buddypoor wrote on Jun 29th, 2009, 11:27am:Besides this point, I would like to point to the fact, that there is no BP of first order. It is a common agreement that the degree of the numerator determines the degree of the function. And the simplest BP - as a result of a transformation of a 1st order LP - is a 2nd order BP.
This is not true for a
complex filter, which is a filter which is NOT symmetrical in the freq=0 domain. As such it can have a "bandpass response" in either the positive
OR negative frequency domain whilst only having a
single complex pole, and so order =1.
Your statement is only true of
real filters which have been created by bilinear transformation of a lowpass (and are symmetrical around freq=0 for +/ve&-ve frequencies).
Ref: Gingel M.J for the classic paper "A symmetric polyphase filter". 1968
or
"Complex analog bandpass filters designed by linearly shifting real low-pass prototypes" Sedra, A. S., Snelgrove, W. M. and Allen, R 1985.