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Integral Fourier Transform - Introductory Microcomputer Interfacing - Exam, Exams of Microcomputers

Kalinga Institute of Industrial TechnologyMicrocomputers

Main points of this exam paper are: Integral Fourier Transform, State, Fourier Convolution Theorem, Periodic Waveform, Discrete Frequencies, Nyquist Sampling Theorem, Frequency Domain

Typology: Exams

2012/2013

Uploaded on 03/22/2013

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Name (Last, First) Student ID number
EECS145M 2009 Midterm #2 Page 1 Derenzo/Peng
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 22, 2009
PROBLEM 1 (30 points)
1.1 (6 points) State the Fourier convolution theorem
1.2 (6 points) Use the Fourier convolution theorem to show that the Integral Fourier Transform
of a periodic waveform contains only discrete frequencies.
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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 22, 2009 PROBLEM 1 (30 points) 1.1 (6 points) State the Fourier convolution theorem 1.2 (6 points) Use the Fourier convolution theorem to show that the Integral Fourier Transform of a periodic waveform contains only discrete frequencies.

1.3 (6 points) State the Nyquist sampling theorem 1.4 (6 points) State the Fourier frequency convolution theorem 1.5 (6 points) Use the Fourier frequency convolution theorem to explain the Nyquist sampling theorem in the frequency domain

PROBLEM 3 (total 45 points): You want to design a digital filter to continuously compensate for the limited frequency response of a loudspeaker (like Lab 24a). Before you can do this, you need to measure the frequency response of the loudspeaker. Assume:

  • You have a computer with analog I/O.
  • The analog I/O has a range from – 5V to +5V.
  • You will excite the speaker with a pseudo-random waveform that you have stored as a floating point vector of 16,384 values that range from – 5V to +5V.
  • You have a microphone that has a uniform response over the 20 to 20 kHz frequency range of interest and an output from – 5mV to +5mV. 3.1 (10 points) Sketch a block diagram of your system. Include the computer, the I/O ports, the loudspeaker, the microphone, and any necessary amplification.

You send the pseudo-random waveform to the loudspeaker once at a frequency of 65, Hz and simultaneously sample the microphone waveform at the same frequency. You then take the FFT of the microphone samples. 3.2 (5 points) To what frequencies do the Fourier amplitudes H 1 and H 1000 correspond? 3.3 (10 points) How would you use the pseudo-random waveform and the loudspeaker response to calculate the digital filter that compensates for the limited frequency response of the loud speaker?