Vedic Mathematics

153

Global J. of Engng. Educ., Vol.8, No.2 Ð'© 2004 UICEE

Published in Australia

INTRODUCTION

Vedic mathematics is the name given to the ancient

system of mathematics, or, to be precise, a unique

technique of calculations based on simple rules and

principles with which any mathematical problem can

be solved Ð'- be it arithmetic, algebra, geometry or

trigonometry. The system is based on 16 Vedic sutras

or aphorisms, which are actually word formulae

describing natural ways of solving a whole range of

mathematical problems. Vedic mathematics was

rediscovered from the ancient Indian scriptures

between 1911 and 1918 by Sri Bharati Krishna Tirthaji

(1884-1960), a scholar of Sanskrit, mathematics,

The Implementation of Vedic Algorithms in Digital

Signal Processing*

Purushottam D. Chidgupkar

Mangesh T. Karad

MIT Women Engineering College, Maharashtra Academy of Engineering and Educational Research

S. No. 124, MIT Eng. College Campus, Ex-Serviceman Colony, Paud Road, Pune - 411038, India

Digital signal processing (DSP) is the technology that is omnipresent in almost every engineering

discipline. It is also the fastest growing technology this century and, therefore, it poses tremendous

challenges to the engineering community. Faster additions and multiplications are of extreme

importance in DSP for convolution, discrete Fourier transforms, digital filters, etc. The core

computing process is always a multiplication routine; therefore, DSP engineers are constantly

looking for new algorithms and hardware to implement them. Vedic mathematics is the name given

to the ancient system of mathematics, which was rediscovered, from the Vedas between 1911 and

1918 by Sri Bharati Krishna Tirthaji. The whole of Vedic mathematics is based on 16 sutras (word

formulae) and manifests a unified structure of mathematics. As such, the methods are complementary,

direct and easy. The authors highlight the use of multiplication process based on Vedic algorithms

and its implementations on 8085 and 8086 microprocessors, resulting in appreciable savings in processing

time. The exploration of Vedic algorithms in the DSP domain may prove to be extremely advantageous.

Engineering institutions now seek to incorporate research-based studies in Vedic mathematics for

its applications in various engineering processes. Further research prospects may include the design

and development of a Vedic DSP chip using VLSI technology.

*A revised and expanded version of a keynote address

paper presented at the 4th Global Congress on Engineering

Education, held in Bangkok, Thailand, from 5 to 9 July

2004. This paper was awarded the UICEE diamond award

(joint first grade with one other paper) by popular vote of

Conference participants for the most significant contribution

to the field of engineering education.

history and philosophy [1]. He studied these ancient

texts for years and, after careful investigation, was

able to reconstruct a series of mathematical formulae

called sutras.

Bharati Krishna Tirthaji, who was also the former

Shankaracharya (major religious leader) of Puri,

India, delved into the ancient Vedic texts and established

the techniques of this system in his pioneering

work, Vedic Mathematics (1965), which is considered

the starting point for all work on Vedic mathematics.

Vedic mathematics was immediately hailed as a new

alternative system of mathematics when a copy of

the book reached London in the late 1960s.

Some British mathematicians, including Kenneth

Williams, Andrew Nicholas and Jeremy Pickles, took

interest in this new system. They extended the

introductory material of Bharati Krishna's book, and

delivered lectures on it in London. In 1981, this was

collated into a book entitled Introductory Lectures

on Vedic Mathematics [2]. A few successive trips to

India by Andrew Nicholas between 1981 and 1987

154 P.D. Chidgupkar & M.T. Karad

renewed interest in Vedic mathematics, and scholars

and teachers in India started taking it seriously.

According to Mahesh Yogi, The sutras of Vedic

Mathematics are the software for the cosmic

computer that runs this universe. A great deal of

research is also being carried out on how to develop

more powerful and easy applications of the Vedic

sutras in geometry, calculus and

...