Signals and Systems
UNIT-I
Introduction to Continuous-time Signals and Fourier series
Part-A: Representation of Continuous-time Signals:
- Introduction to typical signals
- Time-domain operations
- Continuous-time signal characteristics (periodicity, frequency, deterministic and random, symmetry, energy and power)
- Analogy between vectors and signals
- Orthogonal signal space
- Signal approximation using orthogonal functions
- Mean squared error
- Orthogonality in complex functions.
Part-B: Fourier Series:
- Representation of continuous-time periodic signals by Trigonometric and Exponential Fourier series
- Dirichlet’s conditions
- Properties of Fourier series
- Parseval's theorem
- Complex Fourier spectrum, Power Spectrum.
UNIT-II
Fourier Transform, and Laplace Transform:
- Fourier transform via Fourier series
- Convergence of Fourier transform
- Fourier transforms of basic signals like impulse function, unit step, signum function and for various periodic and aperiodic signals
- Properties of Fourier transforms, Parseval's theorem
- Definition of two-& one-sided Laplace Transform (LT)
- Relation between LT and FT
- Region of convergence (ROC) and Properties of LT.
UNIT-III
Signal Transmission through Linear Systems Continuous-time Linear Time-Invariant
systems
- Representation by differential equations
- Properties of continuous-time systems(linearity, time invariance, causality and stability)
- Impulse response
- Convolution
- Transfer function
- frequency response
- Ideal vs. realizable LPF, HPF and BPF characteristics
- Signal bandwidth
- system bandwidth
- rise-time, gain-bandwidth, Distortion
- Causality and Paley-Wiener criterion for physical realization.
UNIT-IV
Discrete Time signal characteristics
- (periodicity, frequency, deterministic, random, symmetry, energy and power)
- Discrete Time (DT) signal representation using complex exponential and sinusoidal components
- z-Transform of a discrete sequence
- Relationship between z-Transform and Discrete Time Fourier Transform
- Transfer function of a LTI system (No difference equations)
- Region of convergence of z-Transform
- Constraints on ROC for various classes of signals
- Properties of z-Transform
- Inverse z-Transform by Partial Fractions (simple poles only).
UNIT-V
Sampling:
- Sampling theorem – Graphical and analytical proof for Band Limited Signals;
- Impulse-train sampling
- Reconstruction of signal from its samples
- Undersampling and Aliasing;
- Natural and Flat-top sampling
- Band pass sampling.
Text/Reference Books
1. Alan V. Oppenheim, Alan S. Willsky and S. Hamid Nawab, “Signals and Systems”, Second
Edition, PHI Learning, New Delhi, 2007.
2.B. P. Lathi, Signals, Systems and Communications-B.S. Publications, 2003.
3. Simon Haykin and Barry Van Veen, “Signals and Systems”, Edition, John Wiley and Sons, 2002.
4. Signals and System book by Anand Kumar
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