Describe the changes in the impulse response

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Reference no: EM132723978

Signal Processing First

Lab Exercise: Real Poles

(a) Use PeZ to place a single pole at z = 1 . You may have to use the Edit by Co-ord button to get the location exactly right. Use the plots for this case as the reference for answering the next four parts.

(b) Move the pole close to the origin (still on the real axis). You can do this by clicking on the pole and dragging it to the new location. Describe the changes in the impulse response h[n] and the frequency response H(ejω).

(c) You can also move poles and zeros under the influence of the Real Time Drag Plots option in PeZ. When this box is checked, the impulse response and frequency response plots are updated while you move the pole (or zero). Once this mode is set, click on the pole you want to move and start to drag it slowly. Watch for the update of the plots in the secondary window. After the real-time updating has started, you can release the mouse button and the pole (or zero) will follow the cursor. Click on the pole once more to stop moving it and to stop the updating. It is sometimes a little tricky to use this feature. Also the display may be jerky unless you have a high-performance computer with fast graphics.
Move the real pole slowly from z = 1 to z = 1 and observe the changes in the impulse response h[n] and the frequency response H(ejω).

(d) Place the pole exactly on the unit circle ( or maybe just inside at a radius of 0.99999999). Describe the changes in h[n] and H(ejω). What do you expect to see for H(ejω)?

(e) Move the pole outside the unit circle. Describe the changes in h[n]. Explain how the appearance of h[n] validates the statement that the system is not stable. In this case, the frequency response H(ejω) is not legitimate because the system is no longer stable.

(f) In general, where should poles be placed to guarantee system stability? By stability we mean that the system's output does not blow up.

Attachment:- Signal Processing First.rar

Reference no: EM132723978

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