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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 11 69 Copyright © Orchard Publications Digital Filters w=linspace(0,Wn,length(t)/2);... % % The magnitude of the positive frequency components Xp are found from:;... % Xp=abs(X(1:length(t)/2));... % We want now to plot Xp versus radian frequency w;... % subplot(222); plot(w,Xp),title('Spectrum of Signal & Noise in Wide Range');... % % We will select the frequencies of interest with the "find" function:;... % k=find(w<=20);... % % Now we will plot this restricted range;... % subplot(212); plot(w(k), Xp(k)),title('Spectrum of Signal & Noise in Narrow Range');... % % The last plot will have grid, labels and title;... % xlabel('Frequency, rads/sec'); ylabel('Frequency Components');... title('Spectrum of Signal & Noise in Narrow Range'); grid The signal is shown in Figure 11.47. Figure 11.47. Waveforms for Example 11.23 We observe the appearance of the sinusoids at and in the lower plot. They were undistinguished in the time domain of the upper left plot. The upper right plot indicates that the signal has frequency components in the lower range of frequencies, but these cannot be identified precisely. 0 5 10 -50 0 50 100 x(t)=Signal plus Noise 0 50 100 150 200 0 1000 2000 3000 Spectrum of Signal & Noise in Wide Range 0 2 4 6 8 10 12 14 16 18 20 0 1000 2000 3000 Spectrum of Signal & Noise in Narrow Range Frequency, rads/sec Frequency Components 2 5 rad s f t ( )

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Chapter 11 Analog and Digital Filters 11 70 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications 11.6 Digital Filter Design with Simulink As stated earlier in this chapter, a digital filter, in general, is a computational process, or algo- rithm that converts one sequence of numbers representing the input signal into another sequence representing the output signal. Accordingly, a digital filter can perform functions as differentia- tion, integration, estimation, and, of course, like an analog filter, it can filter out unwanted bands of frequency. In this section we provide several applications using Simulink models. A given transfer function of a digital filter can be realized in several forms, the most com- mon being the Direct Form I , Direct Form II , Cascade (Series) , and Parallel . These are described in Subsections 11.6.1 through 11.6.4 below. Subsection 11.6.5 describes the Simulink Digital Filter Design block.
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