Discrete-Time Signal Analysis (P01809)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : EEL-P-DTSA

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.

? Keywords : signals, time and frequency domain, correlation, fast Fourier transform

Entry Requirements

? Pre-requisites : Prior attendance of a signals and systems course is recommended.

? Costs : Compulsory book purchase: B. Mulgrew, P.M. Grant, and J.S. Thompson, Digital Signal Processing: Concepts and Applications (2nd Ed), Palgrave, 2003.

Subject Areas

Home subject area

Postgraduate (School of Engineering and Electronics), (School of Engineering and Electronics, Schedule M)

Delivery Information

? Normal year taken : Postgraduate

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 3 hour(s) per week for 10 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	09:00	09:50	KB
Lecture	Friday	09:00	09:50	KB

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.