%% Getting Started with Discrete-Time Filter (DFILT) Objects % DFILT objects allow you to simulate and analyze discrete-time filters in % a variety of structures including direct forms, second-order sections, % lattice, and state-space. % Copyright 1988-2004 The MathWorks, Inc. % $Revision: 1.6.4.7 $ $Date: 2004/12/26 22:02:18 $ %% Getting Help % Typing "helpwin dfilt" in the command window gives you a list of % structures supported by the Signal Processing Toolbox as well as methods % operating on dfilt objects. For further information about a particular % structure or method, type "helpwin dfilt/" or "help % dfilt/". For example: help dfilt/df1 %% help dfilt/freqz %% Constructing a Discrete-Time Filter % To create a DFILT object, you need to select the structure to be used. % For example, you can implement a linear-phase even-order FIR filter % either as a direct-form FIR or as a symmetric direct-form FIR. b = fir1(50,.4); % 50th-order linear-phase FIR filter h1 = dfilt.dffir(b); % Direct-form FIR implementation h2 = dfilt.dfsymfir(b); % Symmetric direct-form FIR implementation %% % IIR filters can be implemented in any of the four direct forms. [b,a] = butter(5,.5); % 5th-order IIR filter hdf1 = dfilt.df1(b,a); % Direct-form I implementation hdf1t = dfilt.df1t(b,a); % Transposed direct-form I implementation hdf2 = dfilt.df2(b,a); % Direct-form II implementation hdf2t = dfilt.df2t(b,a); % Transposed direct-form II implementation %% % Information about discrete-time filters can be obtained by invoking the % info method, for example: info(h1) %% info(hdf2) %% % To create a copy of an object, use the copy method, for example hdf1_2 = % copy(hdf1). Note that using the syntax hdf1_2 = hdf1 copies only the object % handle and does not create a new object. %% Getting and Setting the Filter Coefficients % To manipulate the coefficients of a filter as a regular MATLAB vector, % you can always get them from the object. To modify the coefficients of an % existing DFILT object, you can set new ones. % % Direct-form FIR structures only have numerator coefficients; these are % also known as the filter weights. h1 %% b = get(h1,'Numerator'); % Assign the coefficients to vector b bnorm = b./max(b); % Manipulate the vector as usual set(h1,'Numerator',bnorm); % Set the modified coefficients %% % Direct-form IIR structures have numerator and denominator coefficients. hdf1 %% num = get(hdf1,'Numerator'); den = get(hdf1,'Denominator'); %% Filter Analysis % In addition to filtering, you can perform a wide range of analyses on % DFILT objets. Most analysis functions that work with numerator and % denominator vectors have been overloaded to work with DFILT objects. [H,w] = freqz(hdf2t); % Frequency response [Gd,w] = grpdelay(hdf1); % Group-delay [hi,n] = impz(h2); % Impulse response %% % However, the analysis functions that can produce plots are much more % powerful when working with DFILT objects since they use the Filter % Visualization Tool (FVTool) to plot instead of a regular MATLAB figure. hfvt = fvtool(hdf1t); set(hfvt, 'Color', [1 1 1]) %% % In FVTool it is possible to set different sampling frequencies (by % right-clicking anywhere on the axis), view magnitude, magnitude-squared, % magnitude (dB) or zerophase responses (by right-clicking on the y-label), % and switch between different analysis such as group delay, pole/zero % plot, etc. (by using the toolbar or the 'Analysis' menu). Most of these % actions can also be performed from FVTool's API (see Using FVTool's % Application Program Interface (API) demo for more info). For example: set(hfvt, 'MagnitudeDisplay', 'Magnitude'); %% set(hfvt, 'Analysis', 'polezero'); %% % Other analysis functions are available exclusively for DFILT objects. islinphase(h1) % Checks for linear-phase %% isstable(hdf1) % Checks for stability %% order(hdf2) % Returns filter order %% Filtering with DFILT Objects % The filtering operation is implemented for the structure selected. This % is far more flexible than the usual FILTER(b,a,x) function which always % implements transposed direct-form II. % % To filter, we use the overloaded FILTER function with the DFILT object as % its first input, then the signal to be filtered as its second input. By % default, the states of the filter, stored in the 'States' property, are % each initialized to zero. Furthermore the 'PersistentMemory' property % is false which means that the object is reset before the filter is run. % This allows to filter the same sequence twice and produce the same % output. % To filter, we use the overloaded FILTER function with the DFILT object as % its first input, then the signal to be filtered as its second input. x = ones(5,1); y = filter(hdf1, x) %% zf = hdf1.States % The object stores the final conditions in the 'States' property. %% Multistage Filters % It is possible to connect two or more DFILT objects in either cascade % (serial) or parallel configurations. Because the resulting connected % objects are DFILT objects themselves, all of the DFILT object analysis % functions are available for the composite objects as well. Moreover, % you can connect composite objects with other DFILT objects, resulting in % arbitrary levels of interconnection. Hcas = cascade(h1,hdf1); Hpar = parallel(Hcas,hdf2); y = filter(Hpar,randn(100,1)); %% % For more instructive examples we turn to functions available in the Filter % Design Toolbox. (The following code requires that you have the Filter % Design Toolbox installed) clear h; % Make sure this array is clear [b1,b2]=ifir(6,'low',[.12 .14],[.01 .001]); % Design two FIR filters h(1) = dfilt.dffir(b1); % Create a DFILT for first filter h(2) = dfilt.dffir(b2); % Create a DFILT for second filter hcas = cascade(h(:)); % Cascade both filters set(hfvt, 'Filter', hcas, 'Analysis', 'magnitude', 'MagnitudeDisplay', 'Magnitude (dB)'); %% Frequency Transformations % When the Filter Design Toolbox is installed, you can perform frequency % transformations on DFILT objects. Transformations are performed on a % per-section basis for maximum numerical accuracy. [z,p,k] = butter(30,0.4); % Lowpass Butterworth with cutoff at 0.4 [sos,g] = zp2sos(z,p,k); % Create SOS matrix hsos = dfilt.df1tsos(sos,g); % Construct SOS DFILT object hsos.PersistentMemory = true; htrans = iirlp2hp(hsos,0.4,0.8); % Transformed filter is also SOS set(hfvt, 'Filter', [hsos, htrans]); %% Generating Simulink Models % When the Signal Processing Blockset is installed, you can generate Simulink models of % DFILT objects, that maintain the exact filter structure. realizemdl(hsos, 'Blockname', 'Filter Realization'); % Each 2nd-order section is implemented as transposed direct-form I %% % Single S-Function driven blocks can also be created using the BLOCK % method. This method will use a "Digital Filter" block from the Signal % Processing Blockset and populate its coefficient fields with the % coefficients from the filter object. This method only works for the % filter structures supported by the "Digital Filter" block. bdclose block(h(1), 'Blockname', 'Digital Filter'); %% % Clean up the figures and models. close(hfvt); bdclose %% % See also