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62 MECHATRONICS
–1.0 –0.1 0.1 1.0
–1.1 –0.9 0.9 1.1 ω
sin(2pi*0.9*t) sampled at 1.0 Hz sin(2pi*0.1*t) sampled at 1.0 Hz
1 1
0.5 0.5
0 0
–0.5 –0.5
–1 –1
0 5 10 15 20 0 5 10 15 20
FIGURE 2.12: Example of aliasing as a result of sampling operation and the misleading
picture of the sampled signal.
From the sampling theorem,
w ≥ 2 ∗ w
s signal
In practice, the sampling frequency should be much larger than the minimum requirement
imposed by the sampling theorem, that is
w ≈ 5 to 20 ∗ w signal
s
Therefore, the magnitude relation between the four frequencies of interest is
w ≈ 5 to 20 ∗ w signal ≈ 5 to 20 ∗ w filter ≈ 25 to 200 ∗ w cls (2.44)
s
1+ 0.1 sin(2pi*3*t) sampled at 1.0 Hz
1
0.8
0.6
0.4
0.2
0
0 1 2 3 4 5 6 7 8 9 10
FIGURE 2.13: Hidden oscillations in the samples of a signal when the sampling rate is an
integer multiple of a frequency content in the continuous signal.
