Sampling and Aliasing Overview  

The sampling  theorem states that a band-limited continuous-time signal, with  highest frequency (or bandwidth) equal to B Hz, can be recovered from its samples provided that the sampling frequency, denoted by Fs, is greater than or equal to 2B Hz (or samples per second).  The minimum sampling rate is often called the Nyquist rate.  For example, the minimum sampling rate for a telephone speech signal (assumed low-pass filtered at 4 kHz) should be  8 KHz (or 8000 samples per second),  while the minimum sampling rate for an audio CD signal with frequencies up to 22 KHz should be 44KHz.

In the figure below, you  see the sampling effects on a sinusoidal signal of frequency B Hz that result from the use of different sampling frequencies.

                      Fs > 2B                                             Fs = 2B                                            Fs < 2B
 
 
 
As you already know, sampling of a continuous-time signal results in repeating its spectrum in the frequency domain. The spectrum is repeated every Fs Hz. Assuming that the bandwidth of the continuous-time signal is B Hz, then the repeated bands in the frequency domain will not interfere with each other if the sampling frequency is larger than 2B Hz. In this case, the spectrum of the original signal can be recovered from the spectrum of the sampled signal by low-pass filtering with a cutoff frequency that is equal to Fs/2 Hz. This also means that the original signal can be recovered from the sampled signal via the low-pass filtering operation.  When the sampling rate is not large enough (not larger than 2B Hz), then interference among adjacent bands will occur, and this results in the phenomenon of aliasing. In this case, the original signal cannot be recovered from the sampled signal.

This experiment allows you to hear the sound of a signal and of its reconstructed version after sampling. The signal consists either of a single tone or of two tones, whose frequencies are chosen by the user. The sampling frequency is also chosen by the user. All values are in Hz. In this experiment we focus on the aliasing effect. In a second experiment we shall study the reconstruction of a signal from its samples.