The design of time-varying digital filters which employ binary valued coefficients

Digital filters whose coefficients are limited to 1,0, or -1 are generally too restrictive and require a trial and error design. This paper introduces a recursive filter design whose coefficients ε {1,0,-1} can change at each filter update. The first discussion deals with a general transition matrix state variable formulation similar to Floquet theory for Differential Equations. By defining a time-varying similarity transformation and introducing circulant feedback matrices, a significant simplification of the highly quantized time-varying state recursion equation is realized. This leads to the enumeration of the filter transfer function and more importantly a simple eigenvalue structure that facilitates the design of filters with known pole locations. These analytical results are then verified in a filter simulation experiment by a Chebyshev lowpass filter design.