compute the impulse-response of a system - Maple Help

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DynamicSystems[ImpulseResponse] - compute the impulse-response of a system

Calling Sequence

ImpulseResponse( sys, opts )

Parameters

sys

-

System; linear system

opts

-

(optional) equation(s) of the form option = value; specify options for the ImpulseResponse command

Description

• 

The ImpulseResponse command computes the impulse response of sys, a System object.

• 

The ImpulseResponse command returns an algebraic Matrix, except in the case when the option format=piecewise is selected, as described under Options, and the output may be a piecewise expression of Matrices.

• 

Two methods are provided for computing the impulse response of a system.

• 

The function method generates a transfer-function model of sys, then computes the inverse Laplace transformation or the inverse z-transformation, for continuous and discrete system, respectively.

• 

The matrix method generates a state-space model of sys, then computes the impulse response from the state-transition matrix.

For a continuous system the impulse response is C . exp(A*t) . B + D*Dirac(t).

For a discrete system the impulse response is (C . A^(q-1) . B)(1 - charfcn[0](q)) + D*charfcn[0](q).

Examples

withDynamicSystems:

sys:=NewSystemss2+ω2,s+1s2+3:

imp:=ImpulseResponsesys

imp:=cosωtcos3t+133sin3t

(1)

Use inttrans[laplace] to compute the transfer-functions from the impulse response.

withinttrans:

maplaplace,imp,t,s

ss2+ω2s+1s2+3

(2)

The impulse response of a discrete system consists of expressions in terms of the discrete time variable (generally q).

sys:=NewSystem1z+1,zaz+b,discrete:

imp:=ImpulseResponsesys

imp:=1q+charfcn0qbqa+bqbacharfcn0qb

(3)

Use ztrans to compute the transfer-functions from the impulse response.

simplifymapztrans,imp,q,z

1z+1z+az+b

(4)

Use the matrix method with the piecewise format.

simplifyImpulseResponsesys,method=matrix,format=piecewise

&lcub;01q01qa&plus;bbq1&plus;bq1&plus;b0<q

(5)

See Also

charfcn, Dirac, DynamicSystems, DynamicSystems[ImpulseResponsePlot], inttrans[laplace], LinearAlgebra[MatrixExponential], piecewise, ztrans


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