Aliasing at SamplingSnapshot of the front panel of the simulator:
Description of the system to be simulatedSampling of sinusoid, x(t), is simulated. The sampling results the discrete-time signal x_{s}(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. AimThe aim is to develop an understanding of the aliasing phenomenon. MotivationSampling 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. TheoryGiven a continuous-time signal, x(t), of frequency f_{cont} [Hz] which is sampled with sampling frequency f_{s} [Hz]. The Nyquist frequency f_{N} is defined as half of the sampling frequency: f_{N} = f_{s}/2 It ca be shown that if the signal frequency f_{cont} is larger than f_{N}, there is aliasing, which implies that the resulting discrete-time signal, x_{s}, gets a frequency, f_{disc}, which is smaller than the signal frequency f_{cont}. Figure 1 shows the relation between f_{disc} and f_{cont}.
Figure 1 From the figure one observation is that f_{disc} is equal to the difference f_{s} - f_{cont} if f_{cont} is between f_{N} and f_{s}. Tasks
Updated 21. January 2008. Developed by Finn Haugen. E-mail: finn@techteach.no. |