1.1 Continuous-time and discrete-time signals
1.2 Sampling and quantization
1.3 Description and manipulation of signals

2.1 Introduction to discrete-time systems and its classifications
2.2 Linearity, memory, time-invariance, and causality
2.3 Recursive and non-recursive difference equations
2.4 Finite impulse response (FIR) and infinite impulse response (IIR) type systems
2.5 Impulse response and stability
2.6 Linear convolution
2.7 Solution to difference equation using classical method: Zero-input and zero-state response

3.1 Introduction to z-transform
3.2 Poles and zeros
3.3 Stability and causality
3.4 Solution to difference equation using z-transform method: Zero-input and zero-state response
3.5 Inverse z-transform using contour integration
3.6 Complex convolution theorem
3.7 Parseval’s theorem

4.1 Introduction to DTFT
4.2 DFT and DFS
4.3 Properties of DFT
4.4 Circular Convolution
4.5 Computation of DFT using FFT

5.1 Categories of filter: Low-pass, high-pass, band-pass and band-reject
5.2 Window method for design of FIR filters
5.3 Design of equiripple FIR filters using optimal method

6.1 Analogue-to-digital filter transformation and mathematical relationships
6.2 Formulation of impulse response: Butterworth and Chebyshev IIR filters
6.3 Bilinear transformation for mapping filter function from analogue to digital domain

A1 : Digital signal processing is extensively used in audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression. Its application can be specialized for telecommunications, control systems, biomedical engineering, and seismology, among others.