oops ill chosen values. use 16 samples per second for 2 seconds instead.
Add to the list of things you don't understand: Nyquists theorem.
Educational exercise 1: create 128 random Y values uniformly spaced along the X axis. Delete every other one and fourier transform it. Now pad this out to 2x the frequency and inverse fourier transform it. You get 128 Y values with the original spacing. But they are not the same points you started with.
Educational exercise 2: Create a sine wave at 3.14159 oscilations per second. Sample this at 16 samples per second for 1 second. throw away the second half so you have 8 samples. Fourier transform this. First observe there is no peak at 3.1459 hz because there's no discrete frequency there. Now inverse FT this. You dont get the original 16 points.
I don't think you understand non-linearity and how it can mix down a high frequency signal into an audio range. Another thing you dont understand is what happens when a frequencys period is not an integral multiple of the sample rate. In short are smokeless
The greatest time in that articel is spent claiming that 192Khz is overkill because everything above 20Khz is unhearable. He shows how a square looking waveform has all the right spectral components in the 20Khz range and so therefore it it is not missing anything. This is fourier and nyquist type argument that assumes linearity.
as you put it F( a+b) = F(a) + F(b). When this is true then it's as he said. But if F(a+b) != F(a) + F(b) then you need more than 20Khz to describe the spectrum.
I'm not saying 192Khz is the right thing. I'm just say the entire argument in the article is assuming linearity to draw the conclusions that the 0-20Khz spectrum contains all the information you can hear.
In fact we already know that ears are not linear. This is in fact how some compression algorithms function. They know that as it gets loud that you can't hear quieter frequencies as efficiently so they are removed. This is an example that actually works in the opposite direction-- that there's less information needed. However it supports the notion that describing everything by spectral analysis is wrong when things are linear.
You said, well it's just a change of basis. Sort of. How tightly you want to sample has th be determined first. This is what actually sets the bases that the analysis is going to be changing between. A given point spacing in time for a given lenght of time forces the interval over which the fourier transform exists. Conversely if you insist that the highes frequency is 20K (or 40K for nyquist) then you have fixed the time interval of the sampling. You are then blind to any point in the intervals between which is where the non-linear effects could, conceivebly, hide.
Whats this "early" mean?
The whole analysis at the list site assumed fourier spectral analysis, nysquat limits, etc.... Thats assuming linearity in the way they used them.
Apparently this link hasn't been posted enough times yet. It addresses both your first question (partially) and your second question (in huge detail).
The video you're comparing to is being treated no better than audio. It's simply that human eyes are much better than human ears, so to give a comparable experience much higher bitrates are needed for video than audio.
What all these linear analyses assume is that hearing is a linear process. If its non linear then these analyses are incorrect.
I'm sure Samsung is sending in the blade runner for these replicants hackers
Pono music is an ecosystem to sell music in FLAC audio file format: 1) production of FLAC files from existing recordings, 2) a dedicated player, and 3) a web store to sell FLAC files.
The problem with FLAC is how does one get FLAC? you could use your own encoder to record a CD in FLAC. But then you just have CD quality Why not reach back to the studio quality if you are going the FLAC route?. Cause you don't have access to that. But now you do-- the PONO ecosystem does that. And if you wanted to play that FLAC file, well your mp3 player might not play it and if it does it probably has a lot less memory than you would like. soe PONO players are chubbier in memory. And finally what if you are one of those people who likes to roll there own and prefers to just buy it pre recorded. Well agains the PONO ecosystem is there for you.
googly goggly giggly jiggly jingly tingly tinkly dinkly dinkey dinked winked wicked
guggle (flow in an irregular current with a bubbling noise)
burgee (A triangular sailing flag, a show of force by colors)
burker (to murder or supress without leaving evidence)
Interesting idea about the drone however most drones can only fly slowly so it would be hard to match the speed of a airliner.
The plane was carrying a cargo of 400 million dollars in Bitcoin. nuff said.
yes I meant that postscript was the only laser printer macs would accept. in the PC world every laser printer beand spoke a different language to avoid paying the adobe tax. Most printers sold were not postscript. Apple just forced the issue and postscript caught on. NeXT even standardized to Display Postscript.
this is a viewer to control a mac from a chrome book not to control a chromebook from a mac