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By O'sullivan F., Roy S.

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Unless specifically stated, we consider the input is Gaussian white noise. 1) where x(n) is the input signal and h0 is a constant. The first-order Volterra system is basically the same as the linear system. In other words, the linear system is a subclass of the Volterra system. Consider a general isolated linear system as shown in figure 3-1: x(n) h1(n) y1(n) Figure 3-1. Isolated first order linear system block diagram where the h1(n) represents the linear filter coefficients. 2) where the * means linear convolution.

5) (k −1) p(k) − α ki w k i = pi −1) w M = p (M M where p (k) i indicates the ith vector at stage k. Theoretically, identical results and the same computational complexity will be performed with both versions. The only difference is the operational sequence. , M} is ill-conditioned. Therefore the modified Gram-Schmidt procedure has much better numerical stability and accuracy than the Gram-Schmidt procedure. 5 QR and Inverse QR Matrix Decompositions QR matrix decomposition is frequently used in RLS-type adaptive algorithms.

The benefit is most apparent when some vectors in the set are nearly collinear. , pM vectors orthogonal to the pk vector in each stage k and repeat this operation to (M-1)th stage. 5 below (Brogam 1991). 5) (k −1) p(k) − α ki w k i = pi −1) w M = p (M M where p (k) i indicates the ith vector at stage k. Theoretically, identical results and the same computational complexity will be performed with both versions. The only difference is the operational sequence. , M} is ill-conditioned. Therefore the modified Gram-Schmidt procedure has much better numerical stability and accuracy than the Gram-Schmidt procedure.

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A statistical measure of tissue heterogeneity with application to 3D PET sarcoma data (2003)(en)(16s by O'sullivan F., Roy S.


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