Never mind, I managed to solve this. I assumed that the eyepiece forms a virtual image of the objective at the near point of the eye and used that distance to calculate ##f_e##.
The question:
--------------------
The length of a microscope pipe is $L=160\,\rm mm$,
the transverse magnification of its objective $M_o = 40\times$
and the diameter $d_o = 5\,\rm mm$.
As for the ocular/eyepiece, its magnification is $M_e = 10\times$.
1. Find out the focal length of the...
There seems to be a math processing error preventing the rendering of the biggest part of this exercise. Looking at the source code, I can't spot the error on my part.
Regradless, if it doesn't decide to resolve itself, the correct answer was
\begin{equation}
\digamma\{ f(t) \} = \frac{4}{4 +...
It's not the cosine, that scares me. What I'm ahving trouble with is ##f(t)##. I also made a few mistakes in the opening post because I'm copyin stuff from my offline LaTeX-document. They should be fixed now.
Ok, so right now I have
\begin{align*}
\digamma\{f(t)\}(\omega) = \lim_{a \to \infty} \frac{(2+j\omega)e^{a(2-j\omega) }}{(2+j\omega)(2-j\omega)}
+ \frac{(2-j\omega)e^{-a(2-j\omega)}}{(2+j\omega)(2-j\omega)}
\end{align*}
Not compeltely sure what to do here. I'm trying to edit my offline LaTeX...
Homework Statement
Determine the Fourier-transfroms of the functions
\begin{equation*}
a) f : f(t) = H(t+3) - H(t-3) \text{ and } g : g(t) = \cos(5t) f(t)
\end{equation*}
and
\begin{equation*}
b) f : f(t) = e^{-2|t|} \text{ and } g : g(t) = \cos(3t) f(t)
\end{equation*}Homework Equations
The...
It just occurred to me, that maybe I should be using the periodicity and symmetricity of the DFT, to find out the values of ##G_n## in 4b. Any comment on this?
Homework Statement
This is a combination of two questions, one being the continuation of the other
3) Calculate the DFT of the sequence of measurements
\begin{equation*}
\{ g \}_{k=0}^{5} = \{ 1,0,4,-1,0,0 \}
\end{equation*}
4a) Draw the DFT calculated in question 3 on the complex plane.
4b)...