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TransferFunctionTransform[f,tf]

transforms the TransferFunctionModel object tf using the transformation function f.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Analog Filter Transformations  
Digital Filter Transformations  
Possible Issues  
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TransferFunctionTransform

TransferFunctionTransform[f,tf]

transforms the TransferFunctionModel object tf using the transformation function f.

Details

Examples

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Basic Examples  (1)

Transform a model of a lowpass filter to high pass:

Wolfram Language code: TransferFunctionTransform[1 / #&, TransferFunctionModel[{{{1}}, 1 + s}, s]]

Scope  (1)

Change the cutoff frequency of a lowpass filter from 1 to 2000 radians per second (1000 Hz):

Wolfram Language code: TransferFunctionTransform[# / (2000 Pi)&, TransferFunctionModel[{{{1}}, 1 + s}, s]]

Applications  (2)

Analog Filter Transformations  (1)

An analog lowpass Butterworth filter:

Wolfram Language code: tf = ButterworthFilterModel[3, s]//TransferFunctionExpand//Chop

Lowpass to lowpass transformation of an analog filter:

Wolfram Language code: TransferFunctionTransform[(# / a)&, tf]
Wolfram Language code: lowpass = TransferFunctionTransform[# / 2&, tf]
Wolfram Language code: Plot[{Abs[tf[I x]], Abs[lowpass[I x]]}, {x, 0, 5}, PlotRange -> All]

Lowpass to highpass transformation of an analog filter:

Wolfram Language code: highpass = TransferFunctionTransform[1 / #&, tf]
Wolfram Language code: Plot[{Abs[tf[I x]], Abs[highpass[I x]]}, {x, 0, 5}, PlotRange -> All]

Lowpass to band-stop transformation of an analog filter:

Wolfram Language code: TransferFunctionTransform[(B #/#^2 + a^2)&, tf]
Wolfram Language code: bandstop = TransferFunctionTransform[(2 #/#^2 + 1)&, tf]
Wolfram Language code: Plot[{Abs[tf[I x]], Abs[bandstop[I x]]}, {x, 0, 5}, PlotRange -> All]

Lowpass to bandpass transformation of an analog filter:

Wolfram Language code: TransferFunctionTransform[(1/B)(#^2 + a^2/#)&, tf]
Wolfram Language code: bandpass = TransferFunctionTransform[(1/2)(#^2 + 1/#)&, tf]
Wolfram Language code: Plot[{Abs[tf[I x]], Abs[bandpass[I x]]}, {x, 0, 5}, PlotRange -> All]

Digital Filter Transformations  (1)

A digital lowpass Butterworth filter with a cutoff frequency of :

Wolfram Language code: dtf = TransferFunctionModel[{{{4*(1 + z)^2}}, {{4*(2 - Sqrt[2] + 2*z^2 + Sqrt[2]*z^2)}}}, z, SamplingPeriod -> 1];

Change the cutoff frequency to :

Wolfram Language code: λ = Sin[(π / 2 - π / 4/2)] / Sin[(π / 2 + π / 4/2)]; res = TransferFunctionTransform[(# - λ) / (1 - λ #)&, dtf]
Wolfram Language code: Plot[{Abs[dtf[E ^ (I x)]], Abs[res[E ^ (I x)]]}, {x, 0, Pi}, GridLines -> {{π / 4, π / 2}, {1 / Sqrt[2]}}]

Possible Issues  (1)

Specified transformation might return an invalid transfer function model:

Wolfram Language code: TransferFunctionTransform[f, TransferFunctionModel[{{{1}}, s}, s]]
Wolfram Research (2012), TransferFunctionTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionTransform.html.

Text

Wolfram Research (2012), TransferFunctionTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionTransform.html.

CMS

Wolfram Language. 2012. "TransferFunctionTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TransferFunctionTransform.html.

APA

Wolfram Language. (2012). TransferFunctionTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransferFunctionTransform.html

BibTeX

@misc{reference.wolfram_2026_transferfunctiontransform, author="Wolfram Research", title="{TransferFunctionTransform}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/TransferFunctionTransform.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_transferfunctiontransform, organization={Wolfram Research}, title={TransferFunctionTransform}, year={2012}, url={https://reference.wolfram.com/language/ref/TransferFunctionTransform.html}, note=[Accessed: 13-June-2026]}