An important input-output description of a linear discrete-time system is its (discrete-time) impulse response (or pulse response), which is the response h(k, k0) to a discrete impulse applied at time k0. In time-invariant systems that are also causal and at rest at time zero, the impulse response is h(k, 0), and its z-transform is the transfer function of the system. Expressions for h(k, k0) when the system is described by state variable equations are derived.
Linear systems Discrete-time Time-invariant Time-varying Discrete-time impulse response descriptions Pulse response descriptions Transfer function descriptions Causal At rest
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