Signals and System Notes

# Syllabus

1. Introduction to Signals and Systems

- Classification and representation of signals

- Concepts of linear vector space and orthogonal signal representation

- Classification and properties of signals

- System properties:

- Linearity

- Additivity

- Homogeneity

- Shift-invariance

- Causality

- Stability

- Realizability

2. Fourier Series and Fourier Transform

- Fourier series

- Fourier transform and its properties

- Parseval's Theorem and Signal Bandwidth:

- Parseval’s theorem

- Bandwidth of signals

- Duality of time and frequency representations of signals

3. Discrete-Time Signal Processing

- Sampling, digitization, and reconstruction of analog signals

- Discrete-Time Fourier Transform (DTFT) and Discrete Fourier Transform (DFT)

4. Introduction to Random Signals

- Properties of random signals

- Random variables and processes

- Characterization and analysis of message signal and noise

5. Random Processes

- Classification of random processes

- Geometric representation of random processes

- Gaussian random process

- Auto and cross-correlation

- Power spectral density

6. System and Signal Classification

- Introduction to system classification

- Discrete-time systems

- Signal distortion in transmission

- Distortion-less conditions for signal transmission

- Linear Time-Invariant (LTI) systems:

- Impulse response

- Convolution

- Transfer function

- Bandwidth of systems

- System response to random signals