Fast Hadamard Transforms for Arbitrary Orders

2011 ◽  
pp. 249-274
Keyword(s):  
Hadamard Transforms

Multiquadratic Rings and Walsh-Hadamard Transforms for Oblivious Linear Function Evaluation

2020 ◽  
Author(s):  
Alberto Pedrouzo-Ulloa ◽  
Juan Ramon Troncoso-Pastoriza ◽  
Nicolas Gama ◽  
Mariya Georgieva ◽  
Fernando Perez-Gonzalez
Keyword(s):  
Linear Function ◽  
Function Evaluation ◽  
Hadamard Transforms

scholarly journals New Orthogonal Transforms for Signal and Image Processing

2021 ◽  
Vol 11 (16) ◽  
pp. 7433
Author(s):  
Andrzej Dziech
Keyword(s):  
Symmetric Matrix ◽  
Sparse Matrices ◽  
Orthogonal Expansion ◽  
Orthogonal Matrices ◽  
Exponential Form ◽  
Orthogonal Transforms ◽  
Hadamard Transforms ◽  
The Given ◽  
Transform Domains ◽  
Signal Approximation

In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of the important features of the presented approach. The conditions for creating symmetric, orthogonal matrices are defined. It is shown that for the selection of the elements of an orthogonal matrix that meets the given conditions, it is necessary to select only a limited number of elements. The general form of the orthogonal, symmetric matrix having an exponential form is also presented. Orthogonal basis functions based on the created matrices can be used for orthogonal expansion leading to signal approximation. An exponential form of orthogonal, sparse matrices with variable parameters is also created. Various versions of orthogonal transforms related to the created full and sparse matrices are proposed. Fast computation of the presented transforms in comparison to fast algorithms of selected orthogonal transforms is discussed. Possible applications for signal approximation and examples of image spectrum in the considered transform domains are presented.

Parametric Slant-Hadamard transforms with applications

2002 ◽  
Vol 9 (11) ◽  
pp. 375-377 ◽  
Author(s):  
S. Agaian ◽  
K. Tourshan ◽  
J.P. Noonan
Keyword(s):  
Hadamard Transforms

Fourier and Hadamard: Transforms in Spectroscopy

1995 ◽  
Vol 72 (4) ◽  
pp. 304 ◽  
Author(s):  
Darla K. Graff
Keyword(s):  
Hadamard Transforms

scholarly journals Topological data analysis for true step detection in periodic piecewise constant signals

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180027 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Elizabeth Munch
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Future Research ◽  
Accurate Identification ◽  
Piecewise Constant ◽  
Higher Dimensional ◽  
Powerful Approach ◽  
Hadamard Transforms ◽  
Topological Data

This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.

scholarly journals PAPR reduction for FBMC/OQAM using hybrid scheme of different Precoding transform and mu-law companding

2017 ◽  
Vol 6 (4) ◽  
pp. 154 ◽  
Author(s):  
Imad Shaheen ◽  
Abdelhalim Zekry ◽  
Fatma Newagy ◽  
Reem Ibrahim
Keyword(s):  
Average Power ◽  
Multicarrier Modulation ◽  
Hybrid Scheme ◽  
Discrete Hartley Transform ◽  
High Data ◽  
Sine Transform ◽  
Combination Scheme ◽  
Papr Performance ◽  
Hadamard Transforms ◽  
High Band

The filter banks multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) is developing multicarrier modulation technique used in the next wireless communication system (5G). FBMC/OQAM supports high data rate and high band width efficiency. However, one of the major drawbacks of FBMC system is high peak to Average Power Ratio (PAPR) of the transmitted signal, which causes serious degradation in performance of the system. Therefore, it is required to use a proper PAPR scheme at the transmitter to reduce the PAPR. In this paper, a hybrid scheme is investigated with the combination of preceding transform technique and Mu Law Companding technique to reduce PAPR in FBMC systems. Moreover, four preceding techniques are examined to find the best Precoding technique which can be used with Mu law commanding. We assessed the discrete Hartley transform (DHT). The discrete cosine transformed (DCT), the Discrete Sine Transform (DST), and the Walsh Hadamard transforms (WHT) which are applied separately with Mu Companding. The numerical results verify that the FBMC systems with all Precoding technique combined with Mu law commanding can improve PAPR performance of the signals greatly with the best results achieved when the combination scheme consists of the DST Precoding and Mu law commanding for both PAPR and BER performance.

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