At What Speed Will The Spot Appear To Rotate To The Human Observer?
ECET345 Signals and Systems Homework #4
Name of Student ______________________________
1. A shiny metal disk with a dark spot on it, as shown in figure below, is rotating clockwise at 100 revolutions/second in a dark room. A human observer uses a strobe that flashes 99 times/second to observe the spot on the metal disk (a strobe is a flashing light whose rate of flashing can be varied). The spot appears to the human observer as if it is rotating slowly.
Hint: This is equivalent to sampling a 100 Hz wave with a 99 Hz sampling rate. Because this represents a violation of the Nyquist theorem, an aliasing condition will result. The resulting aliased frequency observed at system output is given by (k * fs - f), where fs is the sampling frequency, f is the frequency of sampled signal, and k is an integer (positive or negative) such that (k * fs - f) produces a positive output less than or equal to fs/2. …show more content…
Fs/2 = 50
K(fs)-fi=50
K(100)-90= 50 where K = 1.4
1.4 *2pie = 8.79
(b) Will the spot appear to rotate clockwise or anticlockwise? Briefly justify your answer.
Clock wise due to positive number between 100-90
(c) Suppose the observer changes the strobe frequency to 101 flashes per second. What differences in rotation will the observer note?
Will move anti clockwise due to 100-101 equalling negative number at 1.51
Name of Student ______________________________
1. A shiny metal disk with a dark spot on it, as shown in figure below, is rotating clockwise at 100 revolutions/second in a dark room. A human observer uses a strobe that flashes 99 times/second to observe the spot on the metal disk (a strobe is a flashing light whose rate of flashing can be varied). The spot appears to the human observer as if it is rotating slowly.
Hint: This is equivalent to sampling a 100 Hz wave with a 99 Hz sampling rate. Because this represents a violation of the Nyquist theorem, an aliasing condition will result. The resulting aliased frequency observed at system output is given by (k * fs - f), where fs is the sampling frequency, f is the frequency of sampled signal, and k is an integer (positive or negative) such that (k * fs - f) produces a positive output less than or equal to fs/2. …show more content…
Fs/2 = 50
K(fs)-fi=50
K(100)-90= 50 where K = 1.4
1.4 *2pie = 8.79
(b) Will the spot appear to rotate clockwise or anticlockwise? Briefly justify your answer.
Clock wise due to positive number between 100-90
(c) Suppose the observer changes the strobe frequency to 101 flashes per second. What differences in rotation will the observer note?
Will move anti clockwise due to 100-101 equalling negative number at 1.51