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

Tania Stathaki and Patrick A. Naylor
18 lectures in the Autumn Term


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


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.



Lecture List

The relevant textbook chapters are indicated as e.g. M1, H1.

  1. Introduction and z-transform [slides, handouts, M1, M6]
  2. Fourier Transforms [slides, handouts, M3, M5]
  3. Discrete Cosine Transforms [slides, handouts, M5]
  4. Linear Time-Invariant Systems [slides, handouts, M4, M5]
  5. Digital Filters [slides, handouts, M6, M7]
  6. Windowed FIR Filter Design [slides, handouts, M10]
  7. Optimal FIR Filter Design [slides, handouts, M10]
  8. IIR Filter Design by transformation [slides, handouts, M9]
  9. Optimal IIR Filter Design [slides, handouts, M9]
  10. Filter structures [slides, handouts, M8]
  11. Multirate Building Blocks [slides, handouts, M13]
  12. Polyphase Filters [slides, handouts, M13, H5]
  13. Sample Rate Conversion [slides, handouts, M13, H7, H8]
  14. DSP in an FM Radio [slides, handouts, H13]
  15. Subband Filterbanks [slides, handouts, M14]

Complete set of handouts (4.1 MB, 204 pages)


The exam will contain 4 questions and lasts for 3 hours. Question 1 is compulsory and comprises several short questions  worth a total of 40%. 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.


The textbook by Mitra includes a large number of problems at the end of each chapter as well as additional MATLAB-based exercises. The chapters corresponding to each lecture are indicated in the list above.

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, 2013, 2014, 2015, 2016, 2017