The Import Filter panel allows you to import
a filter. You can access this region by clicking the **Import
Filter** button in the sidebar.

The imported filter can be in any of the representations listed
in the **Filter Structure** pull-down menu.
You can import a filter as second-order sections by selecting the
check box.

Specify the filter coefficients in **Numerator** and **Denominator**,
either by entering them explicitly or by referring to variables in
the MATLAB^{®} workspace.

Select the frequency units from the following options in the **Units** menu,
and for any frequency unit other than Normalized, specify the value
or MATLAB workspace variable of the sampling frequency in the **Fs** field.

To import the filter, click the **Import Filter** button.
The display region is automatically updated when the new filter has
been imported.

You can edit the imported filter using the Pole/Zero Editor panel.

The available filter structures are:

Direct Form, which includes direct-form I, direct-form II, direct-form I transposed, direct-form II transposed, and direct-form FIR

Lattice, which includes lattice allpass, lattice MA min phase, lattice MA max phase, and lattice ARMA

Discrete–time Filter (

`dfilt`

object)

The structure that you choose determines the type of coefficients that you need to specify in the text fields to the right.

For direct-form I, direct-form II, direct-form I transposed, and direct-form II transposed, specify the filter by its transfer function representation

$$H(z)=\frac{b(1)+b(2){z}^{-1}+b(3){z}^{-2}+\dots b(m+1){z}^{-m}}{a(1)+a(2){z}^{-1}+a(3){Z}^{-3}+\dots a(n+1){z}^{-n}}$$

The

**Numerator**field specifies a variable name or value for the numerator coefficient vector`b`

, which contains`m+1`

coefficients in descending powers of*z.*The

**Denominator**field specifies a variable name or value for the denominator coefficient vector`a`

, which contains`n+1`

coefficients in descending powers of*z.*For FIR filters, the**Denominator**is`1`

.

Filters in transfer function form can be produced by all of
the Signal Processing Toolbox™ filter design functions (such as `fir1`

, `fir2`

, `firpm`

, `butter`

, `yulewalk`

).
See Transfer Function for
more information.

**Importing as second-order sections. **For all direct-form structures, except direct-form FIR, you
can import the filter in its second-order section representation:

$$H(z)=G\text{\hspace{0.05em}}\text{\hspace{0.05em}}{\displaystyle \prod _{k=1}^{L}\frac{{b}_{0k}+{b}_{1k}{z}^{-1}+{b}_{2k}{z}^{-2}}{{a}_{0k}+{a}_{1k}{z}^{-1}+{a}_{2k}{z}^{-2}}}$$

The **Gain** field specifies a variable name
or a value for the gain *G*, and
the **SOS Matrix** field specifies a variable name
or a value for the *L*-by-6 SOS matrix

$$SOS=\left(\begin{array}{cccccc}{b}_{01}& {b}_{11}& {b}_{21}& 1& {a}_{11}& {a}_{22}\\ {b}_{02}& {b}_{12}& {b}_{22}& 1& {a}_{12}& {a}_{22}\\ \xb7& \xb7& \xb7& \xb7& \xb7& \xb7\\ \xb7& \xb7& \xb7& \xb7& \xb7& \xb7\\ {b}_{0L}& {b}_{1L}& {b}_{2L}& 1& {a}_{1L}& {a}_{2L}\end{array}\right)$$

whose rows contain the numerator and denominator coefficients *b*_{ik} and *a*_{ik} of
the second-order sections of *H*(*z*).

Filters in second-order section form can be produced by functions
such as `tf2sos`

, `zp2sos`

, `ss2sos`

,
and `sosfilt`

. See Second-Order Sections (SOS) for
more information.

For lattice allpass, lattice minimum and maximum phase, and lattice ARMA filters, specify the filter by its lattice representation:

For lattice allpass, the

**Lattice coeff**field specifies the lattice (reflection) coefficients,`k(1)`

to`k(N)`

, where`N`

is the filter order.For lattice MA (minimum or maximum phase), the

**Lattice coeff**field specifies the lattice (reflection) coefficients,`k(1)`

to`k(N)`

, where`N`

is the filter order.For lattice ARMA, the

**Lattice coeff**field specifies the lattice (reflection) coefficients,`k(1)`

to`k(N)`

, and the**Ladder coeff**field specifies the ladder coefficients,`v(1)`

to`v(N+1)`

, where`N`

is the filter order.

Filters in lattice form can be produced by `tf2latc`

. See Lattice Structure for
more information.

For Discrete-time filter, specify the name of the `dfilt`

object. See `dfilt`

for more information.

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