Reconstruction from Samples--Pictorial Version

Figure D.1 shows how a sound is reconstructed from its samples. Each sample can be considered as specifying the scaling and location of a sinc function. The discrete-time signal being interpolated in the figure is a digital rectangular pulse:

The sinc functions are drawn with dashed lines, and they sum to produce the solid curve. An isolated sinc function is shown in Fig.D.2. Note the ``Gibb's overshoot'' near the corners of the continuous rectangular pulse in Fig.D.1 due to bandlimiting. (A true continuous rectangular pulse has infinite bandwidth.)

Notice that each sinc function passes through zero at every sample instant but the one it is centered on, where it passes through 1.

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Time-Bandwidth Products are Unbounded Above

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