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A white noise signal has autocorrelation matrix = where is the variance of the signal. In this case all eigenvalues are equal, and the eigenvalue spread is the minimum over all possible matrices. In this case all eigenvalues are equal, and the eigenvalue spread is the minimum over all possible matrices.
In the forward prediction case, we have () = with the input signal () as the most up to date sample. The backward prediction case is d ( k ) = x ( k − i − 1 ) {\displaystyle d(k)=x(k-i-1)\,\!} , where i is the index of the sample in the past we want to predict, and the input signal x ( k ) {\displaystyle x(k)\,\!} is the most recent sample.
The observer design pattern is a behavioural pattern listed among the 23 well-known "Gang of Four" design patterns that address recurring design challenges in order to design flexible and reusable object-oriented software, yielding objects that are easier to implement, change, test and reuse.
The general idea behind Volterra LMS and Kernel LMS is to replace data samples by different nonlinear algebraic expressions. For Volterra LMS this expression is Volterra series. In Spline Adaptive Filter the model is a cascade of linear dynamic block and static non-linearity, which is approximated by splines.
LMS (long, medium, short), is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths.
Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
If one draws the data-flow diagram for this pair of operations, the (x 0, x 1) to (y 0, y 1) lines cross and resemble the wings of a butterfly, hence the name (see also the illustration at right). A decimation-in-time radix-2 FFT breaks a length-N DFT into two length-N/2 DFTs followed by a combining stage consisting of many butterfly operations.
An adaptive equalizer is an equalizer that automatically adapts to time-varying properties of the communication channel. [1] It is frequently used with coherent modulations such as phase-shift keying, mitigating the effects of multipath propagation and Doppler spreading.