Noise (signal processing)In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion. Sometimes the word is also used to mean signals that are random (unpredictable) and carry no useful information; even if they are not interfering with other signals or may have been introduced intentionally, as in comfort noise. Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters.
Pink noisePink noise, noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. In pink noise, each octave interval (halving or doubling in frequency) carries an equal amount of noise energy. Pink noise sounds like a waterfall. It is often used to tune loudspeaker systems in professional audio. Pink noise is one of the most commonly observed signals in biological systems.
Colors of noiseIn audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly different properties. For example, as audio signals they will sound differently to human ears, and as they will have a visibly different texture. Therefore, each application typically requires noise of a specific color.
Covariance functionIn probability theory and statistics, the covariance function describes how much two random variables change together (their covariance) with varying spatial or temporal separation. For a random field or stochastic process Z(x) on a domain D, a covariance function C(x, y) gives the covariance of the values of the random field at the two locations x and y: The same C(x, y) is called the autocovariance function in two instances: in time series (to denote exactly the same concept except that x and y refer to locations in time rather than in space), and in multivariate random fields (to refer to the covariance of a variable with itself, as opposed to the cross covariance between two different variables at different locations, Cov(Z(x1), Y(x2))).
Maximum entropy spectral estimationMaximum entropy spectral estimation is a method of spectral density estimation. The goal is to improve the spectral quality based on the principle of maximum entropy. The method is based on choosing the spectrum which corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values. This assumption, which corresponds to the concept of maximum entropy as used in both statistical mechanics and information theory, is maximally non-committal with regard to the unknown values of the autocorrelation function of the time series.
Long-term memoryLong-term memory (LTM) is the stage of the Atkinson–Shiffrin memory model in which informative knowledge is held indefinitely. It is defined in contrast to short-term and working memory, which persist for only about 18 to 30 seconds. LTM is commonly labelled as "explicit memory" (declarative), as well as "episodic memory," "semantic memory," "autobiographical memory," and "implicit memory" (procedural memory). The idea of separate memories for short- and long-term storage originated in the 19th century.
MemoryMemory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, it would be impossible for language, relationships, or personal identity to develop. Memory loss is usually described as forgetfulness or amnesia. Memory is often understood as an informational processing system with explicit and implicit functioning that is made up of a sensory processor, short-term (or working) memory, and long-term memory.
Scaled correlationIn statistics, scaled correlation is a form of a coefficient of correlation applicable to data that have a temporal component such as time series. It is the average short-term correlation. If the signals have multiple components (slow and fast), scaled coefficient of correlation can be computed only for the fast components of the signals, ignoring the contributions of the slow components. This filtering-like operation has the advantages of not having to make assumptions about the sinusoidal nature of the signals.
Shot noiseShot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where shot noise is associated with the particle nature of light. In a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot.
Spearman's rank correlation coefficientIn statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not).
Demand forecastingDemand forecasting refers to the process of predicting the quantity of goods and services that will be demanded by consumers at a future point in time. More specifically, the methods of demand forecasting entail using predictive analytics to estimate customer demand in consideration of key economic conditions. This is an important tool in optimizing business profitability through efficient supply chain management. Demand forecasting methods are divided into two major categories, qualitative and quantitative methods.
Correlation does not imply causationThe phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase cum hoc ergo propter hoc ('with this, therefore because of this').
