By Peter W. Hawkes
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 positive aspects prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, picture technology and electronic photograph processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in some of these domain names.
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Extra info for Advances in Imaging and Electron Physics, Vol. 125
K − 1, σr := i ski+r t i = i ki + r |σ t i . (14) Extending the notation introduced for the downsampling operator, we denote by Drk the linear operator such that Drk (σ ) = σr for r = 0, 1, . . , k − 1. These operators will be called the k-decimation operators. By deﬁnition, the r th k-decimation operator can be written as Drk = Dk0 Ft r (15) and represented by Hence, the matrix associated with the decimation operator Drk is given by the product R(t k , υ) × R(t, t r ) that yields, using the Product Rule, the Hurwitz matrix R(t k , t r ) (see Fig.
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.
SUBBAND SIGNAL PROCESSING 47 In particular, an M-transmultiplexer (and, hence, the corresponding operator) is said to be free from cross-talk when every output signal σˆ (i) only depends on the corresponding input σ (i) , namely, nonzero Laurent polynomials τ (0) , τ (1) . . , τ (M−1) exist such that, for every i = 0, 1, . . , M − 1, σˆ (i) = τ (i) σ (i) . This last condition is clearly satisﬁed whenever the Toeplitz block matrix (50) associated with the linear operator Tα,γ is block diagonal.