ECET 497 Week 8 Final Exam

1. Find the inverse Laplace transform of:

2. The inverse Laplace transform of 2/(s 2 + 4) is:

3. Given the circuit below, the expression for Vo(s)/Vin(s) is:

4. The inverse Laplace transform of a system with the response given by: H(s) = would be:

5. Frequencies from 0 to in the s plane on the axis, whereis the sampling frequency, correspond to:

6. What x(n) is described by the z domain function X(z) below?

7. Which of the following expressions is a z domain description of the difference equation described below?

y[n] – 3y[n-1] + 5y[n-2] = x[n] + 2x[n-2] – 3x[n-4]

8. For a system described by the following difference equation:

Which expression describes the response, , of h(n) to a unit step function?

9. The following table represents values of the impulse response of a filter, h[n], and the values of an input signal, x[n]. Assume that the input signal starts at n=0; that is, all signal values are zero for n<0. find="" the="" fifth="" output="" sample="" (y[n]="" for="" n="4):">

10. Which of the following difference equations represents an FIR (nonrecursive) filter?

11. Consider the pole-zero plot of a filter as given below. This filter is:

12. The following filter is:

y[n] – 3y[n-1] + 5y[n-2] = x[n] + 2x[n-2] – 3x[n-4] (Filter diff. eq.)

13. From the pole-zero plot given below, the numerator polynomial in the transfer function is which of the following (assume the transfer function polynomials have been put in standard form):

14. Given the transfer function, what type of response does this represent?

15. For a continuous-time second order lowpass system with a and an  radians per second, write an s-domain transfer function that describes this system.

16. The system  is:

17. For the s-plane plot below, what type of frequency response behavior would be expected?

18. For a Bode approximation of a transfer function H(s) described by:

19. For the s-plane plot below, what type of frequency response behavior would be expected?

20. Consider an FIR filter with the impulse response shown below. Does this filter have a linear phase response?

21. Suppose a linear-phase FIR filter is designed such that its impulse response has a length of 401 values. For a DSP system operating with a sampling frequency of 8 kHz, the time delay (in milliseconds) for a signal passing through the filter will be approximately what?

22. Window functions that “taper” the impulse response of computable FIR filters, such as Hamming and Blackman window functions, have what effect(s) on the magnitude frequency response of the filter?

23. If A and B are independent events, then

24. The Lottery “Mega Millions” has you choose five numbers from 1 to 56 and one number from 1 to 46. So what is your chance of winning?

25. A sample of 10 widgets is drawn randomly from a lot of 100, 5% of which are known to be defective. The widgets drawn will be without replacement. What is the probability of exactly one defective widget in each sample drawn?