Related papers: Novel FIR Inversion with Only FIRS
Adaptive algorithms based on sample matrix inversion belong to an important class of algorithms used in radar target detection to overcome prior uncertainty of interference covariance. Sample matrix inversion problem is generally ill…
Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the…
In terms of complex radio environments especially in dense urban areas, a very interesting topic is considered - the utilization of reconfigurable intelligent surfaces. Basically, based on simple controls of the angle of reflection of the…
Data-driven methods keep increasing their popularity in engineering applications, given the developments in data analysis techniques. Some of these approaches, such as Field Inversion Machine Learning (FIML), suggest correcting low-fidelity…
The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that…
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially…
Retrieving a signal from its triple correlation spectrum, also called bispectrum, arises in a wide range of signal processing problems. Conventional methods do not provide an accurate inversion of bispectrum to the underlying signal. In…
Common ISAR radar images and signals can be reconstructed from much fewer samples than the sampling theorem requires since they are usually sparse. Unavailable randomly positioned samples can result from heavily corrupted parts of the…
Image Restoration (IR) methods based on a pre-trained diffusion model have demonstrated state-of-the-art performance. However, they have two fundamental limitations: 1) they often assume that the degradation operator is completely known and…
Digital filters with variable bandwidth can be used for a variety of applications. Arbitrary change in the bandwidth of a digital Finite Impulse Response (FIR) filter can be acquired using sampling rate converters. In this paper, a sampling…
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
Analysis of 1H-NMR spectra is often hindered by large variations that occur during the collection of these spectra. Large solvent and standard peaks, base line drift and negative peaks (due to improper phasing) are among some of these…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…