Accelerating the pace of engineering and science

# dfilt.df2

Discrete-time, direct-form II filter

## Syntax

Hd = dfilt.df2(b,a)
Hd = dfilt.df2

## Description

Hd = dfilt.df2(b,a) returns a discrete-time, direct-form II filter, Hd, with numerator coefficients b and denominator coefficients a.

Hd = dfilt.df2 returns a default, discrete-time, direct-form II filter, Hd, with b=1 and a=1. 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

$\left[\begin{array}{c}z\left(1\right)\\ z\left(2\right)\\ \cdots \\ z\left(n\right)\end{array}\right]$

## Examples

Create a direct-form II discrete-time filter with coefficients from a fourth-order lowpass Butterworth design:

```[b,a] = butter(4,.5);
Hd = dfilt.df2(b,a)
```