A new two-dimensional multirate digital filter
Des McLernon · Spiral (Imperial College London) · 1982
A new two-dimensional multirate digital filter is introduced, where internal shifting and processing of data continue during each spatial sampling interval of the input 0 With coefficients that, can be periodically varying, the basic property of such a system is that it imitates the behaviour of a conventional filter, possibly of a higher order,, A complete mathematical analysis of this multirate filter is first given, using either finite difference equations, complex integration, signal flow graphs, or state-space methods to illustrate its operation and deduce fundamental properties.Computer optimisation methods of design in both the frequency and space-domains are evolved" In some cases, a lower design error is obtained than with a similar design for a conventional filter of the same order.Noise models for input, product, and coefficient rounding are derived for two direct form and one state-space structure,.Comparisons are made with the noise models for conventional filters, and the advantages of a multirate system are noted.Finally, limit cycles are investigated.Firstly, a onedimensional filter is considered and new results presented.This work is then used to show that in many cases where limit cycles exist in a two-dimensional filter they can be totally eliminated by a multirate realisation.Dr. R. A. King for.directing and assisting this research.His readiness to discuss any problems or difficulties that arose from mv work, and his continual interest and encouragement, are deeoly appreciated.