Principles of Signals and Systems
Principles of Signals and Systems. Instructor: Prof. Aditya K. Jagannatham, Department of Electrical Engineering, IIT Kanpur. This course is introduces the fundamental principles of signals and system analysis. These concepts form the building blocks of modern digital signal processing, communication and control systems. Hence, a sound understanding of these principles is necessary for all students of Electronics and Communication engineering (ECE), Electrical and Electronics Engineering (EEE), and Instrumentation Engineering (IE). The course will cover various basic tools of signal and system analysis such as signal classification, LTI systems, Properties of LTI Systems, Frequency Response, Laplace Transform, Z-Transform, Fourier Transform, Fourier Series, Discrete Time Fourier Transform (DTFT), Discrete Fourier Transform (DFT), Cascade/ Parallel structures and their various practical applications. Various concepts such as convolution, impulse/ frequency response, causality, stability of systems will be especially emphasized. Other additional topics such as state space techniques and solutions to state space equations will also be covered.
(from nptel.ac.in
Lecture 60 - Discrete Fourier Transform: Definition, Inverse DFT, etc.
VIDEO
Concepts covered in this lecture: Discrete Fourier Transform - 1. Definition 2. Inverse DFT 3. Relation between DFT and DFS 4. Relation between DFT and DTFT 5. Properties - Linearity, Time Shifting.
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Lecture 01 - Introduction to Signals and Systems, Signal Classification
Lecture 02 - Analog and Digital Signals
Lecture 03 - Energy and Power Signals
Lecture 04 - Real Exponential Signals
Lecture 05 - Memory/Memoryless and Causal/Non-Causal Systems
Lecture 06 - Properties of Linear Systems
Lecture 07 - Example Problems - Plot, Odd/ Even Components, Periodicity
Lecture 08 - Example Problems - Energy, Properties of Impulse, RL Circuit
Lecture 09 - Example Problems - Properties of Modulator, Eigenfunction of LTI System
Lecture 10 - Properties and Analysis of LTI Systems I
Lecture 11 - Properties and Analysis of LTI Systems II
Lecture 12 - Properties and Analysis of LTI Systems III
Lecture 13 - Properties of Discrete Time LTI Systems
Lecture 14 - Example Problems: LTI Systems - Convolution, Periodic Convolution, BIBO Stability
Lecture 15 - Example Problems: LTI Systems - Eigenfunction, etc.
Lecture 16 - Example Problems: Discrete Time LTI Systems - Output of System, etc.
Lecture 17 - Laplace Transform
Lecture 18 - Properties of Laplace Transform: Time Shifting Property, etc.
Lecture 19 - Properties of Laplace Transform: Convolution, Rational Function
Lecture 20 - Laplace Transform of LTI Systems
Lecture 21 - Laplace Transform Example Problems I
Lecture 22 - Laplace Transform Example Problems II
Lecture 23 - Laplace Transform of RL, RC Circuits
Lecture 24 - z-Transform
Lecture 25 - z-Transform Properties I
Lecture 26 - z-Transform Properties II
Lecture 27 - z-Transform of LTI Systems
Lecture 28 - z-Transform Examples: Evaluation of z-Transform, Region of Convergence
Lecture 29 - z-Transform Examples: Inverse z-Transform through Partial Fraction Expansion
Lecture 30 - z-Transform Examples: LTI System Output, Step/Impulse Response of LTI System
Lecture 31 - z-Transform Examples: Impulse Response of LTI System described by Difference Equation
Lecture 32 - Inverse z-Transform
Lecture 33 - Fourier Analysis of Continuous Time Signals and Systems: Introduction
Lecture 34 - Complex Exponential and Trigonometric Fourier Series
Lecture 35 - Conditions for Existence of Fourier Series
Lecture 36 - Introduction to Fourier Transform
Lecture 37 - Properties of Fourier Transforms I
Lecture 38 - Properties of Fourier Transforms II
Lecture 39 - Fourier Transform - Parseval's Relation
Lecture 40 - Fourier Transform of LTI Systems
Lecture 41 - Fourier Transform - Ideal and Non-ideal Filters
Lecture 42 - Fourier Analysis Examples I
Lecture 43 - Fourier Analysis Examples II
Lecture 44 - Fourier Analysis Examples III
Lecture 45 - Fourier Analysis Examples IV
Lecture 46 - Fourier Analysis Examples V
Lecture 47 - Fourier Analysis Examples VI
Lecture 48 - Fourier Analysis Examples VII
Lecture 49 - Fourier Analysis Examples VIII
Lecture 50 - Fourier Transform Examples: Filtering - Ideal Low Pass Filter
Lecture 51 - Fourier Transform Problems: Unit Step Response of RC Circuit
Lecture 52 - Sampling: Spectrum of Sampled Signal, Nyquist Criterion
Lecture 53 - Sampling: Reconstruction from Sampled Signal
Lecture 54 - Fourier Analysis of Discrete Time Signals and Systems: Introduction
Lecture 55 - Fourier Analysis of Discrete Time Signals and Systems: Duality, Parseval's Theorem
Lecture 56 - Discrete Time Fourier Transform: Definition, Inverse DTFT, Convergence, etc.
Lecture 57 - Discrete Time Fourier Transform Properties: Linearity, Time Shifting, etc.
Lecture 58 - Discrete Time Fourier Transform Properties: Differentiation in Frequency, etc.
Lecture 59 - Discrete Time Fourier Transform: Discrete Time LTI Systems
Lecture 60 - Discrete Fourier Transform: Definition, Inverse DFT, etc.
Lecture 61 - Discrete Fourier Transform Properties - Conjugation, Frequency Shift, Duality, etc.
Lecture 62 - Example Problems: DFS Analysis of Discrete Time Signals
Lecture 63 - Example Problems: DTFT of Cosine, Unit Step Signals
Lecture 64 - Example Problems: DTFT - Impulse Response
Lecture 65 - Example Problems: DTFT - Sampling
Lecture 66 - Example Problems: DTFT - FIR, Discrete Fourier Transform
Lecture 67 - Example Problems: DFT
Lecture 68 - Example Problems: DFT, IDFT in Matrix form
Lecture 69 - Group/ Phase Delay - Part I
Lecture 70 - Group/ Phase Delay - Part II
Lecture 71 - IIR Filter Structures: Direct Form I, Direct Form II
Lecture 72 - IIR Filter Structures: Transpose Form
Lecture 73 - IIR Filter Structures: Example
Lecture 74 - IIR Filter Structures: Cascade Form
Lecture 75 - IIR Filter Structures: Parallel Form I, Parallel Form II, Examples