FM and PM Modulation Spectrum (interactive)

This lit­tle wid­get will cal­cu­late the spec­trum for var­i­ous mod­u­la­tion sig­nals with arbi­trary fre­quency and ampli­tude and explain why it looks the way it does. It was writ­ten with opti­cal inter­fer­om­e­try in mind, so the mod­u­la­tion sig­nal is defined in terms of the veloc­ity of a mov­ing object, which is sim­ple to con­vert to a fre­quency devi­a­tion, see below.

num­ber of har­mon­ics: Carson’s rule: 0

Warn­ing: Large dataset required for cal­cu­la­tion may lead to unre­spon­sive browser. Con­tinue any­way


PSD [a.u.] vs Fre­quency [Hz]
total frac­tion of power plot­ted: 0

veloc­ity [m/s] vs Time [a.u.]

Posi­tion [m] vs Time [a.u.]

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Bokeh calculator (interactive)

If you don’t want to do all the math in the the math of bokeh post your­self, you can just enter your data into this here lit­tle applet and get your results much quicker.   bokeh (disk) size: 0mm rel­a­tive bokeh size: 0% (as frac­tion of sen­sor height)  

the math of bokeh

If you don’t know (yet) what bokeh is, check out the Wikipedia arti­cle. In short, bokeh is the blur (or qual­ity thereof) of out-of-focus regions in a pho­to­graph. This post is not about the per­ceived qual­ity of such blur, but rather of its size. For bokeh, more is usu­ally bet­ter, since it allows to sep­a­rate […]

Microsoft Project Lessons

Here are some tips for using MS Project in par­tic­u­lar and project man­age­ment in gen­eral that I picked up, which have either proven use­ful or which sound rea­son­able and which I plan to try out in the future. Feel free to add yours in the com­ments. Leave Buffers Since no project ever goes accord­ing to […]

Adventures in JavaScript: Number Bases

Here’s just a quick lit­tle JavaScript that will con­vert num­bers between dif­fer­ent bases. It grew out of the idea that num­bers in a sys­tem based on π would be much more use­ful in engi­neer­ing that the reg­u­lar old ones. Well, just because one can do it doesn’t mean it’s a good idea, but it was […]

Adventures in JavaScript: Humidity

You thor­oughly air out your rooms dur­ing win­ter time and watch the humid­ity inside drop in the process (pro­vided you own a hygrom­e­ter). But where will it stop? This lit­tle gad­get will tell you. Just enter the out­side tem­per­a­ture and humid­ity and the tem­per­a­ture the air will be heated up to inside.   Ref­er­ences [1] […]


The pre­vi­ous post on the Gauss­ian beam noted that this beam is a solu­tion to the parax­ial wave equa­tion and thus only accu­rate for small diver­gence angles. The limit given in [1] was $w_0 \gt 2\lambda/\pi$ or $\theta \lt 0.5\mathrm{rad}$ or $\approx 29^\circ$. The Gauss­ian beam model is of course not exact up to that […]

the Gaussian beam (interactive)

The Gauss­ian beam “is a con­ve­nient, wide­spread model in laser optics.” [1] It is indeed con­ve­nient that such a math­e­mat­i­cally rel­a­tively sim­ple model can describe the evo­lu­tion of laser light in free space so well. Given the wave­length of the laser, it can be described by a sin­gle para­me­ter. This can be either the beam […]

TiddlyWiki – EditSectionPlugin Keyboard Shortcuts

Like so many of his plu­g­ins, Eric Shulman’s Edit­Sec­tion­Plu­gin for Tid­dly­Wiki is quite awe­some. Espe­cially in long tid­dlers it can save you a lot of scrolling and search­ing. One thing I was miss­ing, though, were the key­board short­cuts ESC to can­cel edit­ing and CTRL+ENTER to fin­ish edit­ing, like the ones you have when edit­ing the […]

The Coupon (Sticker) Collector

Super­mar­ket chain Edeka cur­rently runs this sticker col­lect­ing racket – which used to be smurf col­lect­ing – where you get four stick­ers with ani­mal pic­tures for every €10 spent. The kids are col­lect­ing like crazy, I am told, even though the pic­tures are mediocre at best. Any­way, as geeks we don’t care much about the […]