Most real signals are analog and in order to utilize the processing power of modern digital processors it is necessary to convert these analog signals into some form which can be stored and processed by digital devices. The standard method is to sample the signal periodically and digitize it with an A to D converter using a standard number of bits 8, 16 etc. Digital signal processing is primarily concerned with the processing of these sampled signals. The diagram illustrates the situation. The blue line shows the analog signal while the red lines shows the samples arising from periodic sampling at intervals T.
A mathematical representation of the sampled signal is shown below. This is equivalent to modulating a train of delta functions by the analog signal. The delta function effectively "filters" out the values of the signal at times corresponding to the zeros in the argument of the delta function. This process is also referred to as "ideal" sampling since it results in sampled signals of "zero" width and whose spectrum is perfectly periodic.
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