10.8 The Ideal Sampler

Let us consider the inverse transform of the function e ^{? kTs}. We know that the inverse transform of e ^{? T s} F( s) is f( t ? T)u( t ? T). In our case, F( s) = 1. Thus, f( t) = ?( t). Thus, the inverse transform of e ^{? kT s} is f( t ? kT). We find that the inverse transform of R* ( s), which we denote by r* ( t), is:

That is, r* ( t) is composed of the samples of r( t) multiplied by delta functions located at the time at which the sample was made. The symbol for an ideal sampler is given in Figure 10.2.

Figure 10.2: The Symbol for the Ideal Sampler