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Quiz #1
ME 368 - Engineering Measurements and Instrumentation
Sept 30, 2009, 12:05 – 12:20 pm
Fall Semester 2009
Problem Q1-1:
Three amplitude vs. frequency plots are given below. For each, sketch the corresponding voltage
vs. time plot on the axes provided. You needn’t support your sketches with detailed math, but
make your sketches as quantitative as possible and be sure the differences between your sketches
are clear.
[x/10] sketch resembles a simple sine wave
[x/5] mean = 0
[x/5] ~ 4 cycles / s
[x/5] sketch has an obvious sinusoidal component
[x/5] sketch includes noise (weak content at many frequencies)
[x/5] mean = 0
[x/5] ~ 2 cycles / s
[x/10] DC signal
Problem Q1-2:
Consider 50 consecutive data points sampled from a microphone at 1000 samples / second.
Using this data:
a) could ‘C4’ (262 Hz) on a piano be distinguished from ‘C sharp 4’ (277 Hz)? Why or
why not?
Solution: [x/10] The length of time sampled is (50 samples) / (1000 samples / second) =
0.05 s. [x/10] Therefore the frequency resolution is 1 / 0.05 s = 20 Hz. [x/10] Since 277
Hz – 262 Hz = 15 Hz is smaller than 20 Hz, the two notes cannot be resolved.
b) could ‘C4’ (262 Hz) be distinguished from ‘F sharp 5’ (740 Hz)? Why or why not?
Solution: [x/5] The Nyquist frequency is (1000 samples / second) / 2 = 500 Hz. [x/5]
Since 740 Hz is above this frequency, it is aliased to a frequency below 500 Hz, namely
(500 Hz) – (740 Hz – 500 Hz) = 260 Hz. [x/10] Since the difference between the aliased
F sharp 5 at 260 Hz and C4 at 262 Hz is less than the frequency resolution of 20 Hz, the
two notes cannot be distinguished.