Balder W. Holst

Hello there!

My name is Balder and this is my personal website. Here i write down what i learn to maybe help others some day. For now i will just act like people are reading my articles, and make them for fun.

This website has three main sections:

I write these articles for fun, and even though i try to make sure that they are correct, i am not a perfect human and there are sure to be mistakes. Below is a list of most recent articles in all categories.

Recent Posts

En-en-tydig Funktion
En-en-tydig Funktion $$x_1 \neq x_2 \Rightarrow f(x_1) \neq f(x_2)$$ Har man et input, så kommer der et unikt output ud, som kunne dette input kunne have resulteret i. Betyder at der findes en Omvendt funktion, der kan gøre præcis det samme som $f(x)$ bare modsat. Skal enten have positiv eller negativ hældning.
0001/01/01 · Notes
Energi
Energi Typer Kinetisk Energi Potentiel Energi Mekanisk energi Arbejde se Arbejde.
0001/01/01 · Notes
Ethernet
Ethernet See slides. Standard Ethernet There are 4 generations that are all faster than the last. Does not acknowledge received frames. Parts Preamble: 7 alternating ones and zeroes to alert receiver SFD: Start frame delimiter Length/type of data Data: data (size: 46-1500 bytes) padded with zeros if it is smaller than the minimum data size. The minimum size is to make sure the transmission is at least double propagation time.
0001/01/01 · Notes
Eulers Formel
Eulers Formel (Den bedste formel) $$\cos x = Re(e^{ix}) = \frac{e^{ix} + e^{-ix}}{2}$$ $$\sin x = Im(e^{ix}) = \frac{e^{ix} - e^{-ix}}{2i}$$
0001/01/01 · Notes
Fast Fourier transformation (FFT)
Fast Fourier transformation See slides. An algorithm for computing a Diskret Fourier Transformation. This can be implemented in many ways. Time complexity: $$O\left(\frac{n}{2} \log_{2}(n)\right)$$ Idea $W_N$ can be calculated once, and rotated in the imaginary plane to find the others. There will be $N$ amount of $W_N$ going clockwise around the imaginary unit circle. $$W_{N}^{1}, W_{N}^{2} \dots W_{N}^{N-1}$$ $$W_{N}^{N} = W_{N}^{1},,, W_{N}^{N+2} = W_{N}^{3}$$ Window $$h(n) = h_{\infty}(n)w(n)$$ A good window will be as **narrow as possible** in the frequency domain.
0001/01/01 · Notes
Filter Transformations
Filter Transformations See slide. Other types of filters can be designed by transforming them to low-pass filters, determining their order, and then transforming them back. Creating a high-pass filter We can mirror the filter over the cutoff frequency by dividing the nominated filter by the cutoff frequency itself ($\omega_{s}$). $$H_{hp}(s) = H_{lp}(\bar{s})|_{\bar{s} = \frac{1}{s}}$$ Example of creating of high-pass filter page=57#page=57" Denomering $$s \rightarrow \frac{s}{\omega_{a}}$$ Creating a band-pass filter Lektion 1 - Filterfunktioner.
0001/01/01 · Notes
Filters
Filters Lektion 1 - Filterfunktioner.pdf Filter Types Ideal filters We want three things from a filter: Constant amplification on the pass band Lots of dampening after cutoff frequency Linear phase* (see >Delay through filter (gruppeløstid)) Actual filter types These all only have poles no zero points. Butterworth Filter Chebyshev Filter Bessel (More linear phase) Plots of the three filters Poles of the filters. Note: Butterworth lies on a circle around $(0, 0)$, with a radius of $j\omega_{a}$.
0001/01/01 · Notes
FIR Filtre
FIR Filtre See slides. Can have linear phase! Ingen tilbagekobling: Afhænder kun a det nuværende og tidligere input $M$: Orden Lineær fase FIR filter can have linear phase! Nulpunkter Nulpunker skal ligge i par således $$z_{1} = r\angle \phi, \s z_{2} = r/1\ \angle\phi$$ Dette resulterer i nulpunkter der kunne ligge således. Symetri Et FIR filter med lineær fase er altid spejlet over midterste sample: Koefficienterne er symmetriske. Filtre med Fouré Koefficienter See slide.
0001/01/01 · Notes
Fjederkraft
Fjederkraft $$F = -kx$$ $F$ : Fjederkraften $k$ : Fjederkonstanten $[\frac{\text{N}}{\text{m}}]$ $x$ : Udstrækningen Denne kraft er konservativ. Energien $$P = \frac{1}{2} \cdot k \cdot x^2$$ $P$ : Den potentielle energi oplagret i fjederen $k$ : Fjederkonstanten $x$ : Udstrækningen/sammenpresningen af fjederen Sammensatte fjedre Note Ligner serie og Parallelforbindelser men regnes omvendt! Fjedre at i “serie” $$k_{eff}=\frac{1}{\frac{1}{k_{1}} + \frac{1}{k_{2}}+\dots} $$ $k_{eff}$ : Den ækvivalente $k$-værdi $k_i$ : $k$-værdierne for fjedrene
0001/01/01 · Notes
Flytningsformlen
Flytningsformlen En måde at forskyde rotationsaksen for inertimomenter. $$I_{p}= I_{0} + Md^{2}$$ $I_p$ : Inertimomentet om den forskudte akse. $I_0$ : Det originale inertimoment, typisk gennem massemidtpunktet hvis aflæst fra et skema som dette. $M$ : Legemets *totale* masse. $d$ : Den afstand rotation bliver parallelforskudt med.
0001/01/01 · Notes