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

Impule Inveriant z-transformation
Impule Inveriant z-transformation See slides. Keeps impulse response the same. $$H(z) = T \cdot \mathcal{Z}[h(n)]$$ If $$H(s) = \sum_{i=1}^{N} \frac{k_{i}}{s-s_{i}}$$ then $$H(z) = T \sum_{i=1}^{N}k_{i}\frac{z}{z - e^{s_{i}T}} = T \sum_{i=1}^{N}k_{i}\frac{1}{1 - e^{s_{i}T}z^{-1}}$$ Procedure Eksempel på Procedure lektion8 Eksempel på Procedure af Kasper page=3#page=3" Bestem det analoge prototypefilters frekvensnormerede overføringsfunktion $H(s)$. Partialbrøksopløs $H(s)$ til 1. og 2. ordens overføringsfunktioner (maksimalt antal 2. ordens overføringsfunktioner).
0001/01/01 · Notes
Impulse Response
Impulse Response The response of a system, when it is excited by a dirac delta.
0001/01/01 · Notes
Impulse Sampling
Impulse Sampling See slides. Sample signalet med et impulstog med højden $1$. This method results in the signal being repeated an infinite amount of times along the frequency spectrum. A lowpass-filter can recreate the signal if the sampling frequency is sufficient. Eksempel på et gentaget spektrum Eksempel fra slides page=23#page=23"
0001/01/01 · Notes
Impulsmoment
Impulsmoment Impulsen i en cirkulær bevægelse $$L=m \cdot v \cdot r$$ $L$: Impulsmoment $m$: Partiklens masse $v$: Partiklens fart $r$: Radius fra omdrejningspunktet
0001/01/01 · Notes
impulstog
impulstog Et periodisk signal hvor hver periode begynder med en deltafunktion.
0001/01/01 · Notes
Indre og Ydre Produkt
Indre og Ydre Produkt Måder at “gange” vektorer. $$\vec{a} = \left( \begin{array}{c} 3 \ 6 \ 1 \ \end{array} \right) \s \vec{b}=\left( \begin{array}{c} 1 \ 2 \ -4 \ \end{array} \right)$$ Indre Produkt $$\vec{a}^{T} \cdot \vec{b} = \left( \begin{array}{ccc} 3 & 6 & 1 \ \end{array} \right) \cdot \left( \begin{array}{c} 1 \ 2 \ -4 \ \end{array} \right) = 11$$ Ydre produkt $$\vec{a}^{T} \cdot \vec{b} = \left( \begin{array}{c} 3 \ 6 \ 1 \ \end{array} \right) \cdot \left( \begin{array}{ccc} 1 & 2 & -4 \ \end{array} \right) = \left( \begin{array}{ccc} 3 & 6 & -12 \ 6 & 12 & -24 \ 1 & 2 & -4 \ \end{array} \right)$$
0001/01/01 · Notes
Inertimoment
Inertimoment “Masse i Rotation” - René $$I = \sum_{i} m_{i}r_{i}^{2} \s [\text{kg} \cdot \text{m}^2]$$ $m_{i}$ : Uendelig lille del af objektets masse. $r_{i}$ : Distangen til fra omdrejningspunktet til den uendelig lille masse. Ved punkt masse $$I = m \cdot r^{2}$$ Omdrejningsaksen kan parallelforskydes med Flytningsformlen. Inertimomenter for forskellige objekter Lektion 09-FYS__RT_E22.pdf>page=10 Kontinuært legme $$I = \int r^{2} dm$$
0001/01/01 · Notes
Integral Table
Integral Table These equations are from integral-table.com. Basic Forms $$ \int x^n \mathrm{dx}= \frac{1}{n+1}x^{n+1},\hspace{1ex}n\neq -1 $$ $$ \int \frac{1}{x}\mathrm{dx}= \ln |x| $$ $$ \int u \mathrm{dv}= uv - \int v \mathrm{du} $$ $$ \int \frac{1}{ax+b}\mathrm{dx}= \frac{1}{a} \ln |ax + b| $$ Integrals of Rational Functions $$ \int \frac{1}{(x+a)^2}\mathrm{dx}= -\frac{1}{x+a} $$ $$ \int (x+a)^n \mathrm{dx}= \frac{(x+a)^{n+1}}{n+1}, n\ne -1 $$ $$ \int x(x+a)^n \mathrm{dx}= \frac{(x+a)^{n+1} ( (n+1)x-a)}{(n+1)(n+2)} $$ $$ \int \frac{1}{1+x^2}\mathrm{dx}= \tan^{-1}x $$
0001/01/01 · Notes
Integraler
Integralregning I ulige funkioner er integralet altid $0$, hvis $-a = b$. Noter list from #integraler sort file.name
0001/01/01 · Notes
Integraler Regneregler
Integraler Regneregler Husk at lægge $k$ til alle ubestemte integraler page=26#page=26" Flere Trigonometriske Sammenhlænge $$\int\frac{1}{\sqrt{1-x^{2}}}\dx=\arcsin(x)$$
0001/01/01 · Notes