Design of IIR fan filters using iir hilbert transformer
Kiyoshi Nishikawa, Eiko Morita · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1992
Abstract This paper describes a method of synthesis for the IIR fan filter which applies the IIR Hilbert transformer to the one‐dimensional prototype filter. The method is more direct than the traditional method, which derives the fan filter from the lowpass filter. The design of the quadrant fan filter also is discussed. The bilinear z transform is applied to the analog Hilbert transformer, which is already known as the 90‐deg constant‐phase function, and the result is used as the IIR Hilbert transformer. Only the odd‐order function can be used for the IIR Hilbert transformer for the IIR fan filter, but even‐ as well as odd‐order functions can be used for the quadrant fan filter. The final IIR fan filter transfer function is obtained as the difference of half‐plane type two‐dimensional all‐pass functions. A Chebyshev‐type function is used for the IIR Hilbert transformer. Consequently, the fan filter has the amplitude response with a ripple in the stopband which is one‐half the phase ripple of the Hilbert transformer, while the response is almost flat without a ripple in the passband.