Understanding Fourier Series, Fourier Transform, and Laplace Transform 

I'm excited to share this technical report exploring the relationships between Fourier Series, Fourier Transform, and Laplace Transform. This document was originally created as a university assignment for module EN 1020 and received positive feedback from TA for its clarity and insights. 

 What You'll Find in This Document

This report explores the fundamental mathematical concepts used in signal processing and analysis, including:

• Detailed explanations of Fourier Series for periodic signals

• The transition from Fourier Series to Fourier Transform

• Applications and limitations of Laplace Transform

• Key differences between these transforms including domain representation and convergence requirements

• Visual examples and graphical representations of transform applications

The document walks through both the theoretical foundations and practical applications of these transforms, with special attention to equation 5-7 which illustrates how Fourier Transforms relate to Fourier Series through impulse functions.

I've enhanced the original assignment by adding proper citations and a bibliography to acknowledge the source materials, particularly for figures adapted from Oppenheim's classic text on Signals and Systems.

Whether you're studying electrical engineering, physics, or applied mathematics, I hope you find this exploration valuable!