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Information about two microcomputer-controlled systems designed for testing 12-bit a/d converters and analyzing the harmonic content of musical instruments. Problem statements, instructions, and equations for designing and implementing these systems. Students enrolled in the electrical engineering and computer sciences department at the university of california, berkeley, may find this document useful for studying for the eecs 145m midterm #2 exam.
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College of Engineering Electrical Engineering and Computer Sciences Department
EECS 145M: Microcomputer Interfacing Laboratory
Spring Midterm # Monday, April 21, 1997
PROBLEM 1 (50 points)
Design a computer controlled system for the automatic testing of 12-bit A/D converters.
Y ou are provided with the following:
You may assume the following:
1a. [25 points] Draw a block diagram of the major components, including the A/D circuit being tested. Show and label all essential components, data lines, and control lines.
1b. [10 points] How would you measure the maximum absolute accuracy error of the A/D? (Explain the procedure in steps or with a flow diagram.)
2a. [10 points] How does your design avoid aliasing? Give details.
2b. [10 points] What is the minimum sampling frequency required?
2 c. [5 points] What is the minimum time needed to take all the required samples?
2d. [5 points] What is the minimum number of samples required?
2 e. [5 points] Would a Hanning window be useful in your design? Explain your reasoning.
2 f. [5 points] To what frequency does the first FFT coefficient H 1 correspond?
2 g. (10 points] For a musical instrument with a first harmonic frequency of 500 Hz, which FFT magnitudes would you expect to be non zero?
G ( a ) =
2 πσ^2
exp −
a −μ σ
μ ≈^ a^ =^ m^1 ai i = 1
m
σ a^2 = Var( a ) =
m − 1
(^) Ri^2 i = 1
m
m − 1
i = 1
m
t =
σ∆
a − b
σ^2 a^ + σ^2 b^
a − b
σ a^2 / ma + σ b^2 / mb
σ (^2) f^ =
∂ f ∂ a 1
2 σ a^21 +
∂ f ∂ a 2
2 σ a^2 2 + +
∂ f ∂ an
2 σ an^2