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Pisarenko's method also assumes that + values of the autocorrelation matrix are either known or estimated. Hence, given the ( p + 1 ) × ( p + 1 ) {\displaystyle (p+1)\times (p+1)} autocorrelation matrix, the dimension of the noise subspace is equal to one and is spanned by the eigenvector corresponding to the minimum eigenvalue.
Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. [ citation needed ] A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far ...
Autocorrelation of white noise [ edit ] The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function ) at τ = 0 {\displaystyle \tau =0} and will be exactly 0 {\displaystyle 0} for all other τ {\displaystyle \tau } .
White noise draws its name from white light, [2] although light that appears white generally does not have a flat power spectral density over the visible band. An image of salt-and-pepper noise In discrete time , white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean ...
MUSIC outperforms simple methods such as picking peaks of DFT spectra in the presence of noise, when the number of components is known in advance, because it exploits knowledge of this number to ignore the noise in its final report.
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.
A pseudo-noise code (PN code) or pseudo-random-noise code (PRN code) is one that has a spectrum similar to a random sequence of bits but is deterministically generated. The most commonly used sequences in direct-sequence spread spectrum systems are maximal length sequences, Gold codes, Kasami codes, and Barker codes. [4]
For example, the Wiener filter can be used in image processing to remove noise from a picture. For example, using the Mathematica function: WienerFilter[image,2] on the first image on the right, produces the filtered image below it. It is commonly used to denoise audio signals, especially speech, as a preprocessor before speech recognition.