Peter W. Hawkes's Advances in Imaging and Electron Physics, Vol. 125 PDF

By Peter W. Hawkes

ISBN-10: 012014767X

ISBN-13: 9780120147670

Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The sequence gains prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, picture technological know-how and electronic photograph processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in a lot of these domain names.

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Extra resources for Advances in Imaging and Electron Physics, Vol. 125

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SUBBAND SIGNAL PROCESSING 13 we get (4) by equating the zeroth row on both sides. Identity (5) follows from the well-known fact that the transpose of the Toeplitz matrix R(t, α) is the Toeplitz matrix R(t, α ∗ ). 2. The composition of two Laurent polynomials α, β is the row vector: [α ◦ β]T = [α]T × R(β, υ) (6) or, equivalently, the column vector [α ◦ β] = R(β, υ)T × [α]. (7) In fact, again using the Product Rule, we have: R(t, α) × R(β, υ) = R(β, α ◦ β), and (6) is obtained by equating the zeroth row on both sides.

36) σk−1 This yields the computationally efficient and easily parallelizable description of the action of an FIR analysis operator depicted below: r Synthesis The synthesis operator Fα∗ Uk corresponds to the transposed Hurwitz matrix R(t k , α)T . As in the previous case, the output σˆ is the zeroth column of the matrix R(t k , α)T × R(t, σ ∗ ) = R(t k , α)T × R(t, σ )T = R(t k , (σ ◦ t k )α)T , that is, σˆ = (σ ◦ t k )α. Recalling that k−1 α= i=0 t i (αi ◦ t k ), we get the following algebraic expression for the output of a synthesis operator: k−1 σˆ = i=0 t i ((σ αi ) ◦ t k ) 32 BARNABEI AND MONTEFUSCO that can be schematized as follows: Bearing in mind the bijection between a Laurent polynomial and its kdecimated vector, the action of the synthesis operator can be also described as follows: ∆k (σˆ ) = ∆k (α) σ, (37) that is, ⎤ ⎤ ⎡ σˆ 0 α0 σ ⎢ σˆ 1 ⎥ ⎢ α1 σ ⎥ ⎢ .

VIII. The M-Band Lifting So far, we have mostly been interested in studying conditions under which two assigned filter vectors yield a perfect reconstruction system.

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Advances in Imaging and Electron Physics, Vol. 125 by Peter W. Hawkes

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