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In time series analysis (or forecasting) — as conducted in statistics, signal processing, and many other fields — the innovation is the difference between the observed value of a variable at time t and the optimal forecast of that value based on information available prior to time t.
Identifying the dominant noise type in a time series has many applications including clock stability analysis and market forecasting. There are two algorithms based on autocorrelation functions that can identify the dominant noise type in a data set provided the noise type has a power law spectral density.
In order to define the notion of white noise in the theory of continuous-time signals, one must replace the concept of a random vector by a continuous-time random signal; that is, a random process that generates a function of a real-valued parameter .
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. The mathematical limits for noise removal are set by information theory .
Additive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics: Additive because it is added to any noise that might be intrinsic to the information system.
The graphs in Figure B are a series of masking patterns, also known as masking audiograms. Each graph shows the amount of masking produced at each masker frequency shown at the top corner, 250, 500, 1000 and 2000 Hz. For example, in the first graph the masker is presented at a frequency of 250 Hz at the same time as the signal.
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First, white noise is a generalized stochastic process with independent values at each time. [12] Hence it plays the role of a generalized system of independent coordinates, in the sense that in various contexts it has been fruitful to express more general processes occurring e.g. in engineering or mathematical finance, in terms of white noise.