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TransferFunctionExpand[tfm]

expands polynomial terms in the numerators and denominators of the TransferFunctionModel tfm.

Examples  
Basic Examples  
Scope  
Properties & Relations  
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TransferFunctionExpand

TransferFunctionExpand[tfm]

expands polynomial terms in the numerators and denominators of the TransferFunctionModel tfm.

Examples

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Basic Examples  (1)

Expand the numerator and denominator of a transfer-function model:

Wolfram Language code: TransferFunctionExpand[TransferFunctionModel[(1/s(s + 3)) + (4 s/s + 6), s]]

Scope  (4)

Expand a transfer-function model:

Wolfram Language code: TransferFunctionExpand[TransferFunctionModel[(1/s) (1/s - 1)(1/s - 10)(1/s - 100), s]]

Expand a symbolic transfer-function model:

Wolfram Language code: TransferFunctionExpand[TransferFunctionModel[{{{(q + p*s)^4}}, (b + a*s)^6}, s]]

Expand the transfer function of a MIMO system:

Wolfram Language code: TransferFunctionExpand[ TransferFunctionModel[{{{-0.252, 0.43}, {-0.0435, 0.097}}, {{(1 + 3.3*s)^2*(1 + 1800*s), (1 + 12*s)* (1 + 1800*s)}, {(1 + 25.3*s)^3*(1 + 360*s), (1 + 12*s)*(1 + 360*s)}}}, s]]

Expand the transfer function of a discrete-time system:

Wolfram Language code: TransferFunctionExpand[TransferFunctionModel[{{{0.043476*(-0.99 + z)*(-0.9048 + z)* (0.8636 + z)}}, (-0.999 + z)*(-0.9512 + z)* (-0.6036 + z)}, z, SamplingPeriod -> 0.5]]

Properties & Relations  (2)

TransferFunctionExpand is effectively the inverse of TransferFunctionFactor:

Wolfram Language code: TransferFunctionExpand[TransferFunctionFactor[TransferFunctionModel[ {{{c + b*s + a*s^2}}, r + q*s + p*s^2}, s]]]

TransferFunctionExpand expands each numerator and denominator:

Wolfram Language code: TransferFunctionExpand[TransferFunctionModel[{{{α + β, (s + α)* (s + β), (s + α)* (s + β), (s + α)* (s + β)}}, {{s^2, s^2, 1 + s^2, (s + γ)*(s + δ)}}}, s]]
Wolfram Research (2010), TransferFunctionExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionExpand.html.

Text

Wolfram Research (2010), TransferFunctionExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionExpand.html.

CMS

Wolfram Language. 2010. "TransferFunctionExpand." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TransferFunctionExpand.html.

APA

Wolfram Language. (2010). TransferFunctionExpand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransferFunctionExpand.html

BibTeX

@misc{reference.wolfram_2026_transferfunctionexpand, author="Wolfram Research", title="{TransferFunctionExpand}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/TransferFunctionExpand.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_transferfunctionexpand, organization={Wolfram Research}, title={TransferFunctionExpand}, year={2010}, url={https://reference.wolfram.com/language/ref/TransferFunctionExpand.html}, note=[Accessed: 13-June-2026]}