Walsh Functions and Their Applications

Beauchamp, K. G.; Debnath, Lokenath

doi:10.1109/tsmc.1979.4310078

Cited by 180 publications

(79 citation statements)

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“…Self-similarity is a typical property of fractals [1]. Derived from radial Walsh functions [2][3][4], radial Walsh filters form a set of orthogonal phase filters that take on values either 0 or phase, corresponding to +1 or −1 value of the radial Walsh functions over the prespecified annular regions of the circular filter. They may be considered as binary zone plates [5,6] and have wide range of applications [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Self-Similarity in Transverse Intensity Distributions in the Farfield Diffraction Pattern of Radial Walsh Filters

Mukherjee

Hazra

2014

Advances in Optics

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In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a transverse plane in the farfield diffraction patterns of the self-similar radial Walsh filters.

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Section: Introductionmentioning

confidence: 99%

Self-Similarity in Transverse Intensity Distributions in the Farfield Diffraction Pattern of Radial Walsh Filters

Mukherjee

Hazra

2014

Advances in Optics

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“…This in turn implies saving in processing time and storage allocations when using a digital signal processor. These functions are easy to generate and control using relatively simple hardware and thus readily lend itself for real time signal generation ideal for the synthesis of different periodic signals (Beauchamp, 1975).…”

Section: The Orthogonal Functionsmentioning

confidence: 99%

“…The definition of Rademacher functions may be extended over the whole non-negative real line by the periodicity property (Beauchamp, 1975): The first six Rademacher functions are given in Fig. 1.…”

Section: Rademacher and Walsh Functionsmentioning

confidence: 99%

“…Walsh functions are defined as a set of orthogonal functions that is complete over the normalized interval [0,1), each function taking only values of +1 or −1, except at a finite number of discontinuity points, where it takes the value zero (Beauchamp, 1975). Thus Walsh functions are orthogonal, normalized and complete.…”

Section: Rademacher and Walsh Functionsmentioning

confidence: 99%

“…We selected a definition which results in easier implementation on FPGAs. We denote the Walsh function by ψ(n, x) defined on the interval [0,1) such that Beauchamp (1975):…”

Section: Rademacher and Walsh Functionsmentioning

confidence: 99%

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VHDL Modeling, Simulation and Prototyping of a Novel Arbitrary Signal Generation System

Abbasi¹,

Alamoud²,

Shahrani³

2010

American J. of Engineering and Applied Sciences

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Problem statement: Arbitrary signal generators play an important role in many applications. Several different techniques utilizing both analog and digital approaches are being used for the generation of periodic signals. However, all of them suffer from many drawbacks. In this study, we present modeling, simulation and prototyping of a novel periodic arbitrary signal generation system using FPGAs. The proposed system utilizes orthogonal functions to generate a variety of periodic arbitrary signals. Approach: A new approach for designing arbitrary signals utilizing Walsh and Rademacher functions had been used. The design had been done using state-of-the-art high level design techniques and has been targeted to the latest available FPGA chips from Xilinx and Altera. Results: The simulation results demonstrated both the digital and analog versions were presented. It was found that all the signals generated showed precisely zero error and the signal generated was exactly the same as the desired one. Conclusion: Excellent accuracy with zero error is achieved. The designed and implemented Arbitrary signal Generation System is stand-alone and doesnt require the support of any computer hardware or software, as was needed in earlier attempts It has been concluded that virtually any periodic signal can be generated using the technique developed

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Logic Functions

2007

Spectral Logic and Its Applications for the Design of Digital Devices

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Walsh Functions and Their Applications

Cited by 180 publications

References 0 publications

Self-Similarity in Transverse Intensity Distributions in the Farfield Diffraction Pattern of Radial Walsh Filters

Self-Similarity in Transverse Intensity Distributions in the Farfield Diffraction Pattern of Radial Walsh Filters

VHDL Modeling, Simulation and Prototyping of a Novel Arbitrary Signal Generation System

Logic Functions

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