There are actually two possible definitions for the DFT:
- 1/N, given as "the default" in many sources:
- , known as the "normalized DFT" by some sources: www.dsprelated.com/freebooks/mdft/Normalized_DFT.html, definition which we adopt:
www.threekit.com/blog/gltf-everything-you-need-to-know comparision of several formats
With telescopes however, it is possible. www.quora.com/Can-we-distinguish-individual-stars-in-other-galaxies-or-would-it-be-equivalent-to-say-we-know-there-are-other-forests-of-stars-galaxies-but-we-cant-tell-the-individual-trees-stars-What-is-the-farthest-individual/answer/Jerzy-Micha%C5%82-Pawlak contains an amazing answer that mentions two special cases of the furthest ones:
- gravitational lensing observation
- a star that is far but visible because its light is reflected by a nearby nebulae
But what we can definitely see are globular clusters of galaxies. E.g. the article en.wikipedia.org/wiki/Messier_87 basically gauges the size of galaxies by the number of globular clusters that they contain.
Sample usage by Andy Matuschak (possible coiner): notes.andymatuschak.org/About_these_notes
Previously on EdX: www.edx.org/learn/quantum-physics-mechanics/delft-university-of-technology-topology-in-condensed-matter-tying-quantum-knots "DelftX: Topology in Condensed Matter: Tying Quantum Knots".
But then they regained their sanity and put the source code on GitHub: github.com/topocm/topocm_content and is CC BY-SA.
Proponent of evergreen notes.
He's also curious about quantum computing: quantum.country/ like Ciro Santilli. Some crazy overlaps we get.
Filter graphs are a thing of great beauty. What an amazingly obscure domain-specific language, but which can produce striking results with very little!!!
A quick example from stackoverflow.com/questions/59551013/how-to-generate-stereo-sine-wave-using-ffmpeg-with-different-frequencies-for-eac/77730492#77730492 illustrates some of the fundamentals:
ffplay -autoexit -nodisp -f lavfi -i '
sine=frequency=500[a];
sine=frequency=1000[b];
[a][b]amerge, atrim=end=2
' +--------+
[sine=frequency=500]--->[a]-->| |
| amerge |-->[atrim]-->[output]
[sine=frequency=1000]-->[b]-->| |
+--------+So we see the following syntax patterns:
sine,amergeandatrimare filterssine=frequency=500: the first=says "araguments follow";: separates statements[a],[b]: sets the name of an edge,: creates unnamed edge between filters that have one input and one output
A list of all filters can be obtained ith:and parameters for a single filter can be obtained with:Related question: stackoverflow.com/questions/69251087/in-ffmpeg-command-line-how-to-show-all-filter-settings-and-their-parameters-bef
ffmpeg -filtersffmpeg --help filter=sineTODO dump graph to ASCII art? trac.ffmpeg.org/wiki/FilteringGuide#Visualizingfilters mentions a
-dumpgraph option, but haven't managed to use it yet.Bibliography:
- ffmpeg.org/ffmpeg-filters.html official documentation
- trac.ffmpeg.org/wiki/FilteringGuide some handy tips from the FFMpeg Wiki
Simple sines and variants:
- unix.stackexchange.com/questions/82112/stereo-tone-generator-for-linux/536860#536860
- stackoverflow.com/questions/5109038/linux-sine-wave-audio-generator/57610684#57610684
- superuser.com/questions/724391/how-to-generate-a-sine-wave-with-ffmpeg
- stackoverflow.com/questions/59551013/how-to-generate-stereo-sine-wave-using-ffmpeg-with-different-frequencies-for-eac/77730492#77730492
Video with a solid color:
- 2 second white video:Also add some audio:
ffplay -autoexit -f lavfi -i 'color=white:640x480:d=3,format=rgb24,trim=end=2'TODO how to ffplay the video + audio directly?ffmpeg -lavfi "color=white:640x480:d=3,format=rgb24,trim=end=2[v];sine=f=1000:d=2[a]" -map '[a]' -map '[v]' out.mkv-mapdoes not seem to work unfortunately. - 2 second white followed by 2 second black video:
ffplay -autoexit -f lavfi -i 'color=white:640x480:d=3,format=rgb24,trim=end=2[a];color=black:640x480:d=3,format=rgb24,trim=end=2[b];[a][b]concat=n=2:v=1:a=0' - bibliography:
Display count in seconds on the video:
- black text on white background. Start from 0 and count up to 2:
ffplay -autoexit -f lavfi -i " color=white:480x480:d=3, format=rgb24, drawtext= fontcolor=black: fontsize=600: text='%{eif\:t\:d}': x=(w-text_w)/2: y=(h-text_h)/2 " - count 0 to 2 with one different sine wave per count:
ffmpeg -lavfi " color=white:480x480:d=3, format=rgb24, drawtext= fontcolor=black: fontsize=600: text='%{eif\:t\:d}': x=(w-text_w)/2: y=(h-text_h)/2[v]; sine=f=500:d=1[a1]; sine=f=1000:d=1[a2]; sine=f=2000:d=1[a3]; [a1][a2][a3]concat=n=3:v=0:a=1[a]; " -map '[v]' -map '[a]' count.mkv - bibliography:
Bibliography:
- ffmpeg.org//ffmpeg-filters.html#Video-Sources main section of the documentation listing various video generators
- stackoverflow.com/questions/11640458/how-can-i-generate-a-video-file-directly-from-an-ffmpeg-filter-with-no-actual-in generically asking how to generate the video without an input video
There are unlisted articles, also show them or only show them.