Recent content by TheSodesa

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...

Yeah, I'm wondering why that is. I tried to switch any dollar signs to double pound signs and such, but its still not rendering.

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 +...

Alright, here's the complete derivation this time (hopefully) without errors: \begin{align*} \digamma\{ f(t) \}(\omega) &= \int_{-\infty}^{\infty} e^{-2|u|} e^{-j\omega u} \,du = \int_{-\infty}^{\infty} e^{-2|u|-j\omega u} \,du\\ &= \int_{-\infty}^{0} e^{2u-j\omega u} \,du + \int_{0}^{\infty}...

I got it. Just a sec, and I'll clean up my derivation.

Alright, let me go over it once more. This might take a moment.

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.

It looks like I have a sum of complex conjugates in the numerator.

\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)}\\ &= \lim_{a \to \infty} \frac{(2+j\omega)e^{a(2-j\omega) } +...

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...

Yhea, I just noticed. Fixing.

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)...