Signals and Systems

NOTE: In this course, the explanation will be in Hindi, but the scientific terms, assignments and exams will be in English.

COURSE OUTLINE: This course will introduce the students to the basics of signal processing and systems analysis. We will focus on continuous-time signals and systems, but also give an introduction to discrete-time signals and systems towards the end of the course. This is a very important course for all engineers working in the electronics and communications domain.

Introduction to Signals & Systems.
mod01lec01- Real and Complex Number.
mod01lec02-Sinusoid and Phasor.
mod01lec03-Limits and Continuity.
mod01lec04-Differentiation and Integration.
mod01lec05-L’Hospital’s Rule.
mod01lec06-Input-Output Relation for RLC circuits.
mod01lec07-Unit Step and Delta function.
mod02lec08-Continuous and Discrete Time Systems.
Even Signal; Odd Signal.
mod02lec10-Orthogonality of Signals.
mod02lec11-Shifting and Scaling in Continuous Time - I.
mod02lec12-Shifting and Scaling in Continuous Time - II.
mod02lec13-Shifting and Scaling in Discrete Time.
mod02lec14-Signal and Noise.
mod02lec15-Signals in the Physical World.
mod02lec16-Signals and Sensory Perception.
Frequency Domain Representation.
Definition of Fourier Transform.
Fourier Transform Examples - I.
Dirichlet Conditions.
Inverse Fourier Transform.
Fourier Transform Examples - II.
Frequency-Time Uncertainty Relation.
Fourier Transform : Linearity, Time Shifting and Time Scaling.
Fourier Transform : Derivative Property.
Fourier Transform : Multiplication and Convolution Property.
Fourier Transform : Integral Property.
Fourier Transform Example - III.
Fourier Transform Example - IV.
Fourier Transform of Noise.
Types of Noise.
Overview of Systems and General Properties.
Linearity and Time Invariance.
LTI System Examples.
Frequency Response of RLC circuits - I.
Frequency Response of RLC circuits - II.
LCCDE Representation of Continuous-Time LTI Systems.
Frequency Domain Representation of LCCDE Systems.
Time Domain Representation of LTI Systems.
Continuous-Time Convolution Integral.
Continuous-Time Convolution Example I.
Continuous-Time Convolution Example II.
Continuous-Time Convolution Example III.
LTI Systems : Commutative, Distributive and Associative.
LTI Systems : Memorylessness and Invertibility.
LTI Systems : Causality and Stability.
Fourier Transform in Complex Frequency Domain.
Laplace Transform : Poles and Zeros.
Laplace Transform : Region of Convergence [ROC].
Laplace Transform Examples I.
Laplace Transform Examples II.
Laplace Analysis of LTI Systems.
Laplace Analysis of RLC Circuits I.
Laplace Transform : Linearity, Shifting and Scaling.
Laplace Transform : Derivative and Integral.
Laplace Transform : Causality and Stability.
Laplace Analysis of LTI Systems Example I.
Laplace Analysis of LTI Systems Example II.
Laplace Analysis of First Order RLC Circuits.
Laplace Analysis of Second Order RLC Circuits.
Fourier Transform of Periodic Signals.
Fourier Series Representation in Continuous-Time.
Fourier Series Properties I.
Fourier Series Properties II.
LTI System Response for Periodic Input Signal.
Fourier Series in Continuous-Time : Examples I.
Fourier Series in Continuous-Time : Examples II.
mod10lec68-Discrete-Time Convolution Sum.
mod10lec69-Discrete-Time Convolution Sum Examples and Properties.
mod10lec70-LCCDE Representation of Discrete-Time LTI Systems.
mod10lec71-Impulse Train Sampling.
mod10lec72-Reconstruction of Continuous-Time Signal.
mod10lec73-Nyquist Sampling Theorem and Aliasing.
mod11lec74-Fourier Transform of Sampled Signals.
mod11lec75-DTFT Examples I.
mod11lec76-DTFT Properties I.
mod11lec77-DTFT Properties II.
mod11lec78-DTFT Properties III.
mod11lec79-DTFT Examples II.
mod12lec80-DTFT in Complex Frequency Domain.
mod12lec81-Z-Transform : Properties of ROC.
mod12lec82-Z-Transform Properties II.
mod12lec83-Z-Transform Properties II.
mod12lec84-Z-Transform Properties III.
mod12lec85-Z-Transform Examples I.
mod12lec86-Z-Transform Examples II.
mod12lec87-Block Diagram Representation.