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:
Questions & Answers
anyone know any internet site where one can find nanotechnology papers?
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?