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# dfilt.df1sos

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

## Syntax

Hd = dfilt.df1sos(s)
Hd = dfilt.df1sos(b1,a1,b2,a2,...)
Hd = dfilt.df1sos(...,g)
Hd = dfilt.df1sos

## Description

Hd = dfilt.df1sos(s) returns a discrete-time, second-order section, direct-form I filter, Hd, with coefficients given in the s matrix. The filter states for this object are stored in a filtstates object.

Hd = dfilt.df1sos(b1,a1,b2,a2,...) returns a discrete-time, second-order section, direct-form I filter, 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.df1sos(...,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.df1sos returns a default, discrete-time, second-order section, direct-form I filter, Hd. This filter passes the input through to the output unchanged.

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

To display the filter states, use this code to access the filtstates object.

```Hs = Hd.states     % Where Hd is the dfilt.df1 object and
double (Hs)        % Hs is the filtstates object
```

The vector is

$\left(\begin{array}{cc}zb1\left(1\right)& zb2\left(1\right)\\ zb1\left(2\right)& zb2\left(2\right)\\ za1\left(1\right)& za2\left(1\right)\\ za1\left(2\right)& za2\left(2\right)\end{array}\right)$

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

## Examples

Specify a second-order sections, direct-form I discrete-time filter with coefficients from a sixth order, lowpass, elliptical filter using the following code. The resulting filter has three sections.

```[z,p,k] = ellip(6,1,60,.4);  % Obtain filter coefficients
[s,g] = zp2sos(z,p,k);       % Convert to SOS
Hd = dfilt.df1sos(s,g)
```