Continuous variable in the context of "Digital data"

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.

The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.

Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others.

A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within an infinite set of values.

Simple digital signals represent information in discrete bands of levels. All levels within a band of values represent the same information state. In most digital circuits, the signal can have two possible valid values; this is called a binary signal or logic signal. They are represented by two voltage bands: one near a reference value (typically termed as ground or zero volts), and the other a value near the supply voltage. These correspond to the two values zero and one (or false and true) of the Boolean domain, so at any given time a binary signal represents one binary digit (bit). Because of this discretization, relatively small changes to the signal levels do not leave the discrete envelope, and as a result are ignored by signal state sensing circuitry. As a result, digital signals have noise immunity; electronic noise, provided it is not too great, will not affect digital circuits, whereas noise always degrades the operation of analog signals to some degree.

Continuous optimization is a branch of optimization in applied mathematics.

As opposed to discrete optimization, the variables used in the objective function are required to be continuous variables—that is, to be chosen from a set of real values between which there are no gaps (values from intervals of the real line). Because of this continuity assumption, continuous optimization allows the use of calculus techniques.

In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions.

Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete:

In psychology and psychometrics, the big five personality trait model or five-factor model (FFM)—sometimes called by the acronym OCEAN or CANOE—is a scientific model for measuring and describing human personality traits. The framework groups variation in personality into five separate factors, all measured on a continuous scale:

• openness (O) measures creativity, curiosity, and willingness to entertain new ideas.
• conscientiousness (C) measures self-control, diligence, and attention to detail.
• extraversion (E) measures boldness, energy, and social interactivity.
• agreeableness (A) measures kindness, helpfulness, and willingness to cooperate.
• neuroticism (N) measures depression, irritability, and moodiness.

The five-factor model was developed using empirical research into the language people used to describe themselves, which found patterns and relationships between the words people use to describe themselves. For example, because someone described as "hard-working" is more likely to be described as "prepared" and less likely to be described as "messy", all three traits are grouped under conscientiousness. Using dimensionality reduction techniques, psychologists showed that most (though not all) of the variance in human personality can be explained using only these five factors.