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Let $\left\{y_{k}\right\}$ be the sequence produced by sampling the continuous signal $2 \cos \frac{\pi t}{4}+\cos \frac{3 \pi t}{4}$ at $t=0,1,2, \ldots,$ as shown in the figure. The values of $y_{k},$ beginning with $k=0,$ are $$3,7,0,-7,-3,-7,0,7,3, .7,0, \ldots$$where. 7 is an abreviation for $\sqrt{2} / 2$a. Compute the output signal $\left\{z_{k}\right\}$ when $\left\{y_{k}\right\}$ is fed into the filter in Example 3 .b. Explain how and why the output in part (a) is related to the calculations in Example 3 .

a. table cannot copyb. This is clear because the filter is linear and the output form the input $2 \cos ( \pi t / 4 ) + \cos ( 3 \pi t / 4 )$ should be two times the output from $\cos ( \pi t / 4 )$ and the output from $\cos ( 3 \pi t / 4 )$

Calculus 3

Chapter 4

Vector Spaces

Section 8

Applications to Difference Equations

Vectors

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University of Michigan - Ann Arbor

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Example 3 in Section 4.8 d…

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In Exercises $7-12$ , assu…

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The output of a certain am…

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A The $R C$ high-pass filt…

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Suppose the high-pass filt…

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So, with the signal at the discreet times, the equals 01 of them. And we apply this with them, which can be found on example three on Bates to 48. And we need to evaluate Zakia. Is this good times? Eso We proceed by start of calculations and we find that for J equals zero, their signals at zero equals, huh? 1.4 for Syria calls one. We have zero for K equals two will have minus one over floor. Let's what they get in here, Okay? Of course. Two week of minds one over four. As we've just said for Galia, Quinn's three will have my most 1.9 for Gaia Quinn's four. We have minus one point for. Are you going? Blues five? We have zero. Forget. Vehicle six will have 1.4. Um, we proceed for K vehicle seven. We're having one with nine Ah time. Eight week of, uh, one on one blowing for time. Nine without zero. And at times, then we have Is it off them? Equals minus one. Going for now, we know that we still have been in the city with period. It wa ce eight as it happens, exhibiting an example of three in the signal, in example, for you on Bates to 48. And, uh, the signal bits to 48 on example. Three is just this. They're off the signal that Cassandra is off by the over four. Here. We don't have traditional therapies. We have co signers. Three bitey over four and plus a general this term exams fighting over four with mixed wise. The signal. Bless something that it's a lot of difference in there in the results, but that was it.

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