In this module we shall look at sampling a sinusoidal signal. According to the sampling theorem, a sinusoidal signal can be exactly reconstructed from values sampled at discrete, uniform intervals as long as the signal frequency is less than half the sampling frequency. Any component of a sampled signal with a frequency above this limit, often referred to as the folding frequency, is subject to aliasing.

The applet is based on a fixed sampling rate of Fs=8000 samples per second Fs 8000 samples per second (one sample every 0.125 milliseconds, i.e Ts=18000 Ts 1 8000 ).

Set the frequency of the sinusoidal signal, in Hz, in the "Input frequency" box, i.e choose an ff in the following signal: sin2πft 2 f t . When you click the "Plot" button, with "Input signal" checked, the input signal is plotted against time.

The "Grid" checkbox toggles on and off vertical gridlines indicating the instants at which the signal is sampled. The "Sample points", representing the sampled values of the input signal, can also be toggled.

Finally, the "Alias frequency" checkbox (visible only when aliasing occurs) controls the plotting of the "reconstructed" sinusoidal signal, with f=falias f falias .

When using the applet it is important to have an understanding of where the different signals occur in a sampling system. Relating the applet signals to the figure we get

• Input signal = xt=sin2πft x t 2 f t , where ff is the input frequency chosen by the user.
• The sampled signal = xsn=sin2πfnTs=sin2πfn18000 xs n 2 f n Ts 2 f n 1 8000 .
• The reconstructed signal = x ̂ (t) x ̂ (t) , is shown as the original signal if sampling is done fast enough, or as the aliased signal if sampling is too slow.

(htht is an ideal reconstruction filter).