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Download e-book for iPad: A Cauchy Problem for the System of Elasticity Equations by Makhmudov O. I.

By Makhmudov O. I.

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Indeed 2 ρ (cx,F , cy ) = = = 2 L T l=1 il Rcx ,l hl L l=1 hTl Rcx ,l hl · L T l=1 il Rcx ,l hl L l=1 2 λl + qTl Rv ql · L l=1 L hTl Rcx ,l hl · l=1 λl ρ2 (cx , cx,F ) · ρ2 (cx , cy ) . 34. 83) with equality when hl = il , ∀l. Proof. 82) since ρ2 (cx , cx,F ) ≤ 1. The SPCC between the two vectors cv and cy is ρ2 (cv , cy ) = L l=1 L l=1 qTl Rv ql qTl Ry ql 1 1 + iSNR = ρ2 (v, y) . 84) As expected, the SPCC between the two vectors v(k) and y(k) is identical to the SPCC between the two vectors cv (k) and cy (k).

1. 14) l=1 L oSNR(hl ) ≥ oSNR (h1:L ) . 15) 24 3 Performance Measures This means that the aggregation of the subband SNRs is greater than or equal to the fullband SNR. Proof. 16) where al and bl are positive reals. 2 Noise-Reduction Factor Another important measure in noise reduction is the noise-reduction factor, which quantifies the amount of noise being attenuated by the filter. With the time-domain formulation, this factor is defined as [11], [24] ξnr (H) = tr (Rv ) tr HRv HT . 18) and ξnr (hl ) = qTl Rv ql , l = 1, 2, .

In the next chapter, we will present another criterion, called the Pearson correlation coefficient, in which the output SNR appears naturally. 5 Pearson Correlation Coefficient This chapter develops several forms of the Pearson correlation coefficient in the different domains. This coefficient can be used as an optimization criterion to derive different optimal noise reduction filters [14], but is even more useful for analyzing these optimal filters for their noise reduction performance. 1 Correlation Coefficient Between Two Random Variables Let a and b be two zero-mean real-valued random variables.

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