Contents
Can Infinity be a pole?
Poles at infinity are obtained when the order of the numerator is higher than the order of the denominator. Conversely, if the denominator is of higher order than the numerator (as must be the case for a physically realisable system), m>n, then there will be (m-n) zeros at infinity.
Can the residue of a pole be zero?
. In fact, any counterclockwise path with contour winding number 1 which does not contain any other poles gives the same result by the Cauchy integral formula. More generally, the sum of the residues of a meromorphic one-form on a compact Riemann surface must be zero. …
Can we draw Bode plot for non minimum phase system?
Yes, of course! Non-minimum phase (NMP) systems appear either when a NMP element (such as transport lag) is present in the system or may be when an inner loop is unstable. One can draw Bode plot for NMP systems, but the magnitude and phase-angle plots are not ‘uniquely related’. This does not apply to NMP systems.
Which is a minimum phase function with a zero pole?
You could use a trivial all-pass filter with impulse response h [ n] = δ [ n − 1], i.e. a simple delay by one sample to change your original (non-causal) transfer function to a stable and causal transfer function which is also minimum-phase, because it has a pole at z = 0 and a zero at z = 1 / 2.
Can a system be considered a minimum phase?
If a system is given by a transfer function in the z domain that has all poles and zeros inside the unit circle except for a factor of z − 1 in the denominator (pole at infinity), can it still be considered minimum phase?
Why are there no zeros in a stable all pole filter?
Note that every stable all- pole filter is minimum phase, because stability implies that is minimum phase, and there are “no zeros” (all are at ). Thus, minimum phase is the only phase available to a stable all-pole filter. The contribution of minimum-phase zeros to the complex cepstrum was described in § 8.8 .
Is the inverse filter stable at minimum phase?
In addition, because the zeros must also be inside the unit circle, the inverse filter is also stable when is minimum phase.