Topic
Logarithmic number system
About: Logarithmic number system is a research topic. Over the lifetime, 537 publications have been published within this topic receiving 9690 citations. The topic is also known as: LNS.
Papers published on a yearly basis
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Book•
01 Jan 2007
TL;DR: This book discusses Digital Signal Processing Systems, Pipelining and Parallel Processing, Synchronous, Wave, and Asynchronous Pipelines, and Bit-Level Arithmetic Architectures.
Abstract: Introduction to Digital Signal Processing Systems. Iteration Bound. Pipelining and Parallel Processing. Retiming. Unfolding. Folding. Systolic Architecture Design. Fast Convolution. Algorithmic Strength Reduction in Filters and Transforms. Pipelined and Parallel Recursive and Adaptive Filters. Scaling and Roundoff Noise. Digital Lattice Filter Structures. Bit-Level Arithmetic Architectures. Redundant Arithmetic. Numerical Strength Reduction. Synchronous, Wave, and Asynchronous Pipelines. Low-Power Design. Programmable Digital Signal Processors. Appendices. Index.
1,361 citations
TL;DR: A method of computer multiplication and division is proposed which uses binary logarithms and an error analysis is given and a means of reducing the error for the multiply operation is shown.
Abstract: A method of computer multiplication and division is proposed which uses binary logarithms. The logarithm of a binary number may be determined approximately from the number itself by simple shifting and counting. A simple add or subtract and shift operation is all that is required to multiply or divide. Since the logarithms used are approximate there can be errors in the result. An error analysis is given and a means of reducing the error for the multiply operation is shown.
488 citations
TL;DR: In this paper, the authors present a framework for computing the minimal sampling period of a given digital filter structure when the speed of arithmetic operations is given but the number of processing units is unlimited.
Abstract: This paper presents a framework for Fiding efficient multiprocessor realizations of digital filters. Based on simple graph-theoretic concepts, a method is derived for determining the minimal sampling period of a given digital filter structure when the speed of arithmetic operations is given but the number of processing units Is unlimited. It Is shown how realistic hardware implementations can be found and evaluated by using the timing diagram of this maximal rate realization as a starting point. The minimal sampling periods of several common digital filter structures are given in terms of addition and multiplication times.
305 citations
TL;DR: A signed logarithmic number system, which is capable of representing negative as well as positive numbers is described, and it is shown that negative numbers can be represented in the sign/logarithm number system.
Abstract: A signed logarithmic number system, which is capable of representing negative as well as positive numbers is described. A number is represented in the sign/logarithm number system by a sign bit and the logarithm of the absolute value of the number (scaled to avoid negative logarithms).
273 citations
TL;DR: A method of computation is described in which all signals are encoded logarithmically, giving a great improvement in dynamic range compared with fixed-point linearly encoded arithmetic.
Abstract: A method of computation is described in which all signals are encoded logarithmically, giving a great improvement in dynamic range compared with fixed-point linearly encoded arithmetic. Two ways of adding or subtracting logarithmically encoded numbers are suggested, together with a logarithmic digital-analogue convertor.
175 citations