# dfilt.df1t

Discrete-time, direct-form I transposed filter

## Syntax

`Hd = dfilt.df1t(b,a)Hd = dfilt.df1t`

## Description

`Hd = dfilt.df1t(b,a)` returns a discrete-time, direct-form I transposed filter, `Hd`, with numerator coefficients `b` and denominator coefficients `a`. The filter states for this object are stored in a `filtstates` object.

`Hd = dfilt.df1t` returns a default, discrete-time, direct-form I transposed 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.

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 of states is:

$\left(\begin{array}{c}zb\left(1\right)\\ zb\left(2\right)\\ ⋮\\ zb\left(M\right)\\ za\left(1\right)\\ za\left(2\right)\\ ⋮\\ za\left(N\right)\end{array}\right)$

Alternatively, you can access the states in the filtstates object:

```b = [0.05 0.9 0.05]; Hd = dfilt.df1t(b,1); Hd.States % Returns % Numerator: [2x1 double] % Denominator: [0x1 double] Hd.States.Numerator(1)=1; %Set zb(1) equal to 1.```

## Examples

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

```[b,a] = butter(4,.5); Hd = dfilt.df1t(b,a) ```