Linear parameter varying, finite impulse response filter design with application to reducing rise-time for rapid signal changes

Abstract

Classical linear finite impulse response filters (FIR) with constant coefficients have solid and comprehensive theoretical foundations and design methods. The main advantage of using FIR filters is good linearity of phase diagram. 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 low-pass parameter varying FIR filter is proposed. 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. Properties of the filter with time-varying coefficients are analyzed using proposed previously by the author simplified frequency approach for time-varying systems. The frequency approach for filter analysis takes advantage of SVD-DFT transformation of linear time-varying discrete-time system, employing singular value decomposition, discrete Fourier transformation and power spectral density properties. Considerations are illustrated by numerical example.