EEET2369: Signals and Systems - The Fourier Series - Engineering Assignment Help

Assignment Task:

Learning Outcomes 

Upon successful completion of this laboratory exercise you will be able to: 

• Recognise the spectrum of periodic and aperiodic waveforms and explain the process of generating these. 

• Describe the relationship between the periodic waveforms generated and their Fourier series. 

• Describe the relationship between the aperiodic waveforms generated and their Fourier transforms. 

• Recognise the limitations of the Fourier transform. 

Introduction to the laboratory 

Fourier analysis techniques are essential in signal processing to determine the frequencies that make up various types of signals. The two most common methods used to decompose a signal into its constituent frequency components are: 

- The Fourier series, used in the analysis of periodic signals, and 

- The Fourier transform, used in a more general sense to analyse both periodic and aperiodic signals. 

In digital signal processing (DSP) an algorithm called the fast Fourier transform (FFT) is used to perform Fourier transforms on digital signals, this algorithm was a huge breakthrough in computing as its development allowed for efficient Fourier analysis to be performed on all types of digital signals. 

This lab is going to firstly look at periodic and non-periodic signals and examine how to apply Fourier techniques to these signals to extract frequency information. Since MATLAB is a digital system this lab will also look at how the fft() function can be used to perform Fourier analysis on these different types of signals in a digital environment.

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