The bilinear transformation is defined by the rules s = 2(1 -z−)^{T}(1+z-1).

a. Show that this transformation maps the ω axis in the s plane to the unit circle z = ejΩ in the z plane.

b. Show that this transformation maps Ω to 2 arctan(ωT/2).

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# The bilinear transformation is defined by the rules s = 2(1 -z-) T (1+z-1). a. Show that this…

The bilinear transformation is defined by the rules s = 2(1 -z−)^{T}(1+z-1).

a. Show that this transformation maps the ω axis in the s plane to the unit circle z = ejΩ in the z plane.

b. Show that this transformation maps Ω to 2 arctan(ωT/2).