The discrete time transfer function 1 2z 11 05z 1 is GATE Instrumentational Engineering 2013

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## The discrete-time transfer function (1-2z^-1)/(1-0.5z^-1) is GATE-Instrumentational-Engineering-2013

(A) Non-minimum phase and unstable
(B) Minimum phase and unstable
(C) Minimum phase and stable
(D) Non-minimum phase and stable

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In control theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable.
In contradistinction, a linear, non-minimum phase transfer function can be modeled as minimum phase transfer function in series with an all-pass-filter, the characteristic issue of that series combination will be zeroes in the right-half-plane. A consequence of zeroes in the right-half-plane, is that the inverted function is not stable. The all pass filter (can also be transport delay) inserts 'excess phase', that is why the resulting function would be non-minimum phase.

(D) Non-minimum phase and stable

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