Skip to main content

VLSI architecture for adaptive digital filtering utilising number theoretic transform

Amir-Alikhani, Hamid (1984) VLSI architecture for adaptive digital filtering utilising number theoretic transform. Doctor of Philosophy (PhD) thesis, University of Kent. (doi:10.22024/UniKent/01.02.94170) (KAR id:94170)

Language: English

Click to download this file (63MB) Preview
[thumbnail of 353413.pdf]
This file may not be suitable for users of assistive technology.
Request an accessible format
Official URL:


This thesis investigates the design of a frequency adaptive digital filter in Very Large Scale Integration using the Number Theoretic Transform. The properties of residue numbering systems are investigated, and particularly the possible advantages occured from parallelism, operations without the need for carry, and the absence of round-off errors. The conclusion is reached that this numbering system is in some circumstances more suitable for high speed processing in Very Large Scale Integration. Transform techniques in a finite field are then examined to determine how they could perform filtering operation more efficiently in terms of the number of arithmetic operations required compared with other techniques such as Fast Fourier Transform. Adaptive filtering in the frequency domain using the Number Theoretic Transform, and in particular Fermat Number Transform, with appropriate formulae for filter weight adaptation using the Least Mean Square algorithm are presented. Several result show that the frequency mean square error as a performance index results in convergence to an optimal solution. A complexity' ratio is used to ascertain that frequency adaptive digital filters need less computational power (number of arithmetic operations) than time domain adaptive filters. A design of special purpose processor using Very Large Scale Integration technology is described, several structures using pipelining and systolic arrays are presented which support the main Very large Scale Integration design features. A table look-up approach using Programmable Logic Arrays (PLAs) for processing elements and a measurements of system performance regarding time/area complexity' are described. Finally, it is concluded that, with suitable further development, a Very' Large Scale Integration architecture for frequency adaptive digital filter using number theoretic transform which has high sampling rate, regular internal structure and capability to parallel devices could likely be achieved.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Hinton, O.R.
DOI/Identification number: 10.22024/UniKent/01.02.94170
Additional information: This thesis has been digitised by EThOS, the British Library digitisation service, for purposes of preservation and dissemination. It was uploaded to KAR on 25 April 2022 in order to hold its content and record within University of Kent systems. It is available Open Access using a Creative Commons Attribution, Non-commercial, No Derivatives ( licence so that the thesis and its author, can benefit from opportunities for increased readership and citation. This was done in line with University of Kent policies ( If you feel that your rights are compromised by open access to this thesis, or if you would like more information about its availability, please contact us at and we will seriously consider your claim under the terms of our Take-Down Policy (
Uncontrolled keywords: Very Large Scale Integration, frequency adaptive digital filter, Number Theoretic Transform
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Engineering and Digital Arts
SWORD Depositor: SWORD Copy
Depositing User: SWORD Copy
Date Deposited: 16 Mar 2023 10:45 UTC
Last Modified: 16 Mar 2023 10:45 UTC
Resource URI: (The current URI for this page, for reference purposes)
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.