# Documentation

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# dfilt.df2sos

Discrete-time, second-order section, direct-form II filter

## Syntax

```Hd = dfilt.df2sos(s) Hd = dfilt.df2sos(b1,a1,b2,a2,...) Hd = dfilt.df2sos(...,g) Hd = dfilt.df2sos ```

## Description

`Hd = dfilt.df2sos(s)` returns a discrete-time, second-order section, direct-form II filter, `Hd`, with coefficients given in the `s` matrix.

`Hd = dfilt.df2sos(b1,a1,b2,a2,...)` returns a discrete-time, second-order section, direct-form II object, `Hd`, with coefficients for the first section given in the `b1` and `a1` vectors, for the second section given in the `b2` and `a2` vectors, etc.

`Hd = dfilt.df2sos(...,g)` includes a gain vector `g`. The elements of `g` are the gains for each section. The maximum length of `g` is the number of sections plus one. If `g` is not specified, all gains default to one.

`Hd = dfilt.df2sos` returns a default, discrete-time, second-order section, direct-form II filter, `Hd`. This filter passes the input through to the output unchanged.

### Note

The leading coefficient of the denominator `a(1)` cannot be 0.

The resulting filter states column vector is

`$\left(\begin{array}{cc}z1\left(1\right)& z2\left(1\right)\\ z1\left(2\right)& z2\left(2\right)\end{array}\right)$`

For filters with more than one section, each section is a separate column in the vector.

## Examples

Specify a second-order sections, direct-form II discrete-time filter with coefficients from a sixth order, lowpass, elliptical filter using the following code:

```[z,p,k] = ellip(6,1,60,.4); % Obtain filter coefficients [s,g] = zp2sos(z,p,k); % Convert to SOS Hd = dfilt.df2sos(s,g) ```