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

Unit name Digital Filters and Spectral Analysis (M) EENGM1400 10 M/7 Teaching Block 1 (weeks 1 - 12) Dr. Agrafiotis Not open None None Department of Electrical & Electronic Engineering Faculty of Engineering

## Description including Unit Aims

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.

Elements:

• 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 Information

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 Information

Exam (January, 100%)

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. EENGM1400).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates within the Regulations and Code of Practice for Taught Programmes.