Applications Of Convolution

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Applications of Convolution in Communications
V.V. Jiménez García, F. E. González Bonilla, P.F.N. Castro León, Members, USA

Abstract— The reason of this work is to give a general view of the main purposes of the Convolution process. Within these pages there will be some cases where the Convolution is applied, but there’s going to be a specific instance that is held and emphasized amongthese pages which is, Communication issues. The importance of the Convolution process, applied to the Communications, is focused on the reduction of the signal’s ‘Noise’ present in every Communication Process. This effect is minimized by the Convolution, which is the matter that is going to be held from now on, between these pages.


Key Words—Digitalization, Convolution, Communications,Signals, Noise, LTI


INTRODUCTION

T
he convolution has many applications in the different professional branches and it’s very helpful solving many problems that they present.

In this article, above all things, we want to emphasize in how convolution is useful for the communications, which principally has two very important different processes which help to improve in the rapid development ofthis area.
The first process occurs in mathematics, which obtains a real solution with the frequent problems when we want to transmit information through a communication system.
The second process has enabled people to live in this digital network age; this is an indispensable process for digitalization and filtering continuous signals.

On communications there are many problems transmittingthe information, but the main problem is the “noise" which has not allowed faster progression of this age which is doing this world smaller day after day. Noise is called to any unwanted signal mixed with the useful signal sent. Noise has multiple causes, may be caused by a resistor temperature of an electronic part, interference by other signal or simply because there are not electronic perfectparts. However, this noise may be limited so that the quality of the signal is acceptable; this is possible through to the convolution method.
Convolution refers the distribution process of a function, in each point of another different function and this method only applied in Linear Time-Invariant Systems (LTI). LTI systems are characterized by their impulse responses, that is to say, theiroutput by a impulsive response.

To convert an analog signal to a digital signal is used signal sampling, this in order to be able to save the signal values finitely.
As a rule the electronic parts that get the signal to convert a digital signal have a filter, it depends of the device requirements. Signal digital filtering can be done both time and frequency domain. For example, when someone wantsto have a high-resolution signal, device needs a Low Pass Filter (LPF), which allows a close approximation to the analog signal. LPF is implemented with convolution technique in time domain.


Convolution and communications


As is known by everyone, communications has become so important thanks to internet. Through internet is possible to buy something, study even work. In internet as inother communication systems there are some problems. For example, if someone sends a message to other person, they would like to know if the message received is the same that was sent. There are many facts that could change or damage the message as noise or even intruder.

To be sure of getting the correct message there is an existing technique of forward error correction called convolutionalcode. Convolutional code is a type of error correcting code. An error correcting code is a set of techniques to enhance the reliability of message transmitted in some type of communication. So, convolutional code takes three parameters to encode the input bits: n, number of output bits, k, number of input bits, m, number of memory registers. k/n is called the code rate, and means the efficiency of...