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sp_S21_mud - Lecture S21 Muddiest Points General Comments...

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Lecture S21 Muddiest Points General Comments Today, we began talking about the relationship between duration and bandwidth. For any given signal shape, there is an inverse relationship between duration and bandwidth. The optimal signal shape, in terms of minimizing both duration and bandwidth (as we have defined it) turns out to be a Gaussian. Responses to Muddiest-Part-of-the-Lecture Cards (8 cards) 1. You had 2 π bandwidth T duration 2 T duration × bandwidth = 4 π Should the last equal sign be approximate ( )? (1 student) Yes. 2. Why do we want to minimize the bandwidth multiplied by the duration? I think it is because bandwidth and duration are inversely proportional, and we want to minimize both, but I’m not sure. (1) You are basically correct. Yes, we want to minimize both in many situations. Since for any given signal shape, bandwidth and duration are inversely proportional, minimizing the product will tell us the best shape.
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