A Method of Modeling Multirate Two-Dimensional Recursive Digital Filters Author
A. Gerheim · ODU Digital Commons (Old Dominion University) · 2019
This dissertation presents a method of modeling two dimensional sampled data systems with two sampling rates in each dimension. This methodology is applied to the problem of synthesizing two dimensional velocity filters using one dimensional prototypes and multirate concepts. The modeling method includes the replacement of scalar z-transforms of signals by vectors of polynomials, and the replacement of scalar z-transforms of impulse responses by matrices of polynomials. The synthesis of velocity filters is accomplished through the use of coordinate transformations in the z-transform domain which skew the ω1 -ω2 axes on the unit bidisc. The filters synthesized using these methods operate at sampling rates higher than the input and output data rates. The process of interpolating the input to accommodate the increase in sampling rates is analyzed in the frequency domain. This overall methodology is applied to the synthesis of fan filters of arbitrary order. Simple synthesis and realization methods are given.