Digital Signal Processing and Digital Filters (E4-13, EE9SC1)

Mike Brookes
18 lectures in the Autumn Term

Aims

This course aims to give a thorough grounding in the design of digital filters and in multirate signal processing techniques.

Syllabus

Transforms: Discrete-time Fourier Transform (DTFT), Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), Modified DCT (MDCT). Discrete Time systems: linear and circular convolution, overlap add, overlap save, stability triangle, allpass filters, group delay, minimum phase systems. FIR filter design: windowing, remez exchange algorithm for optimal design. IIR filter design: bilinear transformation, spectral transformations, optimal filter design. Filter implementation: coefficient quantisation, lattice filters. Multirate signal processing: sample rate conversion, polyphase filters, Farrow filters. Subband processing, STFT processing, MDCT-based processing.

Textbooks

•  Main textbook: "Digital Signal Processing" by Sanjit K. Mitra, 4th edition, McGraw Hill, 2011. ISBN 0071289461 [Amazon]
• Also useful: “Multirate Signal Processing” by Fred Harris, Prentice Hall, ISBN:0137009054 £60 covers multirate material in more detail than Mitra. [Amazon]

Lecture List

1. Introduction and z-transform [slides, handouts]
2. Fourier Transforms [slides, handouts]
3. Discrete Cosine Transforms [slides, handouts]
4. Linear Time-Invariant Systems [slides, handouts]
5. Digital Filters [slides, handouts]
6. Windowed FIR Filter Design [slides, handouts]
7. Optimal FIR Filter Design [slides, handouts]
8. IIR Filter Design by transformation [slides, handouts]
9. Optimal IIR Filter Design [slides, handouts]
10. Filter structures [slides, handouts]
11. Multirate Building Blocks [slides, handouts]
12. Polyphase Filters [slides, handouts]
13. Sample Rate Conversion [slides, handouts]
14. DSP in an FM Radio [slides, handouts]
15. Filterbanks [slides, handouts]

Complete set of handouts (4.1 MB)

Exam

The exam will contain 4 questions and lasts for 3 hours. Question 1 is compulsory and comprises eight short questions each worth 5%. You are required to answer two out of the remaining three questions which are each worth 30%.

A formula sheet will be available during the exam.

Past Exam Papers

Note that these exams were based on a slightly different syllabus. I have indicated questions that lie outside the current syllabus.

2001 (not Q3, Q5); 2002 (not Q5); 2003 (not Q2); 2005, 2006 (not Q1, Q5); 2007 (not Q1, Q5); 2009, 2010 (not Q2, Q4); 2011 (course not given), 2012