Signal System Lab 9 Laplace Transform using python

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Module I: Classification of Signals and Systems: Representation of signals, Basic Operation on Signals, Elementary Signals, representation of signals using elementary signals, Classification of Signals: Deterministic and random, periodic and non-periodic, Energy and power, causal and non-causal, even and odd signals,

Module II: Classification of Systems: lumped and distributed parameters, static and dynamic, causal and non-causal, linear and non-linear, time variant and time invariant, stable and unstable, invertible and non-invertible, impulse response and step response,
convolution, input-output behaviour with aperiodic convergent inputs, characterization of causality and stability of linear shift invariant systems, system representation through differential equations and difference equations, Periodic and semi-periodic inputs to an LSI system, the notion of a frequency response and its relation to the impulse response, Linear Time Invariant Systems: Response of a Continuous Time LTI System and Convolution Integral Using a Graphical Method, Properties of continuous time LTI systems, Eigenfunctions of continuous time LTI systems, Systems described by Differential Equations, Response of a discrete time LTI system, Convolution Sum, Properties of a discrete time LTI system, Eigenfunctions of Discrete Time LTI Systems, Systems described by Difference Equations

Module III: Fourier Representation of Signals: Representation of Continuous Time Fourier Series (CTFS), the existence (convergence) of the Fourier series (Dirichlet Conditions), the trigonometric form of a Fourier series, cosine representation, wave symmetry, exponential Fourier series, Fourier spectrum, power representation using Fourier series, Gibbs phenomenon, and properties of CTFS

Fourier Transform: Fourier transform of non-periodic functions, Magnitude and phase representations of the Fourier transform, existence of the Fourier transform, convergence of Fourier Transform, the Fourier transform of standard signals, properties of continuous time Fourier transform, Fourier transform of periodic signals, introduction to the Hilbert transform,

Module IV : the Laplace transform, notion of Eigen functions of LSI systems, a basis of Eigen functions, region of convergence, poles and zeros of system, Laplace domain analysis, solution to differential equations and system behaviour.

Module V: Z Transform: Introduction, some common sequences Z transforms, finite duration sequences, and Z transforms and convergence regions Properties of the region of convergence, Properties of the Z transform, Inverse Z transform, LTI system transform analysis Stability and causality, difference equation solution using the Z transform

Module VI : The sampling theorem and its implications- spectra of sampled signals,
reconstruction: ideal interpolator, zero-order hold, first-order hold, and so on,aliasing and its effects, relation between continuous and discrete time systems.

Module IV:
Module V: Time and Frequency Characterization of Signals and Systems: The magnitude-phase representation of the Fourier transform, and the magnitude-phase representation of the frequency response of LTI systems: Linear and nonlinear phases, group delay

Text Books:
1. Signals & Systems: Alan Oppenheim & Alan Wilsky, S Nawab, PHI.(Unit-IV) 4.

Reference Books:
1. Simon Haykin, Signals and Systems, 2nd Edition, Wiley India.
2. Signals, Systems and Communications: B.P. Lathi, BS Publications.

2. R.F. Ziemer, W.H. Tranter and D.R. Fannin, "Signals and Systems - Continuous and
Discrete," 4th edition, Prentice Hall,1998.

3. B.P. Lathi, "Signal Processing and Linear Systems," Oxford University Press,1998.

4. Douglas K. Lindner, "Introduction to Signals and Systems," McGraw Hill International
Edition:1999.

5. Simon Haykin, Barry van Veen, "Signals and Systems," John Wiley and Sons (Asia)
Private Limited,1998.

6. V. Krishnaveni, A. Rajeswari, “"Signals and Systems," Wiley India Private Limited,
2012.

7. Robert A. Gabel, Richard A. Roberts, "Signals and Linear Systems," John Wiley and
Sons,1995.

8. M. J. Roberts, "Signals and Systems - Analysis using Transform methods and
MATLAB," TMH,2003.

9. J. Nagrath, S. N. Sharan, R. Ranjan, S. Kumar, "Signals and Systems," TMH New Delhi,

Reference Programming Languages:
1. Python : Open source
2. MATLAB