During the years 2003 to 2008 I undertook a PhD in Electronic Engineering at the University of Warwick having finished my undergraduate at the same location. Over the 5 years my PhD topic changed quite a lot, in most part due to a change in supervisor. The eventual title of the thesis was
"Design and real-time hardware implementation of Binary Integer Wavelet Transforms"
The abstract from the thesis follows below however you can download a secured PDF copy of the thesis here. The thesis can not be copied or used in whole or part without my permission except for academic use. Where publications are made as a result of my work a reference to my work must be present. A hard bound copy of the thesis can be obtained through inter library loans by applying to the University of Warwick Library.
If you have any comments about the work in the thesis please use the Contact link to the left.
This thesis explores methods to construct efficient wavelet transforms for operation on Field Programmable Gate Array (FPGA) devices. Additionally the wavelets designed have been used in an audio watermarking application.
Traditional wavelets, such as Daubechies orthogonal wavelets, are based on coefficients that are in general, irrational numbers. This makes them difficult to implement using hardware without either using floating-point arithmetic or by rounding the wavelet coefficients and the intermediate results to a fixed-point or integer arithmetic system. This work has shown that it is possible to use Binary Integer Wavelet Transforms (BIWTs) in-place of traditional wavelets. BIWTs use coefficients that can be stored as a set of integers which greatly simplifies the hardware implementation.
The work presents an original factorisation for a 6/10 wavelet, and two methods of implementing this and a 9/7 wavelet, in hardware using a FPGA development board. These have been designed to work with data rates compatible with CD quality audio data, however multi-channel high fidelity audio has also been considered. The one problem with BIWTs, non-linearity, has also been considered and proposals for its reduction have been made.
To test the quality of the BIWTs an application was considered. Audio watermarking has recently found some successes when performed using wavelets, and so a watermarking scheme has been converted to use the wavelet implementations in both software and hardware. The hardware was successfully designed to work in real-time, watermarking a live input audio stream.
The work has shown that BIWTs can be used in replacement of traditional wavelets without affecting the quality of the application, while gaining the benefits of the implementation, namely simpler hardware.