Postgraduate Course: Discrete-time Signal Analysis (MSc) (PGEE10018)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | 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 design a finite impulse response digital filter. An appreciation of simple sample rate changes and their effect on the filter design process would also be expected. At the end of the course the student will develop skills to use matched and Wiener filters for practical problems. |
| Course description |
L1 Frequency Analysis of Discrete-Time Signals (4.2.1-4.2.3, 4.2.5) Fourier Series for Discrete-Time Signals, Energy and Power Density Spectra
L2 Properties of the Fourier Transform (4.4) Properties and Theorems
L3 Discrete Fourier transform (7.1.1-7.1.2, 7.2.1, 7.4) Frequency-Domain sampling, DFT, Properties of the DFT, Frequency Analysis of Signals using DFT
L4 Correlation of Discrete-Time Signals (2.6.1-2.6.2)
Crosscorrelation and Autocorrelation, Properties
L5 Correlation of Discrete-Time Signals (2.6.3-2.6.4) Correlation of Periodic Signals, Input-Output Correlation Sequences
L6 Linear Time-Invariant Systems (5.2, 5.3.1) Frequency Response of a System, Input-Output Correlation Functions and Spectra
L7 Random Signals, Correlation Functions and Power Spectra (12.1.1-12.1.3, 12.1.5) Random Processes, Stationary Random Processes, Ensemble Averages, Power Density Spectrum
L8 Discrete-Time Random Signals and Ergodicity (12.1.6-12.1.8) Discrete-Time Random Signals, Time averages, Mean-Ergodic Process
L9 Design of FIR filters (I) (10.2.1-10.2.2) Symmetric FIR filters, Design of Linear-Phase FIR filter using Windows
L10 Design of FIR Filters (II) (10.2.3-10.2.4) Design using the Frequency-Sampling method, Optimum Equiripple FIRfilters
L11 Power spectrum estimation (I) (14.1, 14.2.1-14.2.3) Computation of Energy Density Spectrum, Periodogram, Use of DFT, Bartlett, Welch, Blackman & Tukey
L12 Power spectrum estimation (II) (14.2.4-14.2.5, 14.4) Comparison of non-parametric techniques, filterbank realisation of periodogram, Minimum Variance Spectral Estimates
L13 Multirate Signal Processing (11.1-11.4) Decimation, Interpolation, Sample rate conversion
L14 Analogue to digital converter (6.3.1-6.3.3, 6.6.1) Analogue-to-Digital converters, quantization and coding, analysis of quantization errors, oversampling sigma-delta converter
L15 Matched filters Definition and purpose
L16 Matched filter examples Examples
L17 Wiener filters (12.7) Definition and purpose
L18 Wiener filter examples Examples
In addition, a formative class test is run in week 4, and a revision lecture in week 8. Numbers in brackets refer to sections of the course textbook.
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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 | None |
| Additional Costs | Purchase of course textbook (from £56.99) |
Course Delivery Information
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| Academic year 2015/16, Not available to visiting students (SS1)
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Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 10,
Formative Assessment Hours 1,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
63 )
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| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Exam: 100% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S1 (December) | | 2:00 | |
Learning Outcomes
After successful completion of this course a student should be able to:
- explain the relationships between and be able to manipulate 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 density functions and cumulative distribution functions, and be able to manipulate them to find moments of random variables;
- 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;
- 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;
- analyse the effects of downsampling and upsampling on a signal and recognise the importance of decimation and interpolation filtering;
- explain the basis of matched filtering and be able to determine an appropriate filter for a given problem;
- apply a Wiener filter to the detection of a signal corrupted by additive noise, and for signal prediction.
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Reading List
| Digital Signal Processing: Principles, Algorithms and Applications, New International Edition, Proakis & Manolakis - £56.99 from Blackwells or Amazon |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
Exam must run concurrently with ELEE10010. |
| Keywords | Fourier transform, random process, spectral density, digital filters, signal processing |
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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