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ee 341 lab 3

# ee 341 lab 3 - Lab 3 The z-plane impulse and frequency...

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Lab 3: The z-plane, impulse and frequency responses David Rochier 0632577 July 22, 2009 EE 341 Summer 09

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Introduction: Throughout this report we analyze different pole zero plots and filter designs based on these plots. Using the Pole Zero Editor provided with the lab allowed for simple changes to be made easily and the resulting alterations to the impulse response and magnitude of the frequency response were observed. Analyzing these changes and how filters can be developed with these techniques makes up the body of this report. Procedure 1: a) As the pole approaches zero from 0.5, the impulse response approaches an ideal impulse at zero. The magnitude of the frequency response goes from the look of a low pass filter with a maximum of 2 at ω =0 to a flat uniform line with magnitude equal to zero. b) As the pole approaches the unit circle on the positive real axis the magnitude of the frequency response trends toward a single spike at ω =0 with a large maximum of approximately 20. The impulse response takes on the appearance of a slowly decaying exponential. Both of these results can be observed comparing figure 1 and 3. Figure 1: Single pole at 0.5 Figure 2: Single pole at zero Figure 3: Single pole approaching 1
c) As the pole comes in contact with the unit circle on the positive real axis the impulse response makes a dramatic transition. Although its value is still at 1 for n=0, it begins to grow in magnitude for larger n in a linear fashion. The magnitude of the frequency response grows further closer to a single impulse spike at ω =0. These changes can be observed in figure 4. d) A single pole exactly on the origin finalizes the transitions described in part a) of this section and the results are presented in figure 2. e) As the pole is moved outside the unit circle the impulse takes on another dramatic change. It converts from beginning at 1 for n=0 and linearly escalating to beginning at zero and staying uniform until about n=20, where it begins to exponentially grow. The magnitude of the frequency response is also changed. It still has the appearance of a low pass filter, except now the maximum magnitude is greater. As the pole moves further away from the unit circle on the positive axis the magnitude of the

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ee 341 lab 3 - Lab 3 The z-plane impulse and frequency...

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