional formulation involves non-differentiable operations, preventing integration with…
Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information about the unknown signal do we need to select the correct…
This paper formulates a conjectural description of of the space of weightless functions (see\cite{BK}) and raises a question about a possibility of extending such a description in a more general context.