The sampling theorem as we know it today is the technology our modern DVD’s and CD’s rely on.
The theorem itself outlines two distinct processes. The first is the sampling process, during which a continuous signal is transformed into a discrete signal. For example, a single varying line on a graph (meaning a line that goes up and down, or changes over distance) is changed into a “discrete” signal, or a series of unconnected points.
The second process in the sampling theorem is the reconstruction process. During this process, the continuous signal is reconstructed from the discrete signal—meaning a line is drawn to reconnect the points on our graph.
The sampling theorem is important because the bandwidth over which we transmit information is always limited. As a result, no sound frequencies over a certain maximum value can be sent.
The sampling problem preserves the important information without overtaxing the bandwidth, making it possible for the receiver to rebuild the portions of the message that were left out during the sending process. In this way, there are no gaps in the sounds we can send and receive.
DVD’s and CD’s capture a continuous analog signal via discrete sampling. The more often they “look at” the analog signal—or take a discrete sample—the better the sound quality.
The sampling theorem was proved by a mathematician named Harry Nyquist in the 1920’s. As a result, the theorem is often referred to as the Nyquist Theorem. However, it was renowned French mathematician Augustin-Louis Cauchy who first proposed the theorem in 1841. His proposal discussed ways of transforming a signal into a series of numbers.
The sampling theorem makes the recording technology of our time possible. Without it, many of our era’s technological advances would never have come to be. But our technology owes a lot to the past. Many of our most miraculous advances came from ideas born a hundred years ago—or more.