Signal

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A signal is an abstract element of information, or (more commonly) a flow of information (in one or more dimensions). A two-dimensional signal is usually called an image.

Definition

A signal is any physical phenomenon that can be modeled as a function from time or position to some scalar- or vector-valued ___domain that can be real or complex valued. A one-dimensional signal, like a voltage, has a magnitude that is a function of time. A two-dimensional signal, like an image, has a magnitude in two spatial dimensions and becomes video when a function of time.

Continuous versus discrete

The distinction made between a continous and discrete signal is only with respect to the time. A continuous signal is a continuous function of time while a discrete signal is a discrete function of time.

Analog versus digital

Unlike the previous comparison of continuous vs. discrete, this distinction considers all dimensions of a signal. A signal that is continuous in all dimensions is an analog signal while a digital signal is discrete in all dimensions. A digital signal is realized from an analog signal when the signal is sampled in time and quantized or sampled in the other dimensions.

For example, CD quality music is 16-bit (the quantization) and is sampled at 44.1 kilohertz. A digital image is sampled in the two spatial dimensions (giving the image a fixed width and height (e.g., 800x600 pixels)) and quantized in intensity (i.e. the brightness of the image at that point). It might be worth noting that even a photograph is a discrete signal because the film used contains photo-sensitive grains.

Sampling

With the increasing use of computers the usage and need of digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). In order to properly sample an analog signal the Nyquist-Shannon sampling theorem must be satisfied. In short, the sampling frequency must be greater that twice the maximum frequency of the signal. A digital to analog converter (DAC) is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient into digital control systems.

Analog signals

While analog signals exist on paper, they do not exist in reality. This is the result of Planck time, Planck length, and Planck energy units. In other words, all reality-based signals are digital signals but with extremely small quantization levels. In treating a signal as an analog signal it is for mathematical purposes or for simplicity's sake by considering the extremely small quantizations as negligable. This realization that analog signals are only theoretical is one not usually made and so assuming such quantizations as negligable is not one to quibble over except in theoretical arguments.

Frequency spectrum

See frequency ___domain and frequency spectrum.

Other notes

Another important propery of a signal (actually, of a statistically defined class of signals) is its entropy or information contents, measured in bits (or bits per second, or bits per square millimeter, etc.).

See also