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# Principles of Signals and Systems

## Syllabus

Introduction - Principles of Signals and Systems - Prof. Aditya K. Jagannatham.
Principles of Signals and Systems- Introduction to Signals and Systems, Signal Classification.
Analog and Digital Signals.
Energy and Power Signals.
Real Exponential Signals.
Memory/Memory-less and Causal/ Non-Causal Systems.
Properties of Linear Systems.
Example Problems-1.
Example Problems-2.
Example Problem-3.
Properties and Analysis of LTI Systems-I.
Properties and Analysis of LTI Systems-II.
Properties and Analysis of LTI Systems-III.
Properties of Discrete Time LTI Systems.
Example Problems LTI Systems-I.
Example Problems LTI Systems-II.
Example Problems DT-LTI Systems.
Laplace Transform.
Laplace Transform Properties-I.
Laplace Transform Properties-II.
Laplace Transform of LTI Systems.
Laplace Transform Example Problems-I.
Laplace Transform Example Problems-II.
Laplace Transform of RL, RC Circuit.
Z-Transform.
Z-Transform Properties-I.
Z-Transform Properties-II.
Z-Transform of LTI Systems.
Z-Transform Examples-I.
Z-Transform Examples-II.
Z-Transform Examples-III.
Z-Transform Examples-IV.
Inverse Z-Transform.
Fourier Analysis Introduction.
Complex Exponential and Trigonometric FS.
Conditions for Existence of FS.
Fourier Transform (FT) Introduction.
Properties of Fourier Transform-I.
Properties of Fourier Transform-II.
Fourier Transform – Parseval’s Relation.
Fourier Transform of LTI Systems.
FT- Ideal and Non-Ideal Filters.
Fourier Analysis Examples-I.
Fourier Analysis Examples-II.
Fourier Analysis Examples-III.
Fourier Analysis Examples-IV.
Fourier Analysis Examples-V.
Fourier Analysis Examples-VI.
Fourier Analysis Bode Plot-I.
Fourier Analysis Bode Plot-II.
Fourier Transform Examples: Filtering – Ideal Low Pass Filter.
Fourier Transform Problems: Unit Step Response of RC Circuit, Sampling of Continuous Signal.
Sampling: Spectrum of Sampled Signal, Nyquist Criterion.
Sampling: Reconstruction from Sampled Signal.
Fourier Analysis of Discrete Time Signals and Systems – Introduction.
Fourier Analysis of Discrete Time Signals – Duality, Parseval’s Theorem.
Definition, Inverse DTFT, Convergence,DTFT and z-Transform, DTFT.
DTFT Linearity, Time Shifting, Frequency Shifting, Conjugation, Time-Reversal, Duality.
DTFT Differentiation in Frequency, Difference in Time, Convolution, Multiplication.
DTFT: Discrete Time LTI Systems – LTI Systems Characterized by Difference Equations.
Definition, Inverse DFT, Relation between DFT and DFS, Relation between DFT and DTFT, Properties.
Conjugation, Frequency Shift, Duality, Circular Convolution, Multiplication, Parseval’s Relation.
Example Problems: DFS Analysis of Discrete Time Signals, Problems on DTFT.
Example Problems: DTFT of Cosine, Unit Step Signals.
DTFT Example Problems-III.
DTFT Example Problems-IV.
DTFT Example Problems-V.
DFT Example Problems-I.
Example Problems: DFT, IDFT in Matrix form.
Group/ Phase Delay – Part I.
Group/ Phase Delay – Part II.
IIR Filter Structures: DF–I, DF–II.
IIR Filter Structures: Transpose Form.
IIR Filter Structures: Example.
IIR Filter: Parallel Form – I & II.

### Taught by

Principles of Signals and Systems - IITK

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