digital_filters_Examples

digital_filters_Examples - Examples Example 10.3.4, Text...

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Examples Example 10.3.4, Text Convert the analog filter with a transfer function into a gigital IIR filter by means of the bilinear transformation. The digital filter is to have a reso- nant frequency of Solution The analog transfer function has poles at: Therefore, the anlog filter has a resonant frequency at . This is evident if we plot the mag- nitude response of the analog filter versus as shown below. This resonant frequency is to be mapped into by properly selecting the sampling rate to be used for the implementation of the IIR. Therefore, the desired transformation is The IIR transfer function is Hs () s 0.1 + s 0.1 + 2 16 + ----------------------------------- = ω r π 2 -- = s 0.1 + 2 16 +0 s 0.1 + 4 j ± s 0.1 j 4 ± == = Ω r 4 = Ω 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 frequency, radians/sec magnitude magnitude response of the anlog filter ω r π 2 = 4 2 T π 4 tan 2 T T 1 2 === s 2 T z 1 z 1 + ----------- 4 1 z 1 1 z 1 + ----------------
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The magnitude of the frequency response of the IIR filter is shown below. It clearly has a peak at Example 10.3.5
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This document was uploaded on 04/14/2010.

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digital_filters_Examples - Examples Example 10.3.4, Text...

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