# Pulse-code modulation

 related topics {system, computer, user} {math, number, function} {math, energy, light} {rate, high, increase} {work, book, publish}

Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals, which was invented by Alec Reeves in 1937. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems. A PCM stream is a digital representation of an analog signal, in which the magnitude of the analogue signal is sampled regularly at uniform intervals, with each sample being quantized to the nearest value within a range of digital steps.

PCM streams have two basic properties that determine their fidelity to the original analog signal: the sampling rate, which is the number of times per second that samples are taken; and the bit depth, which determines the number of possible digital values that each sample can take.

## Contents

### Modulation

In the diagram, a sine wave (red curve) is sampled and quantized for pulse code modulation. The sine wave is sampled at regular intervals, shown as ticks on the x-axis. For each sample, one of the available values (ticks on the y-axis) is chosen by some algorithm. This produces a fully discrete representation of the input signal (shaded area) that can be easily encoded as digital data for storage or manipulation. For the sine wave example at right, we can verify that the quantized values at the sampling moments are 7, 9, 11, 12, 13, 14, 14, 15, 15, 15, 14, etc. Encoding these values as binary numbers would result in the following set of nibbles: 0111, 1001, 1011, 1100, 1101, 1110, 1110, 1111, 1111, 1111, 1110, etc. These digital values could then be further processed or analyzed by a purpose-specific digital signal processor or general purpose DSP. Several Pulse Code Modulation streams could also be multiplexed into a larger aggregate data stream, generally for transmission of multiple streams over a single physical link. One technique is called time-division multiplexing, or TDM, and is widely used, notably in the modern public telephone system. Another technique is called Frequency-division multiplexing, where the signal is assigned a frequency in a spectrum, and transmitted along with other signals inside that spectrum. Currently, TDM is much more widely used than FDM because of its natural compatibility with digital communication, and generally lower bandwidth requirements.