Discrete Signals and Systems

Sampling, spectrum of naturally sampled signal, reconstruction of continuous-time signal, sampling theorem, frequency aliasing.

Classification and properties of discrete signals(periodic, aperiodic, random signals)

Spectral analysis of discrete signals: discrete time Fourier transform TDFT, discrete Fourier transform DFT.

Discrete linear time invariant systems (LTI):

Characterization of LTI systems: difference equation, impulse response, frequency response, system function, z-transform.

Location of poles and zeroes: stability, phase shift, linear phase systems.

Discrete filters: block scheme, signal flow graph, structures, digital filter specifications.

FIR filter design: windowing, frequency transformations, equiripple filter design.

IIR filter design: invariant impulse response method, bilinear transformation.

Multirate systems: decimation, interpolation.

Effects of digital implementation: quantisation noise, effects of coefficient quantisation. 

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