Postgraduate Course: Discrete-Time Signal Analysis (PGEE11026)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 11 (Postgraduate) |
Credits | 10 |
| Home subject area | Postgrad (School of Engineering) |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | The aim of this course is to impart a knowledge and understanding of statistical analysis of signals and systems when considered in the time and frequency domains, and to enable the student to formally analyse systems through the use of spectral analysis and correlations. The student will also be able to take account of the effects of sampling in the time and frequency domain and understand how these affect the practical analysis procedures. The students will be able to select the appropriate infinite or finite impulse response digital filter and undertake the design of the filter coefficients. The student should gain a familiarity with the derivation of the fast Fourier transform (FFT) algorithm and with its computational advantages. An appreciation of simple sample rate changes and their effect on the filter design process would also be expected.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
Digital Signal Analysis 4 (ELEE10010)
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Other requirements | Course(s) covering Fourier transforms, linear systems and probability |
| Additional Costs | Compulsory book purchase: B. Mulgrew, P.M. Grant, and J.S. Thompson, Digital Signal Processing: Concepts and Applications (2nd Ed), Palgrave, 2003. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
A student should be able to:
- Explain the relationships between time domain and frequency domain representations of signals.
- Apply correlation techniques to an analytic or numerical problem, and relate the outcome to the statistical properties of the signal source(s).
- Correctly define probability and density functions and cumulative distribution functions, and be able to manipulate them to find moments of random variables and their sums.
- Define the distinctions between wide-sense stationary, stationary, and ergodic processes, and be able to reason to which category a random process belongs. .
- Derive the power spectrum of a signal.
- Define techniques for calculating moments in spectral and temporal domains.
- Select an appropriate analogue prototype and use the bilinear transformation method to obtain an IIR digital filter design;
- identify possible problems that can arise in IIR implementation and devise solutions to avoid or minimise their effects;
- explain the importance of linear phase filter design and apply window techniques to design a FIR filter;
- evaluate power spectral density at the output of a linear filter given the PSD at the input and perform a spectral factorisation on the output of a simple linear filter;
- recall how the discrete Fourier transform arises and recognise the effect of resolution and windowing functions upon the discrete Fourier transform;
- derive the structure of the fast Fourier transform from the equation of the discrete Fourier transform and distinguish between decimation-in-time, decimation-in-frequency, radix-2 FFT's;
- analyse the effects of downsampling and upsampling on a signal and recognise the importance of decimation and interpolation filtering.
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Assessment Information
| 100% closed-book formal written examination |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Lectures
Frequency Transforms
L1 Fourier revision
Fourier series, Fourier transform and z-transform revision.
L2 Discrete-time and discrete Fourier transforms
Formulation and properties of discrete-time transforms
L3 Windowing and Zero Padding
The role of windowing and zero padding in discrete Fourier transform processing.
L4 FFTs
FFT - design by radix-2 DIT.
Probability Theory
L5 Probability, random variables and stochastic processes (I)
Notation, distribution functions and moments.
L6 Probability, random variables and stochastic processes (II)
Stationarity, ergodicity, sums of random variables
L7 Correlation functions
Definition, autocorrelation function and properties, correlation of sum of random variables
L8 Correlation and Spectral density
Cross correlation, application to linear systems, Introduction to Spectral density
L9 Spectral density
Spectral density and cross spectral density, definitions and properties
L10 Power spectrum estimation
Classical techniques for Power Spectrum estimation.
L11 Linear filters with random inputs
Properties of linear systems evaluated via correlations and spectral densities
Class test
Digital Filtering
L12 IIR - digital filter design
IIR filter structure, transform of analogue filter, properties
L13 IIR - hardware design, finite precision effects
Spectral properties of IIR filters, lowpass, highpass and bandpass transformations, finite precision effects, and design considerations
Class test feedback
L14 FIR - digital filter design
Transform invariant FIR design process
L15 FIR ¿ implementation
Effects of windowing, finite precision, and performance.
Sampling
L16 Multirate signal processing principles
Upsampling and downsampling structures, spectral properties
L17 A case study - Analogue to digital converters part I
Sampling, dithering, and oversampling
L18 A case study - Analogue to digital converters part II
High rate oversampling, noise shaping, single bit ADCs
Tutorials:
One per teaching week.
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| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | signals, time and frequency domain, correlation, fast Fourier transform |
Contacts
| Course organiser | Dr David Laurenson
Tel: (0131 6)50 5579
Email: |
Course secretary | Mrs Sharon Potter
Tel: (0131 6)51 7079
Email: |
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