Even though a signal is sampled, we may have certain rules about inferring the values between the sample points. The most common assumption made in signal processing is that the signal is bandlimited to an extent consistent with the sampling rate, i.e. that the values change smoothly between samples. The Sampling Theorem guarantees that a continuous signal can be reconstructed perfectly from its samples if the signal was appropriately bandlimited prior to sampling [Oppenheim 75]. Practically speaking, signals are never perfectly bandlimited, nor can we construct a perfect reconstruction filter, but we can get as close as we want in a prescribed manner.

We often want to change from one sampling rate to another. The process of representing a signal with more samples is called interpolation, whereas representing it with less is called decimation.
Examples of interpolation are: zooming up on an image, correcting for non-square pixels, and converting an image from 72 dpi to 300 dpi to feed a high resolution output device. Applications of decimation are: reducing the jaggies on an supersampled image, and correcting for non-square pixels.