LSI systems are expressed mathematically as 2D convolutions:
$$g(x, y)=\int \,d $$∞∞∞∞hxyf where
$h(x, y)$ is the 2D impulse response (also called the
point spread function ).
2d fourier analysis
$$(u, v)=\int \,d y$$∞∞x∞∞fxyuxvy where
$$ is the 2D FT
and
$u$ and
$v$ are frequency variables in
$x(u)$ and
$y(v)$ .
2D complex exponentials are
eigenfunctions for 2D LSI systems:
where
$$\int \,d {}^{}$$∞∞∞∞hu0v0Hu0v0$H({u}_{0}, {v}_{0})$ is the 2D Fourier transform of
$h(x, y)$ evaluated at frequencies
${u}_{0}$ and
${v}_{0}$ .
We can
sample the height of the surface
using a 2D impulse array.
$${f}_{s}(x, y)=S(x, y)f(x, y)$$ where
${f}_{s}(x, y)$ is sampled image in frequency
2D FT of
$s(x, y)$ is a 2D impulse array in frequency
$S(u, v)$
$$\text{multiplication in timeconvolution in frequency}$$$${F}_{s}(u, v)=(S(u, v), (u, v))$$
Nyquist theorem
Assume that
$f(x, y)$ is bandlimited to
$({B}_{x})$ ,
$({B}_{y})$ :
If we sample
$f(x, y)$ at spacings of
$(x)< \frac{\pi}{{B}_{x}}$ and
$(y)< \frac{\pi}{{B}_{y}}$ , then
$f(x, y)$ can be perfectly recovered from the samples by
lowpass filtering:
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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