PRESENTED BY
AKULA PAVAN KUMAR
SONA COLLEGE OF TECHNOLOGY
SALEM-636005. Recent Trends In Engineering Mathematics

Introduction :

Introduction Introduction to Fourier Transform.
Introduction to Vedic Mathematics and 16 sutras.
Introduction to URDHVA TIRYAGBHYAM.
How to use the above sutra by illustrating an example.
How to apply to Fourier Transform.
Introduction to VAN-NEUMANN shift rule.
Comparison between normal mathematics and Vedic Mathematics in terms of multiplication.
Conclusion

Fourier Transform :

Fourier Transform In the present age of Digital Communication the signals are sampled on time axis and amplitude axis.
The information is being carried using binary digits.
Hence any process of transformation proceeds on basis of the operations present in it such as ‘+’, ‘-’… etc.
For this VAN-NEWMAN architecture uses register operations like complement, add, shift, move etc.
The CPU works with the amalgamation of algorithm and implementing architecture.
In Vedic Mathematics TIRTHAJI suggested many effective methods and alternatives.
First the discrete Fourier Transform deals with DTFT and then DFT in which DFT is based on memory and time scale.

DISCRETE FOURIER TRANSFORM :

DISCRETE FOURIER TRANSFORM Almost all branches of engineering and science use Fourier methods. The words frequency, period, phase and spectrum are important parts of an engineer’s vocabulary.
The decomposition of signals into orthogonal trigonometric basic functions, is a natural and powerful tool, which used in a vast number of applications.
JOSPEH FOURIER (1768–1830), French mathematician and physicist, or the mathematics, physics, and engineering terms named in his honor for his work on the concepts underlying them.
When describing a digital system the discrete Fourier transform was introduced because it arises naturally as the frequency function if a digital filter.
The discrete Fourier transform (DFT), occasionally called the finite Fourier transform, because of finite-domain discrete-time signals. It is widely used in finding the frequency of sampled signal, to solve partial differential equations.
Fourier transforms have many important applications in all the branches of pure and applied mathematics.

DFT ANALYSES :

DFT ANALYSES The sequence of N complex numbers x0,………xn-1 is transformed into the sequence of N complex numbers X0,…….,Xn-1 by the DFT according to the formula:
Consider the following sequence,
X {n} = {255,100,150,200,255,100,150,200}
X(0) = x(0).1 + x(1).1 + x(2).1 + x(3).1 + x(4) .1 + x(5).1 + x(6).1 + x(7).1
X(0) = 255+ 100+ 150+ 200+255+100+150+200
X(0) = 1410 (discuss how many no of *’s and +’s are involved).
Similarly if we compute for the X(1), X(2), X(3), X(4), X(5), X(6), X(7)

VEDIC MATHEMATICS :

VEDIC MATHEMATICS The ancient system of Vedic Mathematics was rediscovered from the Indian Sanskrit texts known as the Vedas, between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960).
According to his research all of mathematics is based on sixteen Sutras, or word-formulae.

MULTIPLICATION WITH URDHVA METHOD :

MULTIPLICATION WITH URDHVA METHOD Multiplication are mainly discussed in Vedic mathematics using many methods which are based on
1) Multiplication using deficits and excess
Changing the base to simplify the operation.
The methods used are :
URDHYA TRIYABHYAM
NIKHILAM NAVATASCHARAM DASHATAH
ANURUPYENA
VINCULUM
The method used in this is URDHYA TRIYABHAYAM which means vertically cross wise

MULTIPLICATION BY URDHYA METHOD :

MULTIPLICATION BY URDHYA METHOD

IN CASE OF 3 DIGIT BY 3 DIGIT :

IN CASE OF 3 DIGIT BY 3 DIGIT

VAN NEWMAN METHOD :

VAN NEWMAN METHOD 89*13
1 1011001
0 0000000
1 1011001
1 +1011001
------------------------
10010000101 When number of multiplication increases then for the product of shift add routine will
take time. If we have developed routine where number of multiplication are more by
Vedic mathematics methods. It may be efficient which will reduce our CPU time and
memory.

COMPARISION TABLE :

COMPARISION TABLE

Slide 14:

Conclusion
It can be easily observed from the above comparison table that Vedic mathematical multiplication process is very efficient. Implementation of Vedic multiplication will be more efficient in terms of its implementation using conventional multiplication process.
Looking ahead
Vedic mathematics deals with various topics of mathematics such as basic arithmetic, geometry, trigonometry, calculus etc. All these methods are very efficient as far as manual calculations are concerned.
Advantages of Vedic Mathematics
If all those methods are effectively implemented in computers, it will reduce the computational speed drastically. Therefore, it could be possible to implement a complete ALU using all these methods using Vedic mathematics methods.

REFERENCES :

REFERENCES Books:
Shakaracharya Sri Bharati Krishna Tirthaji ”Vedic Mathematics “–chapter 3, (32-34), published by MOTHILAL BANARASIDASS.
Sites:
Vedic mathematics - Wikipedia, the free encyclopedia

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