pictures from Paris

Here are some pic­tures from our recent week­end trip to Paris. We had a great time (although my legs still hurt two days after we were back from all the walk­ing around) and were very lucky with the weather. I can only rec­om­mend a trip there for any­one who has not seen it yet. You need more than a day and a half, though, too see it all...

Arc de Triomphe (panorama)

Arc de Tri­om­phe (panorama)

look­ing down Avenue des Champs-Élysées in the direc­tion of Palais du Lou­vre (center)...


Arc de Triomphe (panorama) v2

Arc de Tri­om­phe (panorama) v2

This is another ver­sion of the Arc de Tri­om­phe panorama, using the same set of pho­tos, in which the indi­vid­ual shots were stitched together dif­fer­ently to give a more real­is­tic per­spec­tive.
I think I like this one bet­ter, but with this method the panora­mas can­not become too wide since the dis­tor­tions increase sig­nif­i­cantly the fur­ther one goes to the left and right. That is why the Tour Eif­fel is miss­ing in this one...


La Défense (panorama)

La Défense (panorama)

This is another one taken from the Arc de Tri­om­phe, this time look­ing in the oppo­site direc­tion, down the Avenue de la Grand Armée towards La Défense.


La Tour Eiffel

La Tour Eiffel


inside La Tour Eiffel

inside La Tour Eiffel

This was taken going up the stairs inside the south­ern “leg” of the tower, some­where below the low­est plat­form. At night, the whole tower is bathed in yel­low­ish sodium light, inside and out. The round things in the cen­ter of the pic­ture are the lamps, illu­mi­nat­ing upwards away from me.


JSOVT(MB): La Tour Eiffel

JSOVT(MB): La Tour Eiffel

We didn’t have a JSOVT(MB) for quite a while I guess, even though Julia’s been sit­ting every­where. Heh. Well, here’s one that fits nicely into the Eif­fel Tower series that I got going here. It was actu­ally Julia’s idea to do this, it being her series and all.

Okay, so this was taken on the first plat­form of the Eif­fel tower. We took the stairs up to the sec­ond plat­form, from where you have to take the ele­va­tor to the very top. How­ever, after wait­ing in line for this ele­va­tor for about half an hour we were told that our tick­ets were only good for the stairs and thus the sec­ond plat­form, and we would have to buy “exten­sion tick­ets” to go all the way up. This would have meant get­ting in that line again after buy­ing the tick­ets and after a whole day’s walk­ing through Paris we were too tired at 11pm to do that. So I guess we have to come back to Paris one day to fin­ish the Eif­fel Tower...


Arc de Triomphe du Carrousel (panorama)

Arc de Tri­om­phe du Car­rousel (panorama)

There is noth­ing very amaz­ing about this panorama and the only rea­son that I post it is the amount of work that went into it. It’s the lit­tle brother of the Arc de Tri­om­phe that lives between the Lou­vre and the Tui­leries. When we were at the place, there were at least three times as many peo­ple there as you can see in this pic­ture. I shot the panorama with a lot of over­lap between pic­tures and was able to remove a lot of the folks in post, as they were mov­ing around. Lots of cut­ting, though, which took its time.

We didn’t visit the Lou­vre on this trip, since had we done so we wouldn’t have had time for much else, but it’s gonna hap­pen one day. It’s only a 3-hour train ride...


DFT Cheat Sheet

Since I have so much to do with the dis­crete Fourier trans­form (DFT) – both recently and not so recently – I always wanted to make a sort of “cheat sheet” about it with the most impor­tant rela­tions of the var­i­ous time and fre­quency dimen­sions and some of the more impor­tant trans­form pairs all on


Ampersand of the Day

Als ich neulich The Inven­tion of Lying sah, ist mir dieses schicke Amper­sand im Abspann aufge­fallen: Die Schrift heißt Wind­sor Light Con­densed, und wird auch gerne von Woody Allen benutzt, wie man hört.


Optical OFDM - Cyclic Prefix

One of the most com­mon mis­un­der­stand­ings about OFDM that keeps com­ing in most dis­cus­sions on the topic is if sub­chan­nels are still orthog­o­nal when there is a cyclic pre­fix involved. But let’s start at the begin­ning... Dis­per­sion We have seen in this post that the DFT can be used at the receiver to demul­ti­plex the


Cross-Channel Fiber Nonlinearities

In a recent dis­cus­sion with Cur­tis Menyuk, Alexei Pilipet­skii, and Chongjin Xie I was made aware of a slightly inex­act state­ment in the JLT pub­lished last year in which I was a co-author. It con­cerned the sep­a­ra­tion of XPM and XPolM in the non­lin­ear phase evo­lu­tion equa­tion. Since we were writ­ing about XPolM at the


Optical OFDM - Spectrum [updated]

We have seen in this post that the DFT spec­trum of a sin­gle OFDM sym­bol is a line spec­trum with one line for each sub­chan­nel $k$ which car­ries the mod­u­lated data $c_{k}$. Within a sin­gle sym­bol there is no spec­tral over­lap, which is the rea­son why OFDM works. What’s also inter­est­ing is the long-time (more


nicht-repräsentative Statistiken

Math­e­matik ist sicher kein Haupt­fach im Jour­nal­is­musstudium. Oder in der Redak­tion von RTL Extra lan­den nur “Jour­nal­is­ten,” die auf­grund ihrer fehlen­den Math­e­matik­fähigkeiten bei richti­gen Nachricht­en­pro­gram­men nicht genom­men wur­den. Ein Beispiel (und nein, ich gehe nicht darauf ein, warum ich RTL Extra geschaut habe): Gestern Abend wur­den die Ergeb­nisse einer nicht-repräsentativen (immer­hin haben sie das erwähnt


YOTOT(MC) goes Hamburg

Let­ztens waren wir zu der Hochzeit einer Schul­fre­undin von Julia nach Ham­burg ein­ge­laden. Und wenn man schon mal quer durch Schla­hand fliegt, dann bleibt man auch gerne mal länger, um sich die Ecken anzuschauen, die man noch nicht kennt. Nunja, zumin­d­est einer von uns bei­den. Und da das gute Wet­ter dieses Jahr schein­bar nördlich der


Optical OFDM - OFDM Basics

This post con­tin­ues the intro­duc­tion to opti­cal OFDM that I started here. In this post, we’ll dis­cuss what an OFDM sym­bol looks like and show, start­ing from the orthog­o­nal­ity con­di­tion, that the dis­crete Fourier trans­form can be used to demul­ti­plex an OFDM chan­nel into its sub­chan­nels. Using the Fourier trans­form, we also take a look


Optical OFDM - Orthogonality

And now for some­thing com­pletely dif­fer­ent... This will be the first of (hope­fully) a series of posts that will be an intro­duc­tion to opti­cal OFDM (or what I have learned in the past half year or so about it). Opti­cal OFDM has been some­what of a hot topic in recent years in the com­mu­nity, but