User manual MATLAB FILTER DESIGN TOOLBOX 4

[. . . ] Filter Design ToolboxTM 4 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Filter Design ToolboxTM User's Guide © COPYRIGHT 2000­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] For example: · When you select Lowpass with an IIR filter, your transformed filter type can be - Lowpass Highpass Bandpass Bandstop Multiband 4-57 4 Using FDATool with Filter Design ToolboxTM Software - 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 Lowpass FIR Available Transformed Filter Types · Lowpass · Lowpass (FIR) · Highpass · Highpass (FIR) narrowband · Highpass (FIR) wideband · Bandpass · Bandstop · Multiband 4-58 Transforming Filters Original Filter Available Transformed Filter Types · 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) 4-59 4 Using FDATool with Filter Design ToolboxTM Software Original Filter Highpass IIR Available Transformed Filter Types · Lowpass · Highpass · Bandpass · Bandstop · Multiband · Bandpass (complex) · Bandstop (complex) · Multiband (complex) Bandpass FIR Bandpass IIR Bandstop FIR Bandstop IIR · Bandpass · Bandpass (FIR) Bandpass · Bandstop · Bandstop (FIR) Bandstop Note also that the transform options change depending on whether your original filter is FIR or IIR. 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" on page 3-11 and "Frequency Transformations for Complex Filters" on page 3-26. 4-60 Transforming Filters 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. In the next two figures you see the original highpass filter and the transformed bandpass filter. For more information about transforming filters, refer to Chapter 3, "Digital Frequency Transformations". 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 4-61 4 Using FDATool with Filter Design ToolboxTM Software · 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. For more information about transforming filters, refer to "Frequency Transformations for Real Filters" on page 3-11 and "Frequency Transformations for Complex Filters" on page 3-26. 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 Chapter 3, "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. 4-62 Transforming Filters 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. [. . . ] You can verify this by comparing them: max(abs(yf. int - yri. int)) ans = 0 6-15 6 Using Integers and FIR Filters with Filter Design Toolbox Using the set2int Method In this section. . . "Setting Filter Parameters to Work with Integers" on page 6-16 "Reinterpreting the Output" on page 6-17 Setting Filter Parameters to Work with Integers The set2int method provides a convenient way of setting filter parameters to work with integers. The method works by scaling the coefficients to integer numbers, and setting the coefficients and input fraction length to zero. This makes it possible for you to use floating-point coefficients directly. h = dfilt. dffir(b); h. Arithmetic = 'fixed'; The coefficients are represented with 18 bits and the input signal is represented with 12 bits: g = set2int(h, 18, 12); g_dB = 20*log10(g) g_dB = 1. 083707984390332e+002 The set2int method returns the gain of the filter by scaling the coefficients to integers, so the gain is always a power of 2. [. . . ]