Example 721

As a first example of an SMF calculation, consider a one-dimensional, continuous SMF for an image that is a light spot of radius r, centered at x = 0. Thus, s(x) = Io[U(x + r) - U(x - r)] is a pulse of height Io, which has the well-known Fourier transform, S(u) = (Io2r) sin(ru)/(ru), which is real. g(x) is given by real convolution.

FIGURE 7.2-1 Plots of the one-dimensional, input signal intensity, s(x), reversed and translated in the form for real convolution. s(x) is made asymmetrical for illustrative purposes.

The SMF is also a pulse of radius r centered at x = 0, and height KIo. In the real convolution process, shown in Figure 7.2-2, g(x) emerges as a triangle of base 4r and a peak of height Kio 2r at x = 0. Interestingly, if the input object has width 2w, where w > r, the height of gs(x) will still be KI2o 2r, maximum at x = 0. The triangular shape of this g(x) is 2(r + w) wide, however. The ms noise output of the SMF is

No = (n2)^J ™lHm((u) du = (l/2) —J \l02r[sin(ruV(ru)]| du = (n/2)(Klo )22r The peak MS SNR is at x = xo = 0:

Was this article helpful?

0 0
Peripheral Neuropathy Natural Treatment Options

Peripheral Neuropathy Natural Treatment Options

This guide will help millions of people understand this condition so that they can take control of their lives and make informed decisions. The ebook covers information on a vast number of different types of neuropathy. In addition, it will be a useful resource for their families, caregivers, and health care providers.

Get My Free Ebook


Post a comment