Signals and Systems: From Fundamentals to Fourier & Laplace

Master system properties, convolution, Laplace and Fourier analysis, and signal modeling with real-world examples.

What you'll learn
- Key properties of systems: linearity, time invariance, causality, and stability
- Common signal types: unit step, delta, sinusoids, exponentials, and more
- Signal operations: scaling, shifting, even/odd decomposition, and energy/power
- Convolution and its role in analyzing LTI systems
- Laplace transforms and their application in system analysis
- Inverse Laplace transforms and pole-zero analysis
- Modeling and analyzing a DC motor using Laplace techniques
- Fourier series and Fourier transforms for frequency-domain analysis
- AM modulation, sampling theorem, and signal reconstruction

Requirements
- Basic knowledge of calculus and linear algebra
- Familiarity with differential equations is helpful but not required

Description
Understandingsignals and systemsis essential for anyone pursuing a career inelectrical engineering,computer engineering, orsignal processing. These concepts form the theoretical backbone of modern technologies—from communication systems and control engineering to audio processing, robotics, and embedded systems.

But for many students, signals and systems can feel abstract and mathematically intense. That’s where this course comes in.

“Signals and Systems Masterclass: From Fundamentals to Fourier and Laplace”is a comprehensive, student-friendly course designed to make complex topics accessible and practical. This course walks you through the essential building blocks of signals and systems with clarity, structure, and real-world relevance.

You’ll begin by exploring thecore properties of systems—linearity, time invariance, causality, and stability—before diving into thevariety of signalsused in engineering, such as unit step, delta, sinusoidal, exponential, and periodic signals. You’ll learn how to manipulate and classify signals using operations like scaling, shifting, and decomposition into even and odd components.

From there, you’ll masterconvolution, a cornerstone of system analysis, and understand how it reveals the behavior ofLinear Time-Invariant (LTI) systems. You’ll then move into theLaplace transform, learning how to analyze systems in the s-domain, assess stability using pole-zero plots, and apply inverse transforms to return to the time domain.

The course also includes a practical case study:modeling a DC motorusing Laplace transforms to analyze its response to inputs and initial conditions—bridging theory with engineering application.

Finally, you’ll exploreFourier analysis, learning how to represent signals in the frequency domain usingFourier seriesandFourier transforms. You’ll apply these tools to analyze periodic signals, understand modulation, and grasp thesampling theorem, which underpins digital signal processing.

Each topic is supported bystep-by-step examples,visual explanations, andreal-world applicationsto ensure deep understanding and long-term retention.

By the end of this course, you’ll not only understand the theory behind signals and systems—you’ll be able to apply it confidently in engineering contexts, academic exams, and future studies indigital signal processing,control systems, and beyond.

Who this course is for:
- Electrical and computer engineering students
- Anyone studying signals and systems
- Learners preparing for exams like FE, GATE, or university-level courses
- Engineers and professionals seeking a refresher in signal processing fundamentals
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