EL 6183 Week No 6 - Polytechnic University EL 6183 EE 4163...

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Polytechnic University EL 6183 EE 4163 DSP lab Lab #6 IIR Filter: Applications A) Objectives At the end of this lab, students will be able to: Design Low Pass IIR filters that have the same magnitude response as a Low Pass analog filter prototype using bilinear transformation Choose the IIR filter order based on given filter characteristics. Design Low Pass, Band Pass, and Band Stop filters from a Low Pass Filter Implement IIR filters using the TMS320C6711 DSK B) Lab Report For lab report #6, in addition to: 1
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the traditional well formatted cover page, the signed pages of this lab, the conclusion, students are expected to: include a screen capture of waveforms insert their C/C++ source codes, The step by step design details for Activity 2 .a explain the choices made if any, etc. C) Low Pass IIR Filter Design from a Low Pass Analog Prototype using Bilinear Transformation. Consider the transfer function H(s) of an analog Low Pass filter that satisfies some frequency specifications. The goal is to infer from H(s) a digital filter H(z) that has the same frequency characteristics as the analog filter. In that case, it is obvious that we need a relationship between the Laplace variable “ s ” and the Z-domain variable “ z ”. This transformation will need to convert the s-plane to the z-plane, or, more specifically, it will need to convert the imaginary axis in the s-plane to the unit circle in the z-plane. The Bilinear Transformation. The bilinear transformation defined as: 1 1 . 2 + - z z Fs s Eqt 1 where Fs is the sampling rate, achieves that goal. In other words, to obtain H(z) , one only has to replace s by 1 1 . 2 + - z z Fs in H(s) . 2
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Unfortunately, with that substitution, the bandwidth of the digital filter does not match that of the analog filter exactly. This is due to the warping effect of the bilinear transformation. Indeed, since in the frequency domain s becomes , and z becomes e jw , the bilinear transformation becomes: ) 2 tan( 2 ϖ Fs Eqt 2 or ) 2 ( tan 2 1 Fs - Eqt 3 As a result, the bilinear equation, as attested by Et 3, compresses the analog angular frequency scale [0 ∞], to the digital angular frequency scale [0 π]. Therefore, before using the bilinear transformation as stated in Eqt 1, the analog frequency needs to be prewarped using Eqt 2. Design Steps for Low Pass IIR Filter when H(s) is known. Step 1. Convert the given (or identified) analog frequency values in digital using the giving sampling rate. Fs F f = Step 2. Compute the corresponding digital angular frequency value. f π 2 = Step 3. Prewarp the analog frequencies using Eqt 2 correpsonding to the digital frequencies computed in Step 2. Step 4.
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This note was uploaded on 03/04/2010 for the course EE ee taught by Professor Ee during the Spring '10 term at Istanbul Technical University.

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EL 6183 Week No 6 - Polytechnic University EL 6183 EE 4163...

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