4 Sampled Data Systems

AliasingAll Activities

Aliasing means that two different sinusoids have identical samples, and we cannot distinguish between them from their samples. When experimental data are to be sampled, it is essential that an "antialiasing" analog filter be used before sampling to filter out frequencies above one-half the sampling frequency (called the Nyquist frequency). Otherwise, frequencies above the Nyquist frequency in the continuous signal will erroneously appear as lower frequencies after sampling. This is shown in Figure 1, where $f_o = 78 Hz$, and sampling frequency $f_s = 1 Hz$. Then $f_o$ appears at

$$f_a=\frac{7}{8}-1= −\frac{1}{8}$$

The significance of the negative frequency is that the $\frac{1}{8}$ Hz sinusoid in Figure 1 is the negative of the original $\frac{7}{8}$-Hz sinusoid.

aliasing
Figure 1: Plot of two sinusoids which have identical values at the sampling intervals: an example of aliasing.

 

Use the frequency control to change the input frequency in Figure 1.

  1. If a signal is sampled at 1Hz, what is the Nyquist frequency
  2. A 13/16 Hz signal is sampled at 1Hz, what is the lowest frequency at which that signal will appear
  3. A 1.5 Hz signal is sampled at 2 Hz, what is the lowest frequency at which that signal will appear