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Ec 4401 and EC 4203
Signal and Systems- REPRESENTATION OF SIGNALS: Continuous and discrete time signals: Classification of Signals – Periodic aperiodic even – odd – energy and power signals – Deterministic and random signals – complex exponential and sinusoidal signals – periodicity – properties of discrete time complex exponential unit impulse – unit step impulse functions – Transformation in independent variable of signals: time scaling, time shifting.
- Determination of Fourier series representation of continuous time and discrete time periodic signals – Explanation of properties of continuous time and discrete time Fourier series.
- ANALYSIS OF CONTINUOUS TIME SIGNALS AND SYSTEMS: Continuous time Fourier Transform and Laplace Transform analysis with examples – properties of the Continuous time Fourier Transform and Laplace Transform basic properties, Parseval’s relation, and convolution in time and frequency domains.
- Basic properties of continuous time systems: Linearity, Causality, time invariance, stability, magnitude and Phase representations of frequency response of LTI systems -Analysis and characterization of LTI systems using Laplace transform:
- Computation of impulse response and transfer function using Laplace transform.
- SAMPLING THEOREM AND z-TRANSFORMS: Representation of continuous time signals by its sample - Sampling theorem – Reconstruction of a Signal from its samples, aliasing – discrete time processing of continuous time signals, sampling of band pass signals. Basic principles of z-transform - z-transform definition – region of convergence – properties of ROC – Properties of z-transform – Poles and Zeros – inverse z-transform using Contour integration - Residue Theorem, Power Series expansion and Partial fraction expansion, Relationship between z-transform and Fourier transform.
- DISCRETE TIME SYSTEMS: Computation of Impulse and response and Transfer function using Z Transform. DTFT Properties and examples – LTI-DT systems -Characterization using difference equation – Block diagram representation – Properties of convolution and the interconnection of LTI Systems – Causality and stability of LTI Systems.
- SYSTEMS WITH FINITE AND INFINITE DURATION IMPULSE RESPONSE: Systems with finite duration and infinite duration impulse response – recursive and non-recursive discrete time system – realization structures – direct form – I, direct form – II, Transpose, cascade and parallel forms.
Books:
- AlanV.Oppenheim, Alan S.Willsky with S.Hamid Nawab, Signals and Systems, 2nd edn., Pearson Education, 1997.
- John G.Proakis and Dimitris G.Manolakis, Digital Signal Processing, Principles, Algorithms and Applications, 3rd edn., PHI, 2000.
- B.P.Lathi, Signal Processing and Linear Systems, PHI
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