Main Content

Linear System Transformations

A number of Signal Processing Toolbox™ functions are provided to convert between the various linear system models. 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.

To →

From ↓

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

Note

Converting from one filter structure or model to another may produce a result with different characteristics than the original. This is due to the computer's finite-precision arithmetic and the variations in the conversion's round-off computations.

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.

Note

All Signal Processing Toolbox second-order section transformations apply only to digital filters.