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Analyzing Filters with a Noise-Based Method

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Using the Magnitude Response Estimate Method Comparing the Estimated and Theoretical Magnitude Responses Choosing Quantized Filter Structures Converting the Structure of a Quantized Filter Converting Filters to Second-Order Sections Form

Using the Magnitude Response Estimate Method

After you design and quantize your filter, the Magnitude Response Estimate option on the Analysis menu lets you apply the noise loading method to your filter. When you select Analysis > Magnitude Response Estimate from the menubar, FDATool immediately starts the Monte Carlo trials that form the basis for the method and runs the analysis, ending by displaying the results in the analysis area in FDATool.

With the noise-based method, you estimate the complex frequency response for your filter as determined by applying a noise- like signal to the filter input. Magnitude Response Estimate uses the Monte Carlo trials to generate a noise signal that contains complete frequency content across the range 0 to Fs. The first time you run the analysis, magnitude response estimate uses default settings for the various conditions that define the process, such as the number of test points and the number of trials.

Analysis Parameter	Default Setting	Description
Number of Points	512	Number of equally spaced points around the upper half of the unit circle.
Frequency Range	0 to Fs/2	Frequency range of the plot x-axis.
Frequency Units	Hz	Units for specifying the frequency range.
Sampling Frequency	48000	Inverse of the sampling period.
Frequency Scale	dB	Units used for the y-axis display of the output.
Normalized Frequency	Off	Use normalized frequency for the display.

After your first analysis run ends, open the Analysis Parameters dialog box and adjust your settings appropriately, such as changing the number of trials or number of points.

To open the Analysis Parameters dialog box, use either of the next procedures when you have a quantized filter in FDATool:

• Select Analysis > Analysis Parameters from the menu bar

• Right-click in the filter analysis area and select Analysis Parameters from the context menu

Whichever option you choose opens the dialog box as shown in the figure. Notice that the settings for the options reflect the defaults.

Example — Noise Method Applied to a Filter

To demonstrate the magnitude response estimate method, start by creating a quantized filter. For this example, use FDATool to design a sixth-order Butterworth IIR filter.

To Use Noise-Based Analysis in FDATool

1. Enter fdatool at the MATLAB prompt to launch FDATool.

2. Under Response Type, select Highpass.

3. Select IIR in Design Method. Then select Butterworth.

4. To set the filter order to 6, select Specify order under Filter Order. Enter 6 in the text box.

5. Click Design Filter.

   In FDATool, the analysis area changes to display the magnitude response for your filter.

6. To generate the quantized version of your filter, using default quantizer settings, click on the side bar.

   FDATool switches to quantization mode and displays the quantization panel.

7. From Filter arithmetic, select fixed-point.

   Now the analysis areas shows the magnitude response for both filters — your original filter and the fixed-point arithmetic version.

8. Finally, to use noise-based estimation on your quantized filter, select Analysis > Magnitude Response Estimate from the menubar.

   FDATool runs the trial, calculates the estimated magnitude response for the filter, and displays the result in the analysis area as shown in this figure.

   

   In the above figure you see the magnitude response as estimated by the analysis method.

To View the Noise Power Spectrum

When you use the noise method to estimate the magnitude response of a filter, FDATool simulates and applies a spectrum of noise values to test your filter response. While the simulated noise is essentially white, you might want to see the actual spectrum that FDATool used to test your filter.

From the Analysis menu bar option, select Round-off Noise Power Spectrum. In the analysis area in FDATool, you see the spectrum of the noise used to estimate the filter response. The details of the noise spectrum, such as the range and number of data points, appear in the Analysis Parameters dialog box.

For more information, refer to McClellan, et al., Computer-Based Exercises for Signal Processing Using MATLAB 5, Prentice-Hall, 1998. See Project 5: Quantization Noise in Digital Filters, page 231.

To Change Your Noise Analysis Parameters

In Example — Noise Method Applied to a Filter, you used synthetic white noise to estimate the magnitude response for a fixed-point highpass Butterworth filter. Since you ran the estimate only once in FDATool, your noise analysis used the default analysis parameters settings shown in Using the Magnitude Response Estimate Method.

To change the settings, follow these steps after the first time you use the noise estimate on your quantized filter.

1. With the results from running the noise estimating method displayed in the FDATool analysis area, select Analysis > Analysis Parameters from the menubar.

   To give you access to the analysis parameters, the Analysis Parameters dialog box opens as shown here (with default settings).

   

2. To use more points in the spectrum to estimate the magnitude response, change Number of Points to 1024 and click OK to run the analysis.

   FDATool closes the Analysis Parameters dialog box and reruns the noise estimate, returning the results in the analysis area.

   To rerun the test without closing the dialog box, press Enter after you type your new value into a setting, then click Apply. Now FDATool runs the test without closing the dialog box. When you want to try many different settings for the noise-based analysis, this is a useful shortcut.

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Comparing the Estimated and Theoretical Magnitude Responses

An important measure of the effectiveness of the noise method for estimating the magnitude response of a quantized filter is to compare the estimated response to the theoretical response.

One way to do this comparison is to overlay the theoretical response on the estimated response. While you have the Magnitude Response Estimate displaying in FDATool, select Analysis > Overlay Analysis from the menu bar. Then select Magnitude Response to show both response curves plotted together in the analysis area.

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Choosing Quantized Filter Structures

FDATool lets you change the structure of any quantized filter. Use the Convert structure option to change the structure of your filter to one that meets your needs.

To learn about changing the structure of a filter in FDATool, refer to Converting the Filter Structurein your Signal Processing Toolbox documentation.

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Converting the Structure of a Quantized Filter

You use the Convert structure option to change the structure of filter. When the Source is Designed(Quantized) or Imported(Quantized), Convert structure lets you recast the filter to one of the following structures:

• Direct Form II Transposed Filter Structure

• Direct Form I Transposed Filter Structure

• Direct Form II Filter Structure

• Direct Form I Filter Structure

• Direct Form Finite Impulse Response (FIR) Filter Structure

• Direct Form FIR Transposed Filter Structure

• Lattice Autoregressive Moving Average (ARMA) Filter Structure

• dfilt.calattice

• dfilt.calatticepc

• Direct Form Antisymmetric FIR Filter Structure (Any Order)

Starting from any quantized filter, you can convert to one of the following representation:

• Direct form I

• Direct form II

• Direct form I transposed

• Direct form II transposed

• Lattice ARMA

Additionally, FDATool lets you do the following conversions:

• Minimum phase FIR filter to Lattice MA minimum phase

• Maximum phase FIR filter to Lattice MA maximum phase

• Allpass filters to Lattice allpass

Refer to FilterStructure for details about each of these structures.

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Converting Filters to Second-Order Sections Form

To learn about using FDATool to convert your quantized filter to use second-order sections, refer to Converting to Second-Order Sections in your Signal Processing Toolbox documentation. You might notice that filters you design in FDATool, rather than filters you imported, are implemented in SOS form.

To View Filter Structures in FDATool

To open the demonstration, click Help > Show filter structures. After the Help browser opens, you see the reference page for the current filter. You find the filter structure signal flow diagram on this reference page, or you can navigate to reference pages for other filter.

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Quantizing Filters in the Filter Design and Analysis Tool

Scaling Second-Order Section Filters

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