The frequency transformation by matrix operation and its application in IIR filters design

It is known that the transfer function H(z) of the desired digital infinite-impulse response filter can be obtained from the normalized transfer function H_a(s) of the analog low-pass filter. Recently it has been shown that Pascal matrix allows the appropriate transformation for design of the low-pass, high-pass, and bandpass digital filters. Unfortunately, this method is difficult to use in case of transforming H_a(s) to the high-order bandpass filter. This letter proposes a similar method, especially suitable for design of the bandpass and bandstop filters without order limitation. The presented design algorithm is illustrated by a numerical example.