Show that this transformation maps the ? axis in the s plane

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Reference no: EM131316297

1. In an impulse invariance design, show that if Ha(s) is a transfer function of a stable system, the corresponding H[z] is also a transfer function of a stable system.

2. First-order backward differences provide the transformation rule s = (1- z^-1)/T

a. Show that this transformation maps the ω axis in the s plane to a circle of radius 1/2 centered at (1/2, 0) in the z plane.

b. Show that this transformation maps the left-half s plane to the interior of the unit circle in the z plane, which ensures that stability is preserved.

Reference no: EM131316297

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