ABSTRACT

This book is an informative reference, or working textbook, on the mathematics, and general physical and chemical processes behind remote sensor measurements.

chapter 1|11 pages

2A matrix equation

chapter 1|2 pages

4.2 Mean values

chapter 1|2 pages

5.2 Pieces of information

chapter |3 pages

(16)

chapter 1|1 pages

8 Nonlinear systems

chapter |9 pages

(29)

chapter 2|30 pages

1.2 Microwave radiation

chapter |3 pages

(37)

chapter 2|27 pages

5 Line broadening

chapter |17 pages

(13)

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(17)

chapter 5|4 pages

2.1 Vector and matrix transpose

chapter 5|3 pages

2.3 Rank

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(39)

chapter |3 pages

UU=UU=I.

chapter 5|1 pages

2.7 Determinants

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(57)

chapter 5|4 pages

3.1 Trace

chapter 5|3 pages

4.1 Nonsymmetric matrices

chapter 5|1 pages

5 Singular value decomposition

chapter |9 pages

D=diag(s, s , ···, s ),

chapter 5|2 pages

7 Non-negative definite matrices

chapter 5|5 pages

8 Noise and the covariance matrix

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(143)

chapter 5|22 pages

10 Finding eigenvectors

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chapter 8|7 pages

1d-Functions

chapter |2 pages

(31)

chapter 8|2 pages

2.7 Some useful functions

chapter 8|1 pages

3 Fourier series

chapter |6 pages

(55)

chapter 8|1 pages

4 Discrete Fourier transform

chapter |8 pages

(86)

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(113)

chapter 8|6 pages

7.3Z-transform

chapter |8 pages

References

chapter C|2 pages

(t)=E[ƒ*(x)ƒ(x+t )].

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chapter |1 pages

D(t )=E[f

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chapter |1 pages

h(x)=0.

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chapter 10|2 pages

7.1 Symmetric kernel

chapter 10|1 pages

7.2 Asymmetric kernel

chapter |3 pages

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chapter |3 pages

y=f(x), (6)

chapter |4 pages

u=y'+(1-a)u.

chapter 11|4 pages

2.1 Logistic equation

chapter |4 pages

(26)

chapter 11|1 pages

3.1 Outline of the iteration process

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(I -?AA)A =A

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=(aI+AA) A(aI+AA )(aI+AA)

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(51)

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(63)

chapter 11|2 pages

4.2 Truncated iteration

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(104)

chapter 0|7 pages

<||1-aKK||<1.

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(131)

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(138)

chapter 12|2 pages

1 Matrix approach

chapter |4 pages

|y-y|>s.

chapter 12|5 pages

1.3 Effects of noise

chapter |6 pages

(32)

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(57)

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(61)

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(68)

chapter |1 pages

(75)

chapter 12|10 pages

3 Discussion

chapter 13|4 pages

1.1 Spatial filtering

chapter 13|1 pages

3,1 Effects of noise

chapter |1 pages

(27) 13.4 A Backus -Gilbert approach

chapter |6 pages

(31)

chapter |3 pages

(42)

chapter 13|4 pages

6 An integral-equation approach

chapter |2 pages

(65)

chapter |10 pages

(70)

chapter 14|2 pages

1.1 An application of Lagrange multipliers

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(27)

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chapter |2 pages

(52)

chapter |4 pages

(60)

chapter 14|3 pages

5 Inequalities

chapter |4 pages

(90)

chapter |1 pages

(111)

chapter |2 pages

(114)

chapter 14|2 pages

9 Orthogonal expansions

chapter 14|1 pages

10 Orthonormalization

chapter |2 pages

(133)

chapter |1 pages

=f(y-cy-dy) +f(y-cy-dy) +f(y-cy-dy)

chapter |2 pages

b =a t . (143)

chapter 14|2 pages

13 Proof by induction