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If s=jΩ and if Ω varies from -∞ to ∞, then what is the corresponding locus of points in z-plane?(a) Circle of radius 1 with centre at z=0(b) Circle of radius 1 with centre at z=1(c) Circle of radius 1/2 with centre at z=1/2(d) Circle of radius 1 with centre at z=1/2I had been asked this question at a job interview.Origin of the question is IIR Filter Design by Approximation of Derivatives in section Digital Filters Design of Digital Signal Processing

Answer» RIGHT option is (c) Circle of radius 1/2 with centre at z=1/2

To explain I WOULD say: We know that

s=(1-z^-1)/T

=> z=1/(1-sT)

Given s= jΩ => z = 1/(1- jΩT)

Thus from the above equation if Ω varies from -∞ to ∞, then the corresponding LOCUS of POINTS in z-plane is a circle of radius 1/2 with centre at z=1/2.


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