Related papers: Characterizing and Enumerating Walsh-Hadamard Tran…
This paper proposes a new technique for computer modeling linear filters based on the spectral form of mathematical description of linear systems. It assumes the representation of input and output signals of the filter as orthogonal…
This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
Inspired by allocation strategies in multi-armed bandit model, we propose a pathwise construction of Walsh spider diffusions. For any infinitesimal generator on a star shaped graph, there exists a unique time change associated with a…
A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…
Packet reordering is an important property of network traffic that should be captured by analytical models of the Transmission Control Protocol (TCP). We study a combinatorial problem motivated by RESTORED, a TCP modeling methodology that…
We propose a novel quantum approach to signal processing, including a quantum algorithm for low-pass and high-pass filtering, based on the sequency-ordered Walsh-Hadamard transform. We present quantum circuits for performing the…
Suppose we concatenate two directed graphs, each isomorphic to a $d$ dimensional butterfly (but not necessarily identical to each other). Select any set of $2^k$ input and $2^k$ output nodes on the resulting graph. Then there exist node…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
We present a novel algorithm for calculating the discrete fractional Hadamard transform for data vectors whose size N is a power of two. A direct method for calculation of the discrete fractional Hadamard transform requires $N^2$…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
The explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a…
Temporal bipartite graphs are widely used to denote time-evolving relationships between two disjoint sets of nodes, such as customer-product interactions in E-commerce and user-group memberships in social networks. Temporal butterflies,…
This paper investigates the use of quasigroups, Hadamard transforms and Number Theoretic Transforms for use in sequence randomization. This can also be used to generate hash functions for sequence encryption.
We introduce a new kind of linear transform named Deformable Butterfly (DeBut) that generalizes the conventional butterfly matrices and can be adapted to various input-output dimensions. It inherits the fine-to-coarse-grained learnable…
We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…