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Signals and Systems by Smarajit Ghosh

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SIGNIFICANT POINTS

Transfer function of a delay element image

Transfer function           image

ϕ(k) = Inverse z-transform of [zIA]z
= z−1[zIA]−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) = Ak x(0)

 

where ϕ(k) = Ak 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 ...

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