Microprocessors I - Problem Solutions - Prof. William H. Blanton, Exams of Microprocessors

Download Microprocessors I - Problem Solutions - Prof. William H. Blanton and more Exams Microprocessors in PDF only on Docsity! Name Date TEST 3 ENTC 4337 MICROPROCESSORS I (Due Date: End of Class on 12/5/00 [no excuses]) 1. (10 points) Derive the following Laplace transforms. (Show your work.) a. ℒ  ate  b. ℒ  )(tfe at c. ℒ  )sin( t d. ℒ  )(t 2. (10 points) Find the inverse transform of the following. (Show your work.) a. ℒ-1         23 4 2 ss s b. ℒ-1         )( 1 232 ss ss (Hint: Make sure the order of the denominator is larger than the numerator) b. ℒ-1         16 34 2s s d. ℒ-1        221 20 ))(( sss 3. (10 points) Locate each of the poles and zeros from problem 2. 4. (10 points) Use MATLAB to construct a pole-zero plot for functions in problem 2. 5. (10 points) What is the mathematical difference between a FIR and IIR filter. 6. (10 points) What is the output of the following filter for the given input? What is the impulse response of the filter? 7. (10 points) Determine the solution for the following problems. a.   100 10 )(3 dtt b.  97 40 )(7 dtt c.   3 1 )( dtt 8. (10 points) Find the inverse Z transform. a. 642 2 1 22 2 1   zzzzX )( b. ).)(( )( 501 1   zz zY 30 20 10 t t t 0 1 2 y[n] x[n] Z -1 Z -1  0.1 0.2 0.3 t x n d. ℒ  )(t   dtet st   0    dte s   0 00   dt   0 0 1 2. (10 points) Find the inverse transform of the following. (Show your work.) a. ℒ-1         23 4 2 ss s b. ℒ-1         )( 1 232 ss ss (Hint: Make sure the order of the denominator is larger than the numerator) c. ℒ-1         16 34 2s s d. ℒ-1          221 20 ))(( sss c.         23 4 2 ss s            12 4 ss s    12     s B s A   21 4           ss s A 2 1 2           12 4           ss s B 3 1 3        ℒ-1           12 4 ss s = ℒ-1     tt ee ss 223 1 3 2 2             b.         )( 1 232 ss ss sss ss ss ss 2 1 23 1 23 2 22                        )( ℒ-1 2 2 1         )(t s  c.         16 34 2s s                       16 3 16 4 44 34 22 ss s jsjs s ℒ-1 tt ss s 4 4 3 44 16 4 4 3 16 4 22 sincos                 d.  22 22121 20                s D s C s B s A sss ))(( 5 21 20 0 2    s ss A ))(( 20 2 20 1 2    s ss B )(   15 4 60 1 122001 1 20 21 20 2 2 2 2 2 2                               ss ss sss ssds d sss s ds d C )( )()()( )())(( )( 10 1 20 2    s ss D )( ℒ-1   ttt teee ssss 22 2 1015205 2 10 2 15 1 205                  3. (10 points) Locate each of the poles and zeros from problem 2. (SEE PROBLEM 4) 4. (10 points) Use MATLAB to construct a pole-zero plot for functions in problem 2. a.         23 4 2 ss s EDU» n=[0 1 4]; EDU» d=[1 3 2]; EDU» zplane(n,d) EDU» grid -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Real Part Im ag in ar y P ar t b.         )( 1 232 ss ss EDU» n=[1 3 2]; EDU» d=[1 1 0]; EDU» zplane(n,d) EDU» grid c.         16 34 2s s EDU» n=[0 4 -3]; EDU» d=[1 0 16]; EDU» zplane(n,d) EDU» grid -2 -1.5 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 Real Part Im ag in ar y P ar t -5 -4 -3 -2 -1 0 1 2 3 4 5 -4 -3 -2 -1 0 1 2 3 4 Real Part Im ag in ar y P ar t 7. (10 points) Determine the solution for the following problems. d. 33 100 10   dtt)( e.   97 40 07 dtt)( f. 1 3 1   dtt)( 8. (10 points) Find the inverse Z transform. c. 642 2 1 22 2 1   zzzzX )( d. ).)(( )( 501   zz z zY a. )()()()(][ 6 2 1 42220 2 1  nnnnx  b. ).()().)(( )( 501501 1       z B z A zzz zY 2 150 1 1 1 2 50 1 50 1 50 1           .)( .).( .z z z B z A      ).()( )( 50 2 1 2 z z z z zY nny ).(][ 5022  9. (10 points) A system is described by the difference equation )()()(.)(.)( 1220110  nxnxnynyny d. Determine the transfer function H(z). e. Determine the impulse response h(n). f. Determine the response due to a unit step function excitation. a. )()()(.)(.)( zXzzXzYzzYzzY 121 2010   )()()(.)(.)( zXzzXzYzzYzzY 121 2010       )()(.. zXzzYzz 121 120101       2010 1 2010 1 20101 1 22 2 21 1 .. )( ....)( )( )(                 zz zz zz z z z zz z zX zY zH ).)(.( )( )( 5040 1    zz zz zH b. ).().().)(.( )()( 50405040 1        z B z A zz z z zH 555561 90 41 50 1 40 . . . ).( )( .     z z z A 555560 90 50 40 1 50 . . . ).( )( .       z z z B ).( . ).( . )( 50 555560 40 555561     z z z z zH nnnh ).(.).(.][ 5055556040555561  c. ).)(.( )( )( )()()( 5040 1 1     zz zz z z zHzXzY ).().()().)(.)(( )()( 5040150401 1          z C z B z A zzz zz z zY 22222290 2 5160 2 5040 1 1 . .).)(.().)(.( )(     z zz zz A 03704154 56 9060 4140 501 1 40 . . . ).)(.( ).)(.( ).)(( )( .         z zz zz B 185190351 250 9051 5050 401 1 50 . . . ).)(.( ).)(.( ).)(( )( .          z zz zz C ).( . ).( . )( . )( 50 185190 40 037041 1 222222       z z z z z z zY nnny ).(.).(..][ 5018519040037041222222  10. (10 points) Evaluate each example and give the answer in both rectangular and polar form (in all cases, assume that 341 jz  and jz 12 ): a. *1z d. 2jz g. 2ze b. 22z e. 1 1 z h. *11 zz c. *21 zz  f. 2 1 z z i. 21zz a.           131435 34 1 1 .* * z jz b.           902 2 2 2 2 2 z jz c.           871265 43 1 21 .* * z jzz d.           454141 1 2 2 .jz jjz e.             1314320 120160 1 1 1 1 .. .. z jz f.                 871715363 5053 2 1 2 1 .. .. z z j z z g.           3577182 28724691 2 2 .. .. z z e je h.           025 025 11 11 * * zz jzz i.           13980717 71 21 21 ..zz jzz FINAL REVIEW ENTC 4337 I. Matching (30 points). Choose the best match. Remember that all numbers are in hexadecimal format unless otherwise noted. ______ 1. IIR Filter A. N z D z N z ( ) ( ) ( )0 III. Multiple Choice (60 points). Choose the best answer from the lists provided. ______1. What is the output of the following filter at time t1 assuming no previous inputs other than shown? a. 8 b. 2 c..  d. 15 ______2. Which one is the correct impulse response of the filter in Question 1? a. b. c. d. 30 20 10 t t t 0 1 2 y[n] x[n] Z -1 Z -1  0.1 0.2 0.3 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 ______3. The diagram represented in problem 1 is a: a. Recursive Filter b. IIR Filter c. FIR Filter d. Both A & B 4. Which one is the correct unit step response of the filter in Question 1? a. b. c. d. t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.6 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.6 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.6 0.5 0.4 0.3 0.2 0.1 Given the following phasors for problems 1 through 7: z e z e j j 1 4 2 2 4 2       ______1. The real part of z1 is: e. 0 f. –2.83 g..  h. 2.83 ______2. The real part of z2 is: a. 0 b. –2.83 c. –2 d. 2.83 ______3. The imaginary part of z1 is: e. 0 f. –2.83 g. 2 h. 2.83 ______4. The imaginary part of z2 is: a. 0 b. –2.83 c. 2 d. 2.83 ______15. The sampling period (Ts) must be less than a. 0.45 msec b. 0.18 msec c. 0.23 msec d. 0.09 msec ______16. For a desired sampling rate, Fs, of 16 kHz registers A and B which contain TA and TB, respectively would have which of the following (assuming MCLK = 6.25 MHz): a. A = 0x162C, B = 0x4892 b. A = 0x162C, B = 0x3872 c. A = 0x0E1C, B = 0x3872 d. A = 0x0A14, B = 0x3E7E 17. What are the two poles and two zeros of the following function? 21 1 1 22 )(      zz z zH FINAL EXAM ENTC 4337 IV. Matching (20 points). Choose the best match. Remember that all numbers are in hexadecimal format unless otherwise noted. ______ 1. IIR Filter A. N z D z N z ( ) ( ) ( )0 ______ 2. FIR Filter B. N z D z D z ( ) ( ) ( )0 ______ 3. Unit Impulse C.    0 dtetf st)( ______ 4. Euler identity D. y n b x n k a y n kk k N k k M [ ] ( ) ( )        0 1 ______ 5. Pole E. ______ 6. Zero F. re j  ______ 7. Summation G. y n b x n kk k N [ ] ( )    0 ______ 8. Sifting Property H. )()()( oo tftdtftt     ______ 9. Laplace transform I. e j = cosjsin ______10. polar form J. ( )n V. True/False (5 points). Mark T for True and F for False. Make sure your Ts and Fs are distinguishable. ______ 1. A discrete-time signal is represented as a sequence of numbers. ______2. When adding complex numbers, the rectangular form is the easiest to use. ______ 3. Aliasing is a result of oversampling. ______ 4. A binary number with a sign bit (most significant bit) having a value of 1 represents a negative number. ______5. The sampling frequency, Fs, must be greater than the lowest frequency being sampled in order to eliminate aliasing. VI. Multiple Choice (75 points). Choose the best answer from the lists provided. If there is no valid answer, you may enter an E in the blank. ______1. What is the output of the following filter at time t1 assuming no previous inputs other than shown? i. 8 j. 2 30 20 10 t t t 0 1 2 y[n] x[n] Z -1 Z -1  0.1 0.2 0.3 k..  l. 15 ______2. Which one is the correct impulse response of the filter in Question 1? a. b. c. d. t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 t t t t t 0 1 2 3 4 0.5 0.4 0.3 0.2 0.1 ______12. A matrix with only one element: e. scaler f. vector g. matrix h. M-file ______13. A matrix with only one row or one column: e. scaler f. vector g. matrix h. M-file ______14. A text file with a .m extension that is executed as a script: e. scaler f. vector g. matrix h. M-file ______15. The floating point representation, 076B000016, represents the decimal number: e. 10710 f. 10810 g. 23510 h. none of the above Given the following sinusoidal signal for problems 16 through 18: x t t t( ) cos cos  FHG I KJ  F HG I KJ21 10 2200 2 5 5500 4    ______16. What is the highest frequency of the signal? e. 2200 Hz f. 5500 Hz g. 1100 Hz h. 2750 Hz ______17. The sampling frequency (fs) must be greater than: e. 2200 samples/sec f. 5500 samples/sec g. 4400 samples/sec h. 11,000 samples/sec ______18. The sampling period (Ts) must be less than e. 0.45 msec f. 0.18 msec g. 0.23 msec h. 0.09 msec ______19. For a desired sampling rate, Fs, of 16 kHz registers A and B which contain TA and TB, respectively would have which of the following (assuming MCLK = 6.25 MHz): e. A = 0x162C, B = 0x4892 f. A = 0x162C, B = 0x3872 g. A = 0x0E1C, B = 0x3872 h. A = 0x0A14, B = 0x3E7E Given the following function for problems 20 through 22: ))(( )( )( 53 1    zzz z zH 20. Which of the following is a pole of the function? a. -1 b. -2 c. -3 d. -4 21. Which of the following is a zero of the function? a. -1 b. -2 c. -3 d. -4 22. Which of the following plots represents the function? a. b. c. d. 23 Which of the following floating-point numbers represents a negative number? a. 04A8000000 b. 0458000000 c. FD6C000000 d. 8000000000 24. Which of the following floating-point numbers represents a fractional number? a. 04A8000000 b. 0458000000 c. FD6C000000 d. 8000000000 -5 -4 -3 -2 -1 0 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Real Part Im ag in ar y P ar t -5 -4 -3 -2 -1 0 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Real Part Im ag in ar y P ar t -5 -4 -3 -2 -1 0 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Real Part Im ag in ar y P ar t -1 0 1 2 3 4 5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Real Part Im ag in ar y P ar t