Monotonicity of angle of the constant modulus function
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From: vv on 7 Mar 2010 07:27 I am looking for a proof of the monotonicity of the angle of a rational function with constant modulus. That is, let H(z) = z^{-N} A(z^{-1})/A(z), where A(z) = 1+a1 z^{-1} + ... + aN z^{-N} with the coefficients being real-valued (the so-called allpass filter in DSP literature). It is known that the angle of H(z) evaluated on the unit circle is zero at z=1 and -N pi at z=-1, with passage from 0 to -N pi being monotonic. A reference that details the proof would be most welcome. Thanks. PS: Markushevich didn't seem to have any discussion on this topic, unless I missed spotting it. -vv |