GENERALIZATION OF THE TIME INFINITE IMPULSE RESPONSE DIGITAL FILTERS

This work describes the generalization of a new kind of infinite impulse response (IIR) digital filter to filter the pulse signal periods. This kind of digital filter was designed using the previously designed frequency-locked loops (FLL), which are based on the time measurement and processing of both the input and output periods. FLL is a linear discrete system. Starting from the general form of difference equation of the IIR FLL digital filter of the third and fourth orders, the transfer functions and Z transform of the outputs are developed for the IIR FLL digital filter of any order. To demonstrate the capabilities and utility of the general equations, they were applied to design a suitable IIR digital filter using a fourth-order FLL. The filtering abilities and the analyses in the frequency domain of the designed low pass IIR digital filter are demonstrated using the theory of IIR digital filter and the corresponding MATLAB tools. Analyses of the fourth-order IIR FLL digital filter were also performed in the time domain using computer simulation in MATLAB.