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	tf2sos	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.