According to that table, WMAL has slightly worse efficiency than FLAC. Of course, the exact results will depend on the material, but it's not looking good for WMAL.FLAC is not that good although the distance between good and great is very small. My team at Microsoft developed WMA Lossless with the goal of beating all the others in efficiency. You can see that ("WMAL") in this table from HA wiki: https://wiki.hydrogenaud.io/index.php?title=Lossless_comparison
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That extra 1.4% of efficiency cost us in the marketplace as at the time, many CPUs were too slow to decode it in embedded platforms.
This is a bit like getting cream/butter from milk. The first pass will take out most of the fat. What is left over is very little.
Mathematically, I can define a square wave that has a distinct unique value for every time t, no need for a single time t to have multiple values:
F(t) = sign(cos(t))
Consider a transition point (say, t = pi/2). When t = pi/2, my square wave (voltage) is 0. Just before that, it's 1. Just after that, it's -1.
Thus, there are never multiple voltages at the same time. But there is an infinite rate of change, which is impossible in the real world.
Interesting experiment. I just tried it: got 49.7% ratio (FLAC half the size of the original).Upper bound is no compression at all. Try compressing white noise.
It can actually be bigger than the source file due to metadata
Can you link to a paper about the fast integrator?
Thanks. But that misses the last part of my sentence. I like to see @Sergei run his listening tests and post his observation and files. Then we can get somewhere as opposed to a theoretical discussion, or dismissal of the results after the fact because the test files were not this way or that way.
I like the idea.Fair point. With my devil's advicate hat on I'd argue telling you what you're supposed to hear before you hear it would affect what you hear. Is there a way to do a sealed post with the "here's what you should have heard and why" part that can only be opened some time later, or do we just have to trust people not to open spoiler tags in this sort of situation?
Having said that I'm missing how this specific test is relevant. It's an interesting demonstration of a phenomenon I didn't know about, but it's something that can be captured and reproduced by the existing recording/playback chain.
I like the idea.
It demonstrates that the hearing system entangles duration and loudness. The LTI theory doesn't entangle duration and power. Thus, an energy-preserving linear transform valid under the LTI, such as a filter, may not be automatically perceptually faithful.
This was in illustration of the statement that widening an analog "too sharp to represent" pulse by replacing it with a wider "sampling rate friendly" pulse having the same LTI energy, or even the same perceptually accurate energy, may not be faithful because the perceptual timing may be off.
Put differently: construct square wave (A) using 1 MHz bandwidth. Construct square wave (B) using 25 kHz bandwidth. All else equal: frequency, amplitude, phase. We humans can't hear the difference between A and B. At least, I've never seen evidence suggesting this.
The key word in your statement being MAY.
You got it. Precisely. Each of us only MAY get into a car accident on a given day. Still, isn't it wise to wear a seat belt every time anyway?
I view higher sampling rates in a similar light. Most of the time we don't need them to faithfully record music. Yet sometimes we do.
Maybe to capture that once-in-a-lifetime crazy electric guitar solo, the heart-grabbing edginess of which would be smoothed to the point of boredom by a lower sampling rate.
Was it? Didn't someone point out that in terms of sample rate and bandwidth they may simply be hearing audible products of intermodulation in the hardware rather than the format itself..?The fact that some people under ideal conditions can discern 44-16 from higher rate formats was discussed and referenced earlier in this thread.
Could you point me to the part of the paper which talks about a fast integrator working over a time frame of microseconds?That's a good, albeit older, read: https://www.pnas.org/content/100/10/6151.
Please note that the study was done just above the threshold of hearing, so the integration times needed were of the order of milliseconds. At 1000x sound pressures - that is, at normal listening level - they are of the order of microseconds.
In later studies, coefficients of the integration algorithm were refined, yet its formula remained the same.
That doesn't sound right.Interesting experiment. I just tried it: got 49.7% ratio (FLAC half the size of the original).
But that file was at -6 dB, so the top bit of amplitude wasn't used. I made another at digital full scale and it FLAC compressed at 50.2%.
This is waxing hypothetical taken to the extreme.