MAE334 - Introduction to Instrumentation and Computers Final Examination December 11, 2007 o Closed Book and Notes o No Calculators 1. Fill in your name on side 2 of the scoring sheet (Last name first!) 2. Fill in your 8-digit person number on your scoring sheet. 3. Fill in circle 1 under GRADE OR EDUCATION on your scoring sheet. This is your test number! You will receive a ZERO if you do not indicate your test number. o For each question, choose THE BEST ANSWER and mark the corresponding answer on the scoring sheet.MAE 334 – Final Exam, December 11, 2007 2 of 14 Given: a normally distributed data set containing 500 points spanning 0.5 seconds with a Excel standard deviation, STDEV(data), of 2 units and a mean value, AVERAGE(data), of 5 units. [For use with the next 9 questions!] 1. What is the Nyquist frequency of the data set? a. 250 Hz c. 1000 Hz b. 500 Hz d. None of the above 2. What is the frequency spacing, Δf, of this data set after a Fourier transform? a. 1/1000 Hz d. 2 Hz b. 1/500 Hz e. None of the above c. 1 Hz 3. What is the lowest frequency that can be captured by this data set? a. 0.5 Hz c. 4 Hz b. 1 Hz d. None of the above 4. What range should 19 out of 20 of the data points be between? a. d. b. e. None of the above c. 5. What percentage of the data fall in the range of 3 to 5 units? a. 34 % d. 68 % b. 48 % e. 95 % c. 50 % 6. If the input signal contained a periodic signal at 525 Hz at what frequency would it appear in the data set? a. 525 Hz c. 25 Hz b. 475 Hz d. None of the above 7. How would you define your estimate of the true mean value, ? a. c. b. d. 8. The standard deviation of the means, , for this data set is a. c. b. d. None of the above 9. If this data set was collected from a stationary signal. Would you expect repeating the data collection using the same parameters to a. increase the precision of your estimate of the mean value, . b. have mean values normally distributed about x'. c. increase the frequency resolution in the Fourier domain. d. have no effect on your estimation of the signal statistics. e. Both a. and b.MAE 334 – Final Exam, December 11, 2007 3 of 14 Given: An infrared image captured with a digital camera with a 1000 x 1000 pixel sensor. From this image we are able to determine the surface temperature of the material being photographed. The lens magnification results in each pixel recording a 1 mm x 1 mm area. [For use with the next 7 questions!] 10. What is the highest spatial frequency that can be resolved? a. ½ cycle/mm d. 2 cycles/m b. 1 cycles/mm e. None of the above c. 1 cycle/m 11. This type of temperature sensor behaves like a first order system. a. True b. False 12. The lowest spatial frequency that can be captured in this image is a. ½ cycle/mm d. 1 cycle/m b. 1 cycle/mm e. None of the above c. ½ cycle/m 13. If the temperature resolution of this particular camera setup is ½ degree Celsius what is the zero order uncertainty in the measurement? a. ± ½ ºC c. ± 1 ºC b. ± ¼ ºC d. None of the above 14. The manufacturer lists the linearity error associated with this camera as ± 1% of the reading in degrees Kelvin. What would the design stage uncertainty be in determining a single pixel temperature reading at 400 ºK? a. (95%) b. (95%) c. (95%) d. (95%) e. None of the above 15. Is this camera setup going to give accurate measurements of thermal gradients, ΔT/Δx in the range of 2 ºC/1 mm at 400 ºK? a. Yes b. No c. Insufficient information 16. The input impedance of this type of temperature sensor is very low. a. True b. False 17. Temperature is an effort variable. a. True b. False 18. The area under a properly normalized probability distribution function is 100. a. True b. False 19. The static sensitivity of a thermocouple is constant regardless of the convective heat transfer coefficient. a. True b. False 20. Bias error is effectively eliminated by a proper static calibration. a. True b. FalseMAE 334 – Final Exam, December 11, 2007 4 of 14 21. Using the static calibration data from Figure 1.6 above it can be stated that the static sensitivity of the instrument is greater at an input value of 1 [units] than at a value of 3 [units]. a. True b. False 22. There are 21 measured values in the calibration data set. How many degrees of freedom are there in the 2nd order calibration curve y = Ax + Bx2? a. 18 c. 20 b. 19 d. 21 23. The calibration of Figure 1.6 could be used for data spanning the range of 0 to 5 input units. a. True b. False 24. The uncertainty interval around the computed value, yc, from the curve fit is defined as a. c. b. d. (where r is the correlation coefficient) 25. Calibration hysteresis error is made worse by random application of the input signal. a. True b. FalseMAE 334 – Final Exam, December 11, 2007 5 of 14 26. A zero order sensor will delay the output signal with respect to the input signal. a. True b. False 27. The frequency bandwidth in radians/sec of a first order sensor is 1/(time constant), 1/ . a. True b. False 28. A Bourdon Tube pressure transducer is modeled as a first order sensor. a. True b. False 29. The standard deviation of a signal is also known as its variance. a. True b. False 30. What portion of a data set is within 2 standard deviations of the data set mean value. a. 50 % d. 95 % b. 68 % e. 99 % c. 75 % 31. The polynomial, y = a0 + a1x + a2x2 + a3x3, fit to a data set with N points has how many degrees of freedom? a. N-3 c. N-1 b. N-2 d. None of the above 32. A correlation coefficient of 0.5 for a linear fit to a data set indicates a good quality fit. a. True b. False 33. The ADC architecture normally associated with the highest precision is a. Flash c. Pipelined b. Sigma-delta d. Successive approximation 34. A large thermocouple will reach a steady state value sooner if subjected to a small step input than a large step input. a. True b. False 35. A null device has zero input impedance. a. True b. False 36. Which of the following are effort variables a. temperature, voltage, heat flux, pressure b. current, pressure, heat flux c. voltage, pressure, force d. velocity, force, voltage 37. A 65 Hz sine wave sampled at 100 Hz will result in a sampled data set with what frequency a. 15 Hz d. 30 …