Analyze signals, solve circuits and understand harmonics using Fourier series in engineering applications
Hello and welcome!
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.
Course Content
- Introduction to the Course –> 1 lecture • 4min.
- A Quick Recap of Functions –> 10 lectures • 31min.
- A Quick Recap of Elementary Mathematics –> 8 lectures • 29min.
- Fourier Series –> 8 lectures • 33min.
- Waveform Symmetries –> 4 lectures • 15min.
- Properties of Fourier Coefficients –> 8 lectures • 17min.
- Applications of Fourier Series –> 9 lectures • 33min.
- Conclusion and References –> 1 lecture • 2min.
Requirements
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 Functions
Reinforces essential concepts related to mathematical functions that are critical for understanding Fourier series. - Module 2: A Quick Recap of Elementary Mathematics
Covers foundational mathematical tools necessary for performing the computations involved in Fourier analysis. - Module 3: Fourier Series
Introduces and explains the core concept of Fourier series in a step-by-step and accessible manner, starting from the basics. - Module 4: Waveform Symmetries
Explores waveform symmetry properties that simplify mathematical derivations, reducing the complexity of calculations. - Module 5: Properties of Fourier Coefficients
Discusses key properties that allow for efficient computation of Fourier coefficients, even for complex waveforms. - Module 6: Applications of Fourier Series
Applies Fourier series to real-world waveforms, demonstrating practical utility across various engineering scenarios. - Module 7: Conclusion and References
Summarizes 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!