A microprocessor based new software technique for global Walsh function generation
01 Feb 1989-International Journal of Electronics (Taylor & Francis Group)-Vol. 66, Iss: 2, pp 193-200
TL;DR: A new software technique is presented for a global Walsh function generator which removes orthogonality error and allows one to generate the Walsh function set in three different orders, namely, Natural (or Hadamard) order, Dyadic and Sequency order.
Abstract: Walsh function and Walsh transform are important analytical and hardware tools for signal processing and have found wide applications in digital communications as well as in digital image processing. Therefore the use of Walsh function generator is very frequent in the above fields. Implementation of such a generator through hardware logic may give rise to orthogonality error in the generated function set. This paper presents a new software technique for a global Walsh function generator which removes orthogonality error. Further, the presented technique allows one to generate the Walsh function set in three different orders, namely, Natural (or Hadamard) order, Dyadic (or Paley) order and Sequency (or Walsh) order. Using an INTEL 8085 microprocessor the first 16 Walsh functions are generated as an illustration of the proposed software.
Citations
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01 May 1990
TL;DR: A recursive algorithm for Gray-code-ordered Walsh transforms is based on a novel operator called the bisymmetrical pseudo Kronecker product which is the basis for the flow diagram of a constant geometry fast Walsh transform in Gray code ordering.
Abstract: The generation of two new Walsh transforms in Gray code orderings from the straight binary code is shown. A recursive algorithm for Gray-code-ordered Walsh transforms is based on a novel operator called the bisymmetrical pseudo Kronecker product. The recursive algorithm is the basis for the flow diagram of a constant geometry fast Walsh transform in Gray code ordering. The algorithm is fast (N log/sub 2/ N additions/subtractions), is computer efficient, and is implemented in the iterative architecture. >
10 citations
TL;DR: An overview of the Walsh analysis with special stress upon its application in the fields of communication, systems, control and other areas as well is given.
Abstract: The piecewise constant Walsh function is not new in the field of mathematics because it was proposed in the year 1923 by J L Walsh. But its suitability to qualify as an elegant mathematical tool for the analysis of physical systems became apparent to the researchers quite late. Though other functions of the same piecewise constant orthogonal class attracted attentions of scientists as well as technologists to find frequent applications, the Walsh function has maintained its leadership among its clan having wide application areas ranging from the field of communication to the area of systems and control. The applications encompass die areas of digital signal processing image processing, logic circuit design etc.The present paper gives an overview of the Walsh analysis with special stress upon its application in the fields of communication, systems, control and other areas as well. The paper also reviews other non-sinusoidal orthogonal functions of the same class. Considering the present state of applicatio...
5 citations
01 Jan 1991
4 citations
Additional excerpts
...vns in communication, signal analysis and synthesis, sequency filtering, multiplexing and, encoding and decoding [51], [64], [69], [78] and [120]....
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References
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Book•
01 Jan 1969
TL;DR: When you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
Abstract: Read more and get great! That's what the book enPDFd transmission of information by orthogonal functions will give for every reader to read this book. This is an on-line book provided in this website. Even this book becomes a choice of someone to read, many in the world also loves it so much. As what we talk, when you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
366 citations
TL;DR: The Walsh functions are of great practical interest since they lead to equipment that is easily implemented by semiconductor technology, and some interesting applications of electromagnetic Walsh waves have been found theoretically.
Abstract: Communication theory was founded on the system of sine-cosine functions. A more general theory has become known more recently; it replaces the sine-cosine functions by other systems of orthogonal functions, and the concept of frequency by that of sequency. Of these systems, the Walsh functions are of great practical interest since they lead to equipment that is easily implemented by semiconductor technology. Filters, multiplexing equipment, and a voice analyzer/synthesizer have been built successfully for Walsh functions. Some interesting applications of electromagnetic Walsh waves have been found theoretically.
158 citations
TL;DR: It is shown that by using the symmetry properties of the enabling input patterns for a generator consisting of n T flip-flops, only (log2 n)- 1 standard time sequences, from which the remaining could be derived, need be generated.
Abstract: The design procedure of a new synchronous counter type of Walsh function generator for the generation of a set of Walsh functions with the least possible error in orthogonality is developed. Each flip-flop of the counter generates synchronously one particular Walsh function in the interval 1 of normalized time during one cycle of counting. The usual design procedures for synchronous counters are not applicable because of the large number of logic variables. Using a two-dimensional plot of the enabling inputs, it turns out that the T flip-flop is the most suitable type. It is shown that by using the symmetry properties of the enabling input patterns for a generator consisting of n T flip-flops, only (log2 n)- 1 standard time sequences, from which the remaining could be derived, need be generated. These time sequences can be easily obtained by decoding the outputs of those flip-flops generating the subset of Rademacher functions. The procedure is illustrated by taking an example of the generation of the first 16 Walsh functions.
16 citations
TL;DR: In this article, a new operational method for the analysis of pulse-fed power electronic circuits is suggested, where input waveforms are expressed by a series combination of Walsh functions, and output response is obtained in terms of Walsh function after operation by Walsh operational transfer function (WOTF).
Abstract: A new operational method for the analysis of pulse–fed power electronic circuits is suggested, where input waveforms are expressed by a series combination of Walsh functions. The output response is obtained in terms of Walsh functions after operation by Walsh operational transfer function (WOTF). The current waveform of a DC chopper fed R-L load is approximated by piecewise constant solution and various average and r.m.s. currents of the same power electronic circuit are computed as an illustration.
13 citations
TL;DR: The application of low-power Schottky integrated-circuit logic in the design of a 10-Mzps parallel-output array generator for Walsh functions is presented here.
Abstract: Recent development of circuits for generating parallel-programmable and serial-programmable Walsh functions with a high degree of orthogonality is discussed. The realization of these circuits leads to the demand for highly integrated digital circuits with multiple outputs triggered synchronously. Circuits capable of high speed and low input power have just recently come into production. The application of low-power Schottky integrated-circuit logic in the design of a 10-Mzps parallel-output array generator for Walsh functions is presented here. The circuit is designed, built, and tested and the orthogonality error for the Walsh functions is discussed.
11 citations