SIMPLIFIED DESIGN OF LOW-PASS, LINEAR PARAMETER-VARYING, FINITE IMPULSE RESPONSE FILTERS

Abstract

The main aim of the paper is to develop simplified tools and methods for design and analysis of linear parameter-varying (LPV) finite impulse response filters (FIR). FIR filters with constant coefficients have comprehensive theoretical foundations and design methods with the main advantages: good linearity of phase diagram, guaranteed stability, simple practical implementation. Although filters with constant coefficients guarantee particular properties in frequency domain, i.e. noise damping, they also increase rise time for rapid signal changes. In order to avoid such blurring effects a simplified design method for low-pass LPV FIR filters is developed. To synthesize the filter, two cut-off frequencies are needed accompanied with given filter order, shape tuning function and threshold detection condition for sequential operation. Quantitatively assess the filter quality and properties of the tuning functions are analyzed using both time and frequency dependent criteria. In the first case, difference Euclidean norm is used, while the frequency approach for filter analysis takes advantage of SVD-DFT transformation of linear time-varying discrete-time system, as previously defined by the author, employing singular value decomposition, discrete Fourier transformation and power spectral density properties.