Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 3. Ideal Sampling

The concept of ideal sampling can be viewed as the foundation upon which the rest of DSP is built. The simplest way to view ideal sampling is as a mapping process, such as the one depicted in Figure 3.1, that “grabs” uniformly spaced instantaneous values of the continuous-time function, x(t), and uses these values to construct the discrete-time sequence, x[n]:

3.1

where n is the is the integer-valued sample index and T is the real-valued sampling interval. In order to depict ideal sampling in a block diagram, some authors adopt the concept of an ideal sampler, which is usually depicted as a time-driven switch, as in