Discrete Signals and Systems

The basic types of discrete-time signals and their properties are presented. Sampling and reconstruction, used to convert a continuous-time to a discrete-time signal and back, are introduced. The requirements and implications of both procedures are considered. 

Mathematical tools for frequency analysis of discrete-time signals are introduced (DTFT, DFT, DFS). 

Basic building blocks and structures (FIR, IIR) of discrete-time linear time-invariant (LTI) systems are presented along with and various means for their description: difference equation, system diagram, impulse response, frequency response and system function (z-transform of impulse response). 

A few different methods for FIR and IIR filter design are presented.  

The effects of signal quantization, filter coefficients quantization and the effect of rounding errors within discrete-time LTI systems are examined. 

Multirate systems are introduced and the interpolation and decimation methods for sampling rate adjustments are explained.

Basic properties of discrete signals.

Relations between discrete and continuous-time signals due to sampling and reconstruction.

Spectral analysis of analogue signals using DFT

Advantages and drawbacks of FIR filters

Advantages and drawbacks of IIR filters

Significance of proper structure selection for fixed point implementations

Lectures, tutorial, homework