Signals and Systems

SIGNIFICANT POINTS

Transfer function of a delay element

Transfer function           

ϕ(k) = Inverse z-transform of [zI − A]z

= z⁻¹[zI − A]⁻¹ = state transition matrix.

Zero Input Response (ZIR) The response which occurs even without input is known as zero input response and it is due to the initial condition.

 

ZIR = ϕ (k) x(0) = A^k x(0)

 

where ϕ(k) = A^k is termed as a state transition matrix.

Zero State Response The response which occurs when all initial conditions are zero is known as the zero state response.

 

Characteristic Polynomial ...