digital_filters_Examples

# digital_filters_Examples - Examples Example 10.3.4, Text...

This preview shows pages 1–3. Sign up to view the full content.

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 + ----------------

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The magnitude of the frequency response of the IIR filter is shown below. It clearly has a peak at Example 10.3.5
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 04/14/2010.

### Page1 / 9

digital_filters_Examples - Examples Example 10.3.4, Text...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online