A novel concept of phase-compensated continuous-time filters

In this paper, we will address the question of how to design a continuous-time filter that provides both a constant delay and a maximally flat magnitude response over the desired frequency band, and at the same time ensures the transient of the designed filter as short as possible. The paper presents a theoretical concept of time-varying Butterworth filters with compensated group delay response. Using the compensated Butterworth filter, we introduce time-varying parameters to its structure for the purpose of the minimization of the transient that was lengthened because of the process of the compensation. Results verifying the effectiveness of the proposed approach are presented and compared to the traditional filters. This paper is an updated and extended version of Piskorowski, J. (2006). Analog Integrated Circuits and Signal Processing, 47, (2):233–241.

[1]  M. Mansour,et al.  Stability of polynomials with time-variant coefficients , 1993 .

[2]  Srdjan Stankovic,et al.  Time-varying filtering of speech signals using linear prediction , 2000 .

[3]  J. Rhodes.  Filters approximating ideal amplitude and arbitrary phase characteristics , 1973 .

[4]  L. Zadeh,et al.  Time-Varying Networks, I , 1961, Proceedings of the IRE.

[5]  Theo A. C. M. Claasen,et al.  On the time-frequency discrimination of energy distributions: Can they look sharper than Heisenberg ? , 1984, ICASSP.

[6]  M. Fahmy.  Transfer functions with arbitrary phase characteristics , 1979 .

[7]  P. P. Vaidyanathan,et al.  Time-varying filters and filter banks: some basic principles , 1996, IEEE Trans. Signal Process..

[8]  R. Kaszynski,et al.  Stability of parametric, analog low-pass filters , 1999, 1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA '99 (Cat. No.99TH8467).

[9]  M. E. Valkenburg,et al.  Design of Analog Filters , 2001 .

[10]  Roman Kaszynski,et al.  Using the parametric time-varying analog filter to average-evoked potential signals , 2004, IEEE Transactions on Instrumentation and Measurement.

[11]  Wai-Kai Chen,et al.  The circuits and filters handbook , 2009 .

[12]  Gary F. Margrave,et al.  Theory of nonstationary linear filtering in the Fourier domain with application to time‐variant filtering , 1998 .

[13]  N. R. Bartley,et al.  Continuously time-variable recursive digital band-pass filters for seismic signal processing , 1983 .

[14]  T. Claasen,et al.  On stationary linear time-varying systems , 1982 .

[15]  Jacek Piskorowski.  Phase-Compensated Time-Varying Butterworth Filters , 2006 .

[16]  Isaac Kaminer,et al.  Navigation system design using time-varying complementary filters , 2000, IEEE Trans. Aerosp. Electron. Syst..

[17]  Earl R. Ferrara,et al.  Frequency-domain implementations of periodically time-varying filters , 1985, IEEE Trans. Acoust. Speech Signal Process..