# Documentation

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## Design a Filter Using fdesign

Use the following two steps to design a simple filter.

1. Create a filter specification object.

Example 1. Design a Filter in Two Steps

Assume that you want to design a bandpass filter. Typically a bandpass filter is defined as shown in the following figure.

In this example, a sampling frequency of `Fs` = 48 kHz is used. This bandpass filter has the following specifications, specified here using MATLAB® code:

```A_stop1 = 60; % Attenuation in the first stopband = 60 dB F_stop1 = 8400; % Edge of the stopband = 8400 Hz F_pass1 = 10800; % Edge of the passband = 10800 Hz F_pass2 = 15600; % Closing edge of the passband = 15600 Hz F_stop2 = 18000; % Edge of the second stopband = 18000 Hz A_stop2 = 60; % Attenuation in the second stopband = 60 dB A_pass = 1; % Amount of ripple allowed in the passband = 1 dB```

In the following two steps, these specifications are passed to the `fdesign.bandpass` method as parameters.

Step 1

To create a filter specification object, evaluate the following code at the MATLAB prompt:

`d = fdesign.bandpass`

Now, pass the filter specifications that correspond to the default `Specification``fst1`,`fp1`,`fp2`,`fst2`,`ast1`,`ap`,`ast2`. This example adds `fs` as the final input argument to specify the sampling frequency of 48 kHz.

```>> BandPassSpecObj = ... fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2', ... F_stop1, F_pass1, F_pass2, F_stop2, A_stop1, A_pass, ... A_stop2, 48000) ```

### Note

The order of the filter is not specified, allowing a degree of freedom for the algorithm design in order to achieve the specification. The design will be a minimum order design.

The specification parameters, such as `Fstop1`, are all given default values when none are provided. You can change the values of the specification parameters after the filter specification object has been created. For example, if there are two values that need to be changed, `Fpass2` and `Fstop2`, use the `set` command, which takes the object first, and then the parameter value pairs. Evaluate the following code at the MATLAB prompt:

`>> set(BandPassSpecObj, 'Fpass2', 15800, 'Fstop2', 18400) `
`BandPassSpecObj` is the new filter specification object which contains all the required design parameters, including the filter type.

You may also change parameter values in filter specification objects by accessing them as if they were elements in a `struct` array.

`>> BandPassSpecObj.Fpass2=15800;`

Step 2

Design the filter by using the `design` command. You can access the design methods available for you specification object by calling the `designmethods` function. For example, in this case, you can execute the command

```>> designmethods(BandPassSpecObj) Design Methods for class fdesign.bandpass (Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2): butter cheby1 cheby2 ellip equiripple kaiserwin```
After choosing a design method use, you can evaluate the following at the MATLAB prompt (this example assumes you've chosen '`equiripple`'):
```>> BandPassFilt = design(BandPassSpecObj, 'equiripple') BandPassFilt = FilterStructure: 'Direct-Form FIR' Arithmetic: 'double' Numerator: [1x44 double] PersistentMemory: false ```

If you have the DSP System Toolbox™ installed, you can also design your filter with a filter System object™. To create a filter System object with the same specification object `BandPassSpecObj`, you can execute the commands

```>> designmethods(BandPassSpecObj,... 'SystemObject',true) Design Methods that support System objects for class fdesign.bandpass (Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2): butter cheby1 cheby2 ellip equiripple kaiserwin >> BandPassFiltSysObj = design(BandPassSpecObj,... 'equiripple','SystemObject',true) System: dsp.FIRFilter Properties: Structure: 'Direct form' NumeratorSource: 'Property' Numerator: [1x44 double] InitialConditions: 0 FrameBasedProcessing: true Show fixed-point properties ```
Available design methods and design options for filter System objects are not necessarily the same as those for filter objects.

### Note

If you do not specify a design method, a default method will be used. For example, you can execute the command

```>> BandPassFilt = design(BandPassSpecObj) BandPassFilt = FilterStructure: 'Direct-Form FIR' Arithmetic: 'double' Numerator: [1x44 double] PersistentMemory: false```
and a design method will be selected automatically.

To check your work, you can plot the filter magnitude response using the Filter Visualization tool. Verify that all the design parameters are met:

`>> fvtool(BandPassFilt) %plot the filter magnitude response`
If you have the DSP System Toolbox installed, the Filter Visualization tool produces the following figure with the dashed red lines indicating the transition bands and unity gain (0 in dB) over the passband.