# Fourier Series

**Topics:**Square wave, Fourier series, Fourier analysis

**Pages:**18 (3650 words)

**Published:**November 10, 2010

Anthony Njuguna

ee08u122

Abstract Many applications in communication and systems are concerned with propagation of signals through networks. The resultant output signal is dependent on the properties of both the input signal and the processes acting on the signal. This is a laboratory Report will be focusing on using Fourier series to analyze waveforms and the synthesis of waveforms. The report highlights Fourier series analysis is a simple effective approach to analyse periodic signals. It will guide the reader through an experiment conducted in a lab to examine the effects of using Fourier analysis on signals and their waveforms. It should help the reader get a better understanding at signal analysis by looking at meaning of signal spectrum, how different waveforms have different spectrum but that standard results exist for standard waveforms. It should aid in the effects of spectrum limitations on the transmission of signals by looking at their bandwidth and bit rates.

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Anthony Njuguna

ee08u122 Contents

Abstract...............................................................................................................................1 Introduction.........................................................................................................................3 Background Theory...............................................................................................................4 The Experiment.....................................................................................................................6 Part A. To use Fourier analysis to observe the effect of limiting the bandwidth of a real signal....................6

Part B. To use Fourier analysis to decide bandwidth needed to support a binary representation of an analogue signal................................................................................................................................15 Part C. To use Fourier analysis to look at an ‘unusual’ signal. ..........................................................16 Part D. To use Fourier analysis to examine noise............................................................................18

Conclusion.............................................................................................................................19

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Anthony Njuguna Introduction

ee08u122

The report is based on an experiment conducted in a lab using a java applet to simulate Fourier series analysing using time and frequency domain representations of signals. The study of signals and their waveforms is central to circuit theory, telecommunication, control engineering and instrumentation. The signal themselves exist and propagate in the time domain. Using Fourier analysis a real signal in the time domain can be characterised by its spectrum in the frequency domain and can be represented by the appropriate sum of sin and Cos components. This report helps to understand the physical meaning of a signal spectrum, how each different waveform has different spectrum or spectral density, how certain standard results exit for standard waveforms and the effects of spectrum limitation on the transmission of signals. The report is separated into four sections to help understand the points above. The four sections are as follows: Using Fourier analysis to observe the effect of limiting the bandwidth of a real signal. Using Fourier analysis to decide the bandwidth needed to support a binary representation of an analogue signal. Using Fourier analysis to look at an ‘unusual’ signal. Using Fourier analysis to examine noise.

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Anthony Njuguna

ee08u122

Background Theory

Types of signals Signals can be classified in the three main types of signals; periodic, aperiodic and random and each can be analysed by particular mathematical techniques in this report...

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