Learn more about Filter Design Toolbox

Transforming Filters

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FDATool Filter Transformation Capabilities Original Filter Type Frequency Point to Transform Transformed Filter Type Specify Desired Frequency Location

FDATool Filter Transformation Capabilities

The toolbox provides functions for transforming filters between various forms. When you use FDATool with the toolbox installed, a side bar button and a menu bar option enable you to use the Transform Filter panel to transform filters as well as using the command line functions.

From the selection on the FDATool menu bar — Transformations — you can transform lowpass FIR and IIR filters to a variety of passband shapes.

You can convert your FIR filters from:

• Lowpass to lowpass.

• Lowpass to highpass.

For IIR filters, you can convert from:

• Lowpass to lowpass.

• Lowpass to highpass.

• Lowpass to bandpass.

• Lowpass to bandstop.

When you click the Transform Filter button, , on the side bar, the Transform Filter panel opens in FDATool, as shown here.

Your options for Original filter type refer to the type of your current filter to transform. If you select lowpass, you can transform your lowpass filter to another lowpass filter or to a highpass filter, or to numerous other filter formats, real and complex.

Note   When your original filter is an FIR filter, both the FIR and IIR transformed filter type options appear on the Transformed filter type list. Both options remain active because you can apply the IIR transforms to an FIR filter. If your source is as IIR filter, only the IIR transformed filter options show on the list.

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Original Filter Type

Select the magnitude response of the filter you are transforming from the list. Your selection changes the types of filters you can transform to. For example:

• When you select Lowpass with an IIR filter, your transformed filter type can be

  • Lowpass

  • Highpass

  • Bandpass

  • Bandstop

  • Multiband

  • Bandpass (complex)

  • Bandstop (complex)

  • Multiband (complex)

• When you select Lowpass with an FIR filter, your transformed filter type can be

  • Lowpass

  • Lowpass (FIR)

  • Highpass

  • Highpass (FIR) narrowband

  • Highpass (FIR) wideband

  • Bandpass

  • Bandstop

  • Multiband

  • Bandpass (complex)

  • Bandstop (complex)

  • Multiband (complex)

In the following table you see each available original filter type and all the types of filter to which you can transform your original.

Original Filter	Available Transformed Filter Types
Lowpass FIR	Lowpass Lowpass (FIR) Highpass Highpass (FIR) narrowband Highpass (FIR) wideband Bandpass Bandstop Multiband Bandpass (complex) Bandstop (complex) Multiband (complex)
Lowpass IIR	Lowpass Highpass Bandpass Bandstop Multiband Bandpass (complex) Bandstop (complex) Multiband (complex)
Highpass FIR	Lowpass Lowpass (FIR) narrowband Lowpass (FIR) wideband Highpass (FIR) Highpass Bandpass Bandstop Multiband Bandpass (complex) Bandstop (complex) Multiband (complex)
Highpass IIR	Lowpass Highpass Bandpass Bandstop Multiband Bandpass (complex) Bandstop (complex) Multiband (complex)
Bandpass FIR	Bandpass Bandpass (FIR)
Bandpass IIR	Bandpass
Bandstop FIR	Bandstop Bandstop (FIR)
Bandstop IIR	Bandstop

Note also that the transform options change depending on whether your original filter is FIR or IIR. Starting from an IIR filter, you can transform to IIR or FIR forms. With an IIR original filter, you are limited to IIR target filters.

After selecting your response type, use Frequency point to transform to specify the magnitude response point in your original filter to transfer to your target filter. Your target filter inherits the performance features of your original filter, such as passband ripple, while changing to the new response form.

For more information about transforming filters, refer to Frequency Transformations for Real Filters and Frequency Transformations for Complex Filters.

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Frequency Point to Transform

The frequency point you enter in this field identifies a magnitude response value (in dB) on the magnitude response curve.

When you enter frequency values in the Specify desired frequency location option, the frequency transformation tries to set the magnitude response of the transformed filter to the value identified by the frequency point you enter in this field.

While you can enter any location, generally you should specify a filter passband or stopband edge, or a value in the passband or stopband.

The Frequency point to transform sets the magnitude response at the values you enter in Specify desired frequency location. Specify a value that lies at either the edge of the stopband or the edge of the passband.

If, for example, you are creating a bandpass filter from a highpass filter, the transformation algorithm sets the magnitude response of the transformed filter at the Specify desired frequency location to be the same as the response at the Frequency point to transform value. Thus you get a bandpass filter whose response at the low and high frequency locations is the same. Notice that the passband between them is undefined. In the next two figures you see the original highpass filter and the transformed bandpass filter.

For more information about transforming filters, refer to Digital Frequency Transformations.

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Transformed Filter Type

Select the magnitude response for the target filter from the list. The complete list of transformed filter types is:

• Lowpass

• Lowpass (FIR)

• Highpass

• Highpass (FIR) narrowband

• Highpass (FIR) wideband

• Bandpass

• Bandstop

• Multiband

• Bandpass (complex)

• Bandstop (complex)

• Multiband (complex)

Not all types of transformed filters are available for all filter types on the Original filter types list. You can transform bandpass filters only to bandpass filters. Or bandstop filters to bandstop filters. Or IIR filters to IIR filters.

For more information about transforming filters, refer to Frequency Transformations for Real Filters and Frequency Transformations for Complex Filters.

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Specify Desired Frequency Location

The frequency point you enter in Frequency point to transform matched a magnitude response value. At each frequency you enter here, the transformation tries to make the magnitude response the same as the response identified by your Frequency point to transform value.

While you can enter any location, generally you should specify a filter passband or stopband edge, or a value in the passband or stopband.

For more information about transforming filters, refer to Digital Frequency Transformations.

Example — Transform Filters

To transform the magnitude response of your filter, use the Transform Filter option on the side bar.

1. Design or import your filter into FDATool.

2. Click Transform Filter, , on the side bar.

   FDATool opens the Transform Filter panel in FDATool.

   

3. From the Original filter type list, select the response form of the filter you are transforming.

   When you select the type, whether is lowpass, highpass, bandpass, or bandstop, FDATool recognizes whether your filter form is FIR or IIR. Using both your filter type selection and the filter form, FDATool adjusts the entries on the Transformed filter type list to show only those that apply to your original filter.

4. Enter the frequency point to transform value in Frequency point to transform. Notice that the value you enter must be in KHz; for example, enter 0.1 for 100 Hz or 1.5 for 1500 Hz.

5. From the Transformed filter type list, select the type of filter you want to transform to.

   Your filter type selection changes the options here.

   • When you pick a lowpass or highpass filter type, you enter one value in Specify desired frequency location.

   • When you pick a bandpass or bandstop filter type, you enter two values — one in Specify desired low frequency location and one in Specify desired high frequency location. Your values define the edges of the passband or stopband.

   • When you pick a multiband filter type, you enter values as elements in a vector in Specify a vector or desired frequency locations — one element for each desired location. Your values define the edges of the passbands and stopbands.

     After you click Transform Filter, FDATool transforms your filter, displays the magnitude response of your new filter, and updates the Current Filter Information to show you that your filter has been transformed. In the filter information, the Source is Transformed.

     For example, the figure shown here includes the magnitude response curves for two filter. The original filter is a lowpass filter with rolloff between 0.2 and 0.25. The transformed filter is a lowpass filter with rolloff region between 0.8 and 0.85.

     

   • To transform your lowpass filter to a highpass filter, select Lowpass to Highpass.
     
     When you select Lowpass to Highpass, FDATool returns the dialog box shown here. More information about the Select Transform... dialog box follows the figure.

     

     
     
     

     To demonstrate the effects of selecting Narrowband Highpass or Wideband Highpass, the next figure presents the magnitude response curves for a source lowpass filter after it is transformed to both narrow- and wideband highpass filters. For comparison, the response of the original filter appears as well.

     

     
     
     

     For the narrowband case, the transformation algorithm essentially reverses the magnitude response, like reflecting the curve around the y-axis, then translating the curve to the right until the origin lies at 1 on the x-axis. After reflecting and translating, the passband at high frequencies is the reverse of the passband of the original filter at low frequencies with the same rolloff and ripple characteristics.

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Importing XILINX Coefficient (.COE) Files

Designing Multirate Filters in FDATool

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