Transform Methods and Signal Processing

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Description

Objective

The aim of this course is to introduce various Transform Techniques including Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) as well as Wavelet Transforms, and to introduce the basic principles of signal processing to provide an understanding of the fundamentals, implementation and applications of signal processing. At the end of this subject the students should have good concepts of: various Transform Techniques and their applications in Communication Theory, Information Theory, etc. digital signal processing, convolution, correlation, filtering, sampling, etc. discrete-time signals in both time domain and frequency domain spectral analysis use of Wavelets Transform for signal analysis

Content

Introduction to Integral Transforms; Laplace Transform, Fourier sine and cosine Transform, Hankel Transform, Mellin Transform, Hilbert Transform, Z-Transform, Fourier Transform Pair, Discrete Fourier Transform, Fast Fourier Transform. Convolution, Linear Time Invariant Systems; the Sampling Theorem, Energy Spectrum, Rayleigh's Theorem, Parceval's Theorem; Frequency Domain description, Signal Averaging, Time and Frequency Resolution; Classical Spectral Analysis, Power Spectra of Stationary Processes. Introduction to Wavelet Transforms, Short time Fourier Transforms, Comparison of Wavelets with Fourier Transforms, Continuous Wavelet Transform and its Inverse, Multi-resolution and Discrete time Transforms.

Matthew Roughan Lecturer for this course

Delivery

2 one-hour lectures per week.

Assessment

80% (2 hour) examination, 20% assignments (including computer assignments).

Graduate attributes

• Applying mathematical knowledge (1)
• Interpreting data and drawing conclusions (2)
• Formulating mathematical problems (3)
• Problem solving skills (4)
• Flexibility in working environment (5)
• Team participation and leadership (7)
• Self-directed study (8)
• Career development (9)

Linkage past

Prerequisite is Level II Fourier Series and Differential Equations.

Linkage present

This subject is useful especially for those who are thinking of doing research in Telecommunications, Advanced Applied Mathematics, Advanced Signal Processing and many areas in Mechanical and Electrical Engineering.

Linkage future

See above.

Restrictions

None.

Recommended text

None.