Aliasing at Sampling

Snapshot of the front panel of the simulator:

Description of the system to be simulated

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.

Figure 1

From the figure one observation is that fdisc is equal to the difference fsfcont if  fcont is between fN and fs.


  1. Select fcont and fs so that there is no aliasing (cf. Figure 1). Run the simulator. Is it confirm that there is no aliasing?
  2. Select fcont and fs so that there is aliasing (e.g. fcont = 0.5 and fs = 0.6 Hz), cf. Figure 1. Calculate from Figure 1 the resulting frequency fdisc (of the discrete-time signal). Run the simulator. Do you observe aliasing? If so, what is the frequency fdisc? Is the observation in accordance with the calculation?
  3. What is fdisc if fcont is equal to the Nyquist frequency? Run the simulator. Is the result confirmed?

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Updated 2 September 2017. Developed by Finn Haugen. E-mail: