CALENDAR:

Classical filter theory; DFT and FFT; FIR and IIR digital filters; effects of finite precision;  implementation of DSP-based systems; adaptive filtering; spectral analysis; signal compression.

Three lectures, one tutorial, one laboratory (every other week); first term

Prerequisite: ELEC ENG 3TJ4 or 3DB3 or 4TQ4

Antirequisite:  ELEC ENG 4EA3

COURSE OBJECTIVES:

In this course, the student will become familiar with the fundamental theoretical and practical ideas in implementing DSP systems, such as in modems, wireless, telephony, etc. The objective is to consolidate previous material, as well as introduce new concepts.

COURSE LOADING:

• Lectures: 3 1-hour lectures per week
• Tutorial: 1 1-hour tutorial per week
• Lab: 1 3 hour session every other week
• prelab preparation and assignments: 1.5 hrs per week
• Study time: 4 hours per week

CEAB WEIGHTING:

• ES = 80%, D = 10%, M = 10%

• Oppenheim and Shafer
• Porat (Ref).

Introduction (1)

• The scope of DSP and basic digital signals

• The Fourier series, the Fourier transform, properties

• The Discrete-Time Fourier Transform, DTFT development
• Freqency Domain Effects of Sampling: periodic repetitions in frequency domain due to sampling in time domain, normalization (T = 1): -fs/2 to fs/2, 0 to fs., recovery of continuous-time signal from its samples (reconstruction)
• Examples and Applications: generic digital system structure (role of anti-aliasing and reconstruction filters),
• Examples of aliased signals (show how waveform is distorted)

• Basic Theory: background idea behind the z-transform (solution to LTI discrete-time diff. eq.), calculation of z-transform and its inverse (briefly), regions of convergence
• Properties of z-transforms: role in solution of discrete-time LTI systems, convolution property and graphical interpretation of the convolution operation, z-transforms of cascaded systems, stability and causality
• Realization and Frequency Response: Frequency response (Magnitude and Phase), representation of LTI systems with rational polynomials, block-form implementations of a rational polynomial transfer function

• Relation between the z-transform and the discrete-time FT
• Development of the DFT from the discrete-time FT
• Representation of time and freq axes.
• Aliasing issues
• Implementation by the FFT

• Applications of Filters, what they are
• Magnitude, Phase, Group delay responses and their properties
• Distortionless transmission and linear phase
• Butterworth, Chebychev, Bessel filters
• Means of Implementation (briefly)
• Overview of filter types (microwave, digital)

• FIR Filters: concept of design, windowing, CAD methods
• IIR Filters: concept of design, bilinear transformation
• Finite precision effects in implementing digital filters

• Applications
• Architectural features

• Applications
• Periodogram and its properties
• Fefined methods: Bartlett, Welch

• Applications
• Optimal Wiener filter
• The LMS algorithm and its properties

• Transform-based compression, role of DCT, examples
• Principal components based compression

LABORATORIES:

• Lab 1: Introduction to MATLAB and Basic Signals
• Lab 2: Time-domain signal analysis
• Lab 3: DTFT and its properties
• Lab 4: DFT and FFT
• Lab 5: Digital filtering
• Lab 6: Adaptive filtering and spectral analysis