Consider sampling input cosine functions, with a sample rate of 100Hz.
(a) What is Nyquist Frequency in Hz?
(b) What is the period associated with Nyquist Frequency?
(c) During one period, how many samples are taken at the Nyquist frequency signal?
(d) Give the values at the sample times when you start sampling at time zero.
(e) Give the values at the sample times if you are sampling a sine function that is oscillating at
Nyquist frequency.
(f) Give the values at the sample times if you are sampling a cos (𝜔’𝑡 −
*
+) at times 𝑡 = 𝑘𝑇
where T is the sample time interval for Nyquist frequency (the
*
+ means that the cosine is
shifted 45 degrees back in time compared to the original cosine, i.e. a phase delay from input to
output).
(g) We commented in class that if a cosine is sampled such that there are 4 or more samples in
each period, then the control action based on the sampled values might be able to make some
effective corrective action. If Nyquist frequency is 100Hz, what sample rate is needed for this
condition.
(h) Now consider sampling a cosine whose frequency is 75 Hz. Use the Slide 15 and Slide 21 to
give all other frequencies that will have the same values at the sample times.