Recursive formulation of class 1 and 2 time domain Wiener estimation matrix filters

Matrix filters can be implemented using block processing or recursive processing. Recursive processing is used to generate the output of time-invariant periodic and nonperiodic systems and time-varying memoryless systems for Class 1 and 2 filters. Simulations are presented to illustrate the relationships among signal characteristics, smoothing effects, and computational efficiency. It is noted that the types of estimation problems define the structure of the impulse response matrices: periodic time-invariant circulant filters estimate periodic signals; nonperiodic time-invariant Toeplitz filters estimate nonperiodic signals; and memoryless time-varying diagonal filters estimate wideband signals. The outputs obtained using Class 1 systems are in general better than those obtained using Class 2 systems