Aliasing at Sampling
Snapshot of the front panel of the simulator:
Sampling of sinusoid, x(t), is simulated. The sampling results the discrete-time signal xs(k) where k is a time index (number of samples). Both signals are plotted simultaneously. You can adjust both the signal frequency and the signal frequency.
The aim is to develop an understanding of the aliasing phenomenon.
Sampling av continuous-time signals takes place in all applications where a computer is used to read measurement data. If the sampling rate is too low compared to the frequency of the signal to be sampled, aliasing occurs. Aliasing means that the discrete-time signal gets a lower frequency than the original signal. Obviously, sampling can cause problems in applications, e.g. in audio applications.
Given a continuous-time signal, x(t), of frequency fcont [Hz] which is sampled with sampling frequency fs [Hz]. The Nyquist frequency fN is defined as half of the sampling frequency:
fN = fs/2
It ca be shown that if the signal frequency fcont is larger than fN, there is aliasing, which implies that the resulting discrete-time signal, xs, gets a frequency, fdisc, which is smaller than the signal frequency fcont. Figure 1 shows the relation between fdisc and fcont.
From the figure one observation is that fdisc is equal to the difference fs - fcont if fcont is between fN and fs.