Digital Electronics: Fourier Series and Noise in Digital Communication

Digital Electronics
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LAB TWO
PART I: FOURIER SERIES
Introduction
A Fourier series is an enlargement of an intermittent function in form of an unlimited
summation of sines and cosines. Fourier series utilize orthogonally interactions of
the sine and cosine tasks. The calculation and learning of Fourier series is identified
as harmonic investigation and is particularly beneficial as a method to break up
a random intermittent function to a set of modest terms that are able to be worked out, solved
independently, and then recombined to get the answer to the inventive task or an estimate to
it to whatever precision is anticipated or hands-on1. Illustrations of uninterrupted estimates to
collective functions by use of Fourier series are demonstrated in this task.
In general, since the superposition norm holds for answers of a linear consistent ordinary
differential equation, if this kind of equation can be answered in the instant of a single
sinusoid, the answer for a random function is directly accessible by expressing the initial
function as a Fourier series and then plugging in the answer for every sinusoidal element. In
some unusual circumstances where the Fourier series can be summed in an enclosed form,
this method can even produce logical answers.6
Lab 2 Part i Objectives
General Objective
To check that any periodic signal can certainly be seen as a sum of sine waves in order to
demonstrate the model of Fourier series.
Specific Objective
i. To illustrate the model of Fourier series.
1Brey, B. B. (2015). Digital electronics. Indianapolis, Ind, Bobbs-Merrill.
6Predko, M. (2015). Digital electronics guidebook. New York, McGraw-Hill.

Digital Electronics 3
ii. To check that periodic signal can be a summation of sine waves.
EXPERIMENT 1: SQUARE WAVE
EXPERIEMENT 2: TRIANGULAR WAVE
2Barnes, C., & O'Farrell, N. (2016). Hack proofing your wireless network. Rockland, MA:
Syngress Pub.
3Kleitz, W. (2014). Digital electronics: a practical approach with VHDL. Harlow, Pearson
Education Limited.
4Ndjountche, T. (2016). Digital electronics. 1, 1. http://search.ebscohost.com/login.aspx?
direct=true&scope=site&db=nlebk&db=nlabk&AN=1253855.

EXPERIEMENT 3: SAWTOOTH WAVE
Comment
From the simulations in the square the signal with has harmonics with order 3 and 7 while the
other two signals are sinusoidal. The Fourier series of triangular signal results with sinusoidal
harmonics while in saw-tooth the signal with 4th harmonic is non-sinusoidal.
1Brey, B. B. (2015). Digital electronics. Indianapolis, Ind, Bobbs-Merrill.
6Predko, M. (2015). Digital electronics guidebook. New York, McGraw-Hill.