stest3-2005

# stest3-2005 - your outline 3 A reverb digital ±lter is...

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Name BME 171, Spring 2005 - IN-CLASS FINAL 1. Consider a system whose frequency response is X ( f ) = 10 2 . 5 + j 2 πf . (a) Determine impulse response h ( t ) of this system. Then show that this system is causal and BIBO stable. (b) Use convolution to compute the response of this system to input x ( t ) = u ( t - 3) + δ ( t - 2). (c) Sketch the input and the response. Make sure to label all pertinent features and to pay attention to time constant when drawing exponential functions. How does this graph illustrate the causality of this system? 2. A second order LTI system is governed by the following equation: d 2 y dt 2 + 8 dy dt + 20 y ( t ) = dx dt . We want to use Laplace transform to determine the response of this system to a step function x ( t ) = 5 u ( t - 20). (a) First write down a short outline enumerating all the steps that have to be performed in order to determine the response y ( t ). (b) Then perform the calculations, clearly marking the outcomes of each step of

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Unformatted text preview: your outline. 3. A reverb digital ±lter is given by the following block diagram: + z-4 x[n] y[n] 0.6561 (a) What is the type and the order of this ±lter? Do not forget to justify your answers. (b) Determine the transfer function H ( z ) of this ±lter. (c) Draw the pole-zero plot of this ±lter, then determine its stability (with justi±-cation). 4. The signal x ( t ) is a fully rectiFed sinusoid shown below:-20-10 10 20 1 2 3 x(t) t (a) Write an exponential ±ourier series representation of x ( t ). (b) Determine how many terms must be used if the reconstructed signal were to carry 99.5% of the power of the original signal. Show and shortly explain all your calculations. (c) If the reconstructed signal that carries 99.5% of the power were to be sam-pled, what is the smallest sampling frequency that you could use? 2...
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stest3-2005 - your outline 3 A reverb digital ±lter is...

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