Engineering Mathe | Z-Transform :Definition, Formula, Examples & Unilateral vs Bilateral Z-Transform

Welcome to Study Stepwise! In this Engineering Mathematics lecture, we introduce the **Z-Transform**, an essential mathematical tool for analysing discrete-time signals and systems. ⏱️ VIDEO CHAPTERS 00:00 Introduction to the Z-Transform 00:20 Choosing the Right Mathematical Tool 00:47 Why Do We Use the Z-Transform? 0234:00 The Z-Transform Formula 04:53 What Is a Discrete-Time Sequence? 06:10Building a Sequence from Shifted Impulses 07:43 Deriving the General Formula 09:29 Worked Example 10:23 Practice Question 12:12 Unilateral vs Bilateral Z-Transform 13:31 Summary and Key Takeaways 📚 WHAT YOU WILL LEARN 1. Introduction to the Z-Transform and its applications. 2. Why we use transforms to simplify mathematical problems. 3. The Z-Transform formula and the meaning of its symbols. 4. How powers of z⁻¹ represent delays in discrete-time sequences. 5. Representing a sequence using shifted unit impulses. 6. Deriving the Z-Transform from its definition. 7. Solved examples using finite discrete-time sequences. 8. The difference between unilateral (one-sided) and bilateral (two-sided) Z-Transforms. 9. A practice question to test your understanding. 🎓 WHO SHOULD WATCH? University students studying Engineering Mathematics, Signals and Systems, Digital Signal Processing (DSP), and Z-Transform fundamentals. 💡 Pause the lecture and attempt the practice question before watching the solution. Subscribe to Study Stepwise for step-by-step lessons in Mathematics, Physics, and Chemistry. 📌 Learn • Understand • Apply #EngineeringMathematics #ZTransform #SignalsAndSystems #DiscreteTimeSignals #DSP #StudyStepwise