The student is measuring temperature in a complicated part subjected to a fluctu

Question

The student is measuring temperature in a complicated part subjected to a fluctuating heat transfer at 2 hz. Since the relationship between temperature and heat transfer is linear, it is expected that the temperature fluctuations will also be at 2 hz. 4. What Nyquist frequency is required so that the 2 hz signal will not be aliased? a. For different reasons, the signal is sampled at 20 hz. What is the time between samples? b. The sampled temperature (sampled at 20 hz) is passed to an FFT routine to create a spectrum of the signal. It is desired to have a 0.01 Hz increment between points. How many points are required? c. d. How long will the signal be sampled to generate that many points? e. What is the lowest frequency returned by the FFT? f. What is the highest frequency returned by the FFT? g. Prove whether there will be leakage for this set-up: Since there are not 2" points (where m is an integer), the FFT routine in Excel will not work. What simple trick can be used to generate the FFT with this signal in Excel? h.

Explanation / Answer

a)

Nyquist frequency=2*fm=2*2=4 Hz.

b)

Time between samples=(1/20)=0.05 sec

c)

Points=(20/0.01)=2000

d)

time=1/2000=0.5 ms

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