By Richard H. Vollmerhausen
Advances in sturdy country detector arrays, flat panel monitors, and electronic snapshot processing have brought on an expanding number of sampled imaging items and probabilities. those know-how advancements supply new possibilities and difficulties for the layout engineer and method analyst--this tutorial's meant reader.
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Extra resources for Analysis of sampled imaging systems
N −1 g ( x) = f ( x − x′) δ( x − nX ) ∗ r ( x). 17) n =0 The Fourier transform is taken before the delta functions multiply f(x). 18) n=0 where (*) denotes convolution. 17 for the space domain, the function f(x) multiplies the delta functions and the products are convolved with the reconstruction function r(x). 18 for the frequency domain, the spatial products become frequency convolutions and the spatial convolutions become frequency products. 18 provides a general expression for G(ξ) based on F(ξ), R(ξ), the sample spacing X, and the offset x′.
That is, we want the mathematics to tell us what happens when the pre-sample image is moved with respect to the sample points. The pre-sample signal, f(x), could be defined as whatever the intensity pattern is in the coordinate system of the samples. This would appear to simplify the derivation. However, in such a case, f(x) must be re-defined every time the sensor moves or rotates relative to the scene. The constant re-definition of f(x) would obscure the relationship between the scene, the sample phase, and the final displayed image.
43) 42 Chapter 2 The transfer function of the circuit is the ratio of the output spectrum over the input spectrum. H (ω) = Vout (ω) 1 = . 44) The impulse response is determined by taking the inverse Fourier transform of the transfer function h(t ) = 1 − t / RC e step(t ). 45) The impulse response of a low pass filter is an exponential decay starting at the time the circuit is stimulated. Part of every input is delayed forward in time, nothing is propagated backward in time. 45 is the function that is convolved with the detector output to give the response of the electronics.