Fourier Series Analysis

by Ashley Pena

Submitted : Spring 2018

This project report examines how to represent a complex waveform using its sinusoidal components and average value. It presents how a square wave could be represented in its Fourier series components signal using the average and the respective sinusoidal harmonics. A Fourier series is the summation of an infinite series of sine and cosine functions which can represent the expanded form of a periodic function (Hayt and Kemmerly). This approach is used to represent a 120 VAC supply at an amplitude 120 V_rms and at a frequency of 60 Hz. By using the equation of a Fourier series, the series representation of the respective cosine and sine functions are derived and plugged back into the original Fourier series equation. The project concludes from the results that the mathematical representation using Fourier series of a square waveform signal obtained indeed represents the complex waveform in its sinusoidal components and average value which is verified using the program MATLAB.

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