Fourier Series For Engineers: From Basics To Applications

Analyze signals, solve circuits and understand harmonics using Fourier series in engineering applications

What you'll learn

Introduction to Functions. Periodicity of a Function, Average Value of a Function, Correlation between Mathematical Functions and Electrical Signals

Even and Odd Functions, Half Wave Symmetry (HWS), Quarter Wave Symmetry (QWS), Delta Function, Periodic Pulse Function, Sinc Function

Vectors and Orthogonality, Orthogonality of Functions, Introduction to Elementary Calculus, Trigonometric Identities

Integration by Parts, Introduction to Complex Numbers, Complex Conjugate, Euler's Formula

Evolution of Fourier Series, Introduction to Fourier Series, Convergence of Fourier Series, Convergence of Fourier Series at Discontinuities

Trigonometric Fourier Series, Exponential Fourier Series, Importance of TFS and EFS, Correlation between Time and Frequency Domain

Fourier Series of Even Functions, Fourier Series of Odd Functions, Fourier Series of HWS Functions, Fourier Series of QWS Functions

Properties of Fourier Coefficients, Linearity Property, Symmetry Property, Time Shifting Property

Time Reversal Property, Frequency Translation Property, Differentiation Property, Integration Property

Real World Applications of Fourier Series, Fourier Coefficients using LTSpice Simulation, Periodic Pulse Waveform, Rectangular Waveform

Gibbs Phenomenon, Triangular Waveform, Sawtooth Waveform, Non-ideal Square Waveform, Fourier Series to Fourier Transforms

Requirements

Understanding of Basic Electrical Circuits

Basic proficiency in mathematics - algebra, calculus, complex numbers

Genuine Interest in the Subject Matter

Description

Hello and welcome!Thank you for choosing this course titled “Fourier Series for Engineers: From Basics to Applications.”This comprehensive, three-hour course is thoughtfully designed to provide you with a strong theoretical foundation in Fourier series while bridging the gap between abstract theory and real-world applications.Rather than spending countless hours navigating multiple textbooks, this course offers a well-structured and time-efficient learning path—from fundamental principles to advanced concepts. To support your learning, the course includes knowledge-check quizzes and LTSpice simulation files at key points, allowing you to apply what you've learned in practical, simulation-based scenarios. Course Curriculum Overview:Module 1: A Quick Recap of FunctionsReinforces essential concepts related to mathematical functions that are critical for understanding Fourier series.Module 2: A Quick Recap of Elementary MathematicsCovers foundational mathematical tools necessary for performing the computations involved in Fourier analysis.Module 3: Fourier SeriesIntroduces and explains the core concept of Fourier series in a step-by-step and accessible manner, starting from the basics.Module 4: Waveform SymmetriesExplores waveform symmetry properties that simplify mathematical derivations, reducing the complexity of calculations.Module 5: Properties of Fourier CoefficientsDiscusses key properties that allow for efficient computation of Fourier coefficients, even for complex waveforms.Module 6: Applications of Fourier SeriesApplies Fourier series to real-world waveforms, demonstrating practical utility across various engineering scenarios.Module 7: Conclusion and ReferencesSummarizes key takeaways and provides curated references for deeper exploration.By the end of this course, you’ll have built a solid theoretical foundation with practical insights—essential for mastering Fourier analysis and its applications in various engineering domains.We are excited to have you onboard and look forward to guiding you on this enriching learning journey.Let’s get started!

Overview

Section 1: Introduction to the Course

Lecture 1 Introduction

Section 2: A Quick Recap of Functions

Lecture 2 Introduction to Functions

Lecture 3 Periodicity of a Function

Lecture 4 Average Value of a Function

Lecture 5 Correlation between Mathematical Functions and Electrical Signals

Lecture 6 Even and Odd Functions

Lecture 7 Half Wave Symmetry (HWS)

Lecture 8 Quarter Wave Symmetry (QWS)

Lecture 9 Delta Function

Lecture 10 Periodic Pulse Function

Lecture 11 Sinc Function

Section 3: A Quick Recap of Elementary Mathematics

Lecture 12 Vectors and Orthogonality

Lecture 13 Orthogonality of Functions

Lecture 14 Introduction to Elementary Calculus

Lecture 15 Trigonometric Identities

Lecture 16 Integration by Parts

Lecture 17 Introduction to Complex Numbers

Lecture 18 Complex Conjugate

Lecture 19 Euler's Formula

Section 4: Fourier Series

Lecture 20 Evolution of Fourier Series

Lecture 21 Introduction to Fourier Series

Lecture 22 Convergence of Fourier Series

Lecture 23 Convergence of Fourier Series at Discontinuities

Lecture 24 Trigonometric Fourier Series

Lecture 25 Exponential Fourier Series

Lecture 26 Importance of TFS and EFS

Lecture 27 Correlation between Time and Frequency Domain

Section 5: Waveform Symmetries

Lecture 28 Fourier Series of Even Functions

Lecture 29 Fourier Series of Odd Functions

Lecture 30 Fourier Series of Half Wave Symmetric Functions

Lecture 31 Fourier Series of Quarter Wave Symmetric Functions

Section 6: Properties of Fourier Coefficients

Lecture 32 Properties of Fourier Coefficients

Lecture 33 Linearity Property

Lecture 34 Symmetry Property

Lecture 35 Time Shifting Property

Lecture 36 Time Reversal Property

Lecture 37 Frequency Translation Property

Lecture 38 Differentiation Property

Lecture 39 Integration Property

Section 7: Applications of Fourier Series

Lecture 40 Real World Applications of Fourier Series

Lecture 41 Fourier Coefficients using LTSpice Simulation

Lecture 42 Periodic Pulse Waveform

Lecture 43 Rectangular Waveform

Lecture 44 Gibbs Phenomenon

Lecture 45 Triangular Waveform

Lecture 46 Sawtooth Waveform

Lecture 47 Non-ideal Square Waveform

Lecture 48 Fourier Series to Fourier Transforms

Section 8: Conclusion and References

Lecture 49 The Conclusion

Analog circuit design engineers, Signal processing engineers,All engineering students,Power electronics and power converter designers,Anyone preparing for job interviews,Anyone looking for a quick subject revision