By Ashok K. Goel

Lately, buyer calls for for greater speeds and smaller chips have ended in using interconnections in multilevel and multilayer configurations. a variety of concerns linked to very huge scale built-in circuit (VLSIC) interconnections used for high-speed functions are emphasised. Written in case you are looking to achieve a greater realizing of the criteria linked to modeling, studying and simulating high-density, high-speed interconnections, the chapters are designed so that you can be learn independently.

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**Example text**

2 shows one and the same image represented with a diﬀerent number of pixels as indicated in the legend. With large pixel sizes (Fig. 2a, b), not only is the spatial resolution poor, but the gray value discontinuities at pixel edges appear as disturbing artifacts distracting us from the content of the image. As the pixels become smaller, the eﬀect becomes less pronounced up to the point where we get the impression of a spatially continuous image. This happens when the pixels become smaller than the spatial resolution of our visual system.

7 million colors (3 channels with 8 bits each), can be displayed on inexpensive PC graphic display systems with a resolution of up to 1600 × 1200 pixels. Consequently, a modern frame grabber no longer requires its own image display unit. It only needs circuits to digitize the electrical signal from the imaging sensor and to store the image in the memory of the computer. The direct transfer of image data from a frame grabber to the memory (RAM) of a microcomputer has become possible since 1995 with the introduction of fast peripheral bus systems such as the PCI bus.

We denote such a basis image with a one at row m, column n by m,n P: m,n pm ,n = 1 m=m ∧n=n 0 otherwise. 10) Any arbitrary scalar image can then be composed from the basis images in Eq. 11) m=0 n=0 where Gm,n denotes the gray value at the position (m, n). It is easy to convince ourselves that the basis images m,n P form an orthonormal base. To that end we require an inner product (also known as scalar product ) which can be deﬁned similarly to the scalar product for vectors. 11: The ﬁrst 56 periodic patterns, the basis images of the Fourier transform, from which the image in Fig.