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

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