Show whether they are right or wrong by an example. uestion 6: (A DEBATE: IS HE/

Question

Show whether they are right or wrong by an example.

uestion 6: (A DEBATE: IS HE/SHE RIGHT OR WRONG? NO 85 points 1. Hayley claims that a system is more BIBO stable if its poles are farther away from the jo axis in the left half of the s-plane. NOTE: We know what “BIBO stable" means. “More stable" here means than we need a “larger, disturbance (input) to get the system out of its way to the wilderness- Angelica thinks that Hayley is right because then the system's impulse response h(t) will be shorter in the time domain. Mark agrees with both Angelika and Hayley and he recalls that the memory of the system would then be short too, and argues that systems (e.g. people with Alzheimer) with shorter memory are more stable than the ones with longer memory 2. 3. 4. Kevin recalls the duality between the time and frequency domain and adds that the system then 5. James agrees with all the above and gives the final conjecture: systems with large bandwidth are 6. The two Hannahs however say that this is the Gain/Bandwidth game and that one has to consider must have a large bandwidth. more stable than the ones with smaller bandwidth. Parseval's theorem and conservation of energy. This means that a system with a larger bandwidth will have a smaller gain compared to a system with smaller bandwidth and larger gain. So, Alzheimer's patients may indeed be more stable but with a less impact (gain output) Multiple DEBATES: IS HE/SHE RIGHT OR WRONG? NO W Sameyah and Caleb claim that a filter with zeroes AND poles is more probably a band-pass than low-pass filter Anna and Elizabeth are sure that if a pole of a system is complex with non-zero imaginary part, the system's h(t) will be oscillatory with angular frequency equal to the imaginary part of the 7. 8. 9. Natalie and Hasna add that if the real part of the pole is large, h(t) is short in duration. 10. Tatiana, Luke, Julie and Sanskar have reservations about this business with the poles and they definitely like zeroes. They claim that in the design of the stopband of filters, zeroes and their location in the s-plane are more important than that of the poles, while poles' location is more important to create the pass-bands. They point to section 6-6 and Figure 6-23! 11. Hunter likes to design filters with OP-AMPs. He claims that such a 4th order filter has at most4 non-repeatable poles. 12. Nick is sure that the signal e3t cos(10t 6) u(t) has two complex conjugate poles

Explanation / Answer

1). Hayley claims the system is more BIBO stable if its poles are farther away form the jw axis in the left half of S-plane.

RIGHT

2). Angelica thinks that Hayley is right because then the system impulse response h(t) will be shorter in time domain.

RIGHT

3). Mark agrees with both Angelica and Hayley and he recall that memory of the system would then be short too, and argues that systems with shorter memory are more stable that ones longer memory.

WRONG (stability does not depends on memory).

4). Kevin recalls the duality between the time and frequency domain and adds that the system that much have larger bandwidth.

RIGHT

5). Systems with large bandwidth are more stable than the ones with smaller bandwidth.

RIGHT

6). RIGHT

7). Sameyah and caleb claim that a filter with zeros AND poles is more probabily a band pass filter than low pass filter.

RIGHT

8). RIGHT

9). WRONG

10). RIGHT

11). RIGHT

12). WRONG

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