CTFT Explained in One Shot: Convolution, Parseval’s & Properties | Signals and Systems Module 2 ;L2

Welcome to Module 2 (Lecture 2) of Signals and Systems! 📶📉

In this video, Er Amit Kumar Verma moves from Fourier Series to the Continuous Time Fourier Transform (CTFT). While Fourier Series is for periodic signals, CTFT is the ultimate tool for analyzing Aperiodic Signals.

Based on the JUT (Jharkhand University of Technology) and AICTE Model Curriculum for B.Tech 2nd Year (3rd Sem) students, this lecture simplifies complex integration into easy algebraic operations.

📽️ Topics Covered in Module 2 - Lecture 2 (Based on PPT):
✅ 1. Introduction to CTFT:
Why do we need Fourier Transform? (Analysis of Aperiodic Signals).
Linearity Property: Superposition principle explained ($ax_1 + bx_2 \leftrightarrow aX_1 + bX_2$) 4
✅ 2. Important Properties of CTFT:
Time Shifting:
How shifting in time affects phase but keeps magnitude constant ($e^{-j\omega t_0}$) 5.
Time Scaling: The Tape Recorder Effect – Compression in time = Expansion in frequency 6.
Differentiation: Why differentiation amplifies high frequencies7.
Parseval’s Relation: Conservation of Energy in Time and Frequency domains 8.
Convolution Property: The most powerful tool! Convolution in Time = Multiplication in Frequency ($Y(j\omega) = X(j\omega)H(j\omega)$) 9.

🎓 Why is this Lecture Crucial?

Exam Point of View: Derivation of "Rectangular Pulse to Sinc Function" and "State and Prove Convolution Property" are frequent questions in JUT exams.


Concept Clarity: Understanding the inverse relationship between Time and Frequency duration.

👨‍🏫 Instructor & Credits:

Subject Expert: Er Amit Kumar Verma

Channel Name: EduSpark by Amit

Subject: Signals and Systems (EC305PC)

Module: Unit 2 - Fourier Transform

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📌 Important Playlists:

🔴 Signals & Systems Full Course: [Playlist Link Yahan Dalein]

🔴 Module 2 Lecture 1 (Fourier Series): [Link Here]

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