Related papers: Discrete Linear Canonical Transform Based on Hyper…

In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…

Quaternion-valued signals along with quaternion Fourier transforms (QFT)provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In…

Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…

The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay…

Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…

We consider discrete-time (DT) systems S in which a DT input is first tranformed to a continuous-time (CT) format by phase-amplitude modulation, then modified by a non-linear CT dynamical transformation F, and finally converted back to DT…

The matrix expressions for every parts of a transformer are firstly described. Based on semi-tensor product (STP) of matrices the hypervectors are reconsidered and the linear transformation over hypervectors is constructed by using…

We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…

Low-dose Computed Tomography (LDCT) reconstruction is an important task in medical image analysis. Recent years have seen many deep learning based methods, proved to be effective in this area. However, these methods mostly follow a…

We consider a strictly stationary and ergodic sequence of random elements taking values in some Hilbert space. Our target is to study the weak convergence of the discrete Fourier transforms under sharp conditions. As a side-result we obtain…

The notion of linear finite transducer (LFT) plays a crucial role in some cryptographic systems. In this paper we present a way to get an approximate value, by random sampling, for the number of non-equivalent injective LFTs. By introducing…

We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation…

The quaternionic offset linear canonical transform (QOLCT) can be thought as a generalization of the quaternionic linear canonical transform (QLCT). In this paper we define the QOLCT, we derive the relationship between the QOLCT and the…

Diffusion Transformers (DiT) have become a leading architecture in image generation. However, the quadratic complexity of attention mechanisms, which are responsible for modeling token-wise relationships, results in significant latency when…

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we…

Combining the linear canonical transform and the Riesz transform, we introduce the linear canonical Riesz transform (for short, LCRT), which is further proved to be a linear canonical multiplier. Using this LCRT multiplier, we conduct…

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…

Deep-learning (DL) has emerged as a powerful machine-learning technique for several classic problems encountered in generic wireless communications. Specifically, random Fourier Features (RFF) based deep-learning has emerged as an…

Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing…

We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain…