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Linear System Transformations

The Signal Processing Toolbox provides a number of functions that convert between the various linear system models; see Function Reference for a complete description of each. You can use the following chart to find an appropriate transfer function: find the row of the model to convert from on the left side of the chart and the column of the model to convert to on the top of the chart and read the function name(s) at the intersection of the row and column.

Note that some cells of this table are empty.

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Transfer Function


State- Space

Zero-
Pole-
Gain


Partial Fraction


Lattice Filter

Second-
Order Sections


Convolution
Matrix

Transfer Function

tf2ss
tf2zp roots
residuez
tf2latc
none
convmtx
State-Space
ss2tf

ss2zp
none
none
ss2sos
none
Zero-Pole- Gain
zp2tf poly
zp2ss

none
none
zp2sos
none
Partial Fraction
residuez
none
none

none
none
none
Lattice Filter
latc2tf
none
none
none

none
none
SOS
sos2tf
sos2ss
sos2zp
none
none

none

Many of the toolbox filter design functions use these functions internally. For example, the zp2ss function converts the poles and zeros of an analog prototype into the state-space form required for creation of a Butterworth, Chebyshev, or elliptic filter. Once in state-space form, the filter design function performs any required frequency transformation, that is, it transforms the initial lowpass design into a bandpass, highpass, or bandstop filter, or a lowpass filter with the desired cutoff frequency. See the descriptions of the individual filter design functions in Function Reference, for more details.


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