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Unit information: Digital Filters and Spectral Analysis (M) in 2021/22

Unit name Digital Filters and Spectral Analysis (M)
Unit code EENGM1400
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Agrafiotis
Open unit status Not open




School/department Department of Electrical & Electronic Engineering
Faculty Faculty of Engineering


This course provides students with an understanding of the theory, interpretation, design and application of DSP techniques. In particular the course covers the theory and practice of digital filters and Fourier transform based spectrum analysis. Spectral descriptions of continuous-time and discrete-time waveforms are reviewed and related, and the FFT algorithm is used as a spectral analysis tool. The behaviour of digital filters is analysed through the use of difference equations and transfer functions via the z-transform. Methods for designing IIR and FIR filters are described, and various issues associated with their practical implementation are discussed.

To complement and aid understanding of the lecture material, students will be required to use Matlab to complete a series of coursework activities. These will provide practical experience of spectral analysis, digital filtering and digital filter design. The coursework will be assessed by means of four Matlab assignments with electronic submission of results.


  • Spectral Analysis Continuous time Fourier series (FS), continuous time Fourier transform (FT), sampling and aliasing, discrete time Fourier transform (DTFT), discrete Fourier transform (DFT), spectral smearing, windowing, time frequency trade-offs, implementation of DFT, fast Fourier transform (FFT), applications of FFT.
  • Digital Filter Design and Implementation Finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Design of FIR filters, linear phase response, zero-placement, design using windowing, design using frequency sampling, optimal design methods, variable transforms. Design of IIR filters, pole-zero placement, impulse invariance, bilinear transform. Implementation of digital filters, direct form, cascade and parallel forms, lattice form, finite word-length effects, limit-cycle oscillations in recursive filters, joint complexity/performance design. Introduction to multi-dimensional and multi-rate signal processing.

Intended learning outcomes

Having completed this unit students will be able to:

  1. Analyse and design FIR and IIR digital filters, taking into account the influence of finite precision arithmetic in their implementation.
  2. Apply DFT and FFT based spectrum analysis methods, interpret the resulting spectra and describe the limitations of these approaches.
  3. Use simulation tools such as MATLAB.

Teaching details

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, practical activities supported by drop-in sessions, problem sheets and self-directed exercises.

Assessment Details

Exam (January, 100%)


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