## 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`

`residuez`

`tf2latc`

none

`convmtx`

State-Space

`ss2tf`

`ss2zp`

none

none

`ss2sos`

none

Zero-Pole- Gain

`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.