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Computer System - Introductory Microcomputer Interfacing - Exam, Exams of Microcomputers

Baddi University of Emerging Sciences and TechnologiesMicrocomputers

Main points of this exam paper are: Computer System, Sampling Frequency, Number of Samples, Butterworth, Anti-Aliasing Filter, Hanning, Frequency Range

Typology: Exams

2012/2013

Uploaded on 03/22/2013

satayu
satayu 🇮🇳

4.4

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Name (Last, First)
Student ID number
EECS145M 2006 Midterm #2 Page 1 Derenzo
UNIVERSITY OF CALIFORNIA
College of Engineering
Electrical Engineering and Computer Sciences Department
EECS 145M: Microcomputer Interfacing Laboratory
Spring Midterm #2 (Closed book- equation sheet provided- calculators OK)
Full credit can only be given if you show your work.
Wednesday, April 12, 2006
PROBLEM 1 (54 points)
You have designed and built a computer system to sample waveforms and perform the FFT.
It has the following characteristics:
• Sampling frequency = 218 Hz = 262,144 Hz
• Number of samples = 216 = 65,536
• Low-pass Butterworth anti-aliasing filter of order 8 and fc = 100,000 Hz
• Hanning (raised cosine) window
Answer the following questions:
1.1 (3 points) For what frequency range does the anti-aliasing filter have gain >0.99?
(Hint: Use the Butterworth gain table on the equation sheet)
1.2 (3 points) For what frequency range does the anti-aliasing filter have gain <0.01?
1.3 (2 points) How long does it take to acquire the samples?
pf3
pf4
pf5

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UNIVERSITY OF CALIFORNIA

College of Engineering Electrical Engineering and Computer Sciences Department EECS 145M: Microcomputer Interfacing Laboratory Spring Midterm #2 (Closed book- equation sheet provided- calculators OK) Full credit can only be given if you show your work. Wednesday, April 12, 2006 PROBLEM 1 (54 points) You have designed and built a computer system to sample waveforms and perform the FFT. It has the following characteristics:

  • Sampling frequency = 2^18 Hz = 262,144 Hz
  • Number of samples = 2^16 = 65,
  • Low-pass Butterworth anti-aliasing filter of order 8 and fc = 100,000 Hz
  • Hanning (raised cosine) window Answer the following questions: 1.1 (3 points) For what frequency range does the anti-aliasing filter have gain >0.99? ( Hint: Use the Butterworth gain table on the equation sheet) 1.2 (3 points) For what frequency range does the anti-aliasing filter have gain <0.01? 1.3 (2 points) How long does it take to acquire the samples?

1.4 (3 points) To what frequencies do the FFT coefficients H 0 and H 1 correspond? 1.5 (4 points) What is the FFT coefficient with the highest frequency index and to what frequency does it correspond? 1.6 (4 points) What is the FFT coefficient that corresponds to the highest frequency and what is that frequency? 1.7 (6 points) You sample a 4,000 Hz sinewave with the system and take the FFT. What FFT coefficients should be non-zero?

1.11 (8 points) You sample a sinewave of frequency 218 – 84,000 Hz = 178,144 Hz and take the FFT. What FFT coefficients should be non-zero? How does the magnitude of the largest FFT coefficient compare with that you would get if you sampled an 84,000 Hz sinewave? 1.12 (3 points) How would you change the system to reduce the closeness in problem 1.10 by a factor of two?

PROBLEM 2 (46 points) You have been asked to help design a Doppler ultrasound system for measuring the speed of approaching vehicles on a highway. The system sends a continuous tone of 100 kHz sound waves in a well-defined direction and there is a receiver alongside that receives the Doppler- shifted echo. Your part in the project is to design the sampling and signal processing hardware and software, starting from the echo receiver.

  • The Doppler-shifted frequency is given by f ' = f / [1 – v / c ], where v is the speed of the approaching vehicle and c is the speed of sound in air (assume 300 m/s).
  • To simplify and speed your calculations, use the approximation f' ≈ f [1 + v / c ].
  • Assume that the echo receiver signal is the sum of a 0.1 volt p-p echo from the vehicle plus a 100 kHz 10V p-p echo from stationary objects.
  • The echo circuit has wide-band amplification with white noise, so you decide to use a low-pass Butterworth anti-aliasing filter that you need to design.
  • You do not use a windowing function (like the raised cosine)
  • Your system must be able to determine the speed of an approaching vehicle between 3 m/s and 60 m/s to an accuracy of ±0.3 m/s. 2.1 (5 points) What are the echo frequencies for vehicle speeds of 3 m/s, 30 m/s (67 mph), and 60 m/s (134 mph)? 2.2 (5 points) What is the minimum length of time that you need to sample to sample to clearly detect a change in speed of 0.3 m/s? 2.3 (5 points) Even though you do not use a windowing function, how could you reduce the spectral leakage from the ≈10 volt p-p 100 kHz primary onto the 0.1 v p-p echo frequency?