'Alchemical' Forecasting and High-Frequency Restorative (and Anti-aliasing) Up-Sampling

[BertKoor]

Guitar players have a joke
Q: how many guitars do you need?
A: just one more...

http://www.livingstonintegralstudies.com/ (404 - not found)
https://www.theimplicateorder.com/bohmian-up-sampling
https://deserdi.org/bohmian-up-sampling.html
https://deserdi.xyz/bohmian-up-sampling.html

[Winkie]

Thanks Sir.

[Winkie]

Well, I agree that jumping into the website, as per Bert's observations, was a bit like being dropped out of a helicopter into the middle of the Atlantic. I have tried to follow what suggestions I was able to, although I still haven't annotated the MATLAB code. The code has been largely reconceived and revamped, to the point where I feel like the "boy who cried wolf," but I think the value of the goal is worth looking like an idiot in the short run.

I have discussed, and also discuss in the Intro Page, my psychological issues with looking too directly at the results... it almost seems like the "microphone placed too close to the speaker" phenomenon.

However, that said, on the Bohmian Up-sampling page, the output signal envelope as viewed in Soundcloud seemed, at a quick glance, to closely match the envelope of the input... a necessary (but not sufficient) test of validity, though perhaps worth mentioning.

Again, I thank you guys for the patience you have shown.

[Winkie]

Once again, slight, but substantive changes to the MATLAB code have resulted in an even closer match between Bohmian Up-sampling input and output signal envelopes as they appear in Soundcloud windows.

I should mention that the Soundcloud signal envelopes for restorative up-sampling input 'C' and output 'D' are, I believe, done on LUFS meters, so the close match between the bass-heavy input 'C' and treble-restored output 'D', though not exact, may be similar enough to be statistically unlikely if we were not at least 'on to something.'

As to why I don't just "check the friggin' signals properly," I refer you to the psychological hiccups mentioned in earlier posts...

KVR'ers who were interested and kind enough to donate hard drive space to saving copies of the website and MATLAB files, I thank you. Now would be a good time to refresh your voluntary archive of these files, as changes have been made, and I'm hanging up work on this project for a while.

If anyone cares to carry this work forward, in any regard, they are more than welcome to use the website files... the whole thing may wind up being an unintentional red herring, but that's for the community to decide.

Thanks for your interest and attention.

-Winkie

[Winkie]

Alchemy reportedly involves recursive (and somewhat messy) operations, as the Microcosmic realm of thought is purified and brought into alignment with the "Idea," or pure Platonic Form, as it exists "in the ethers" of the Macrocosmic realm.

If we have finally brought our Vision of Fourier Forecasting and Recursive Up-Sampling to fruition, that has certainly been the case. We wandered so far afield into realms of unnecessary complexity in trying to make the Vision manifest, but each step seemed to be leading someplace vital and potentially important. Finally, after much thought combined with meditation and attentiveness to what seemed Macrocosmic "signals," both from human and non-human realms, the Visions coalesced into much simpler forms than we had been considering.

The website has changed somewhat, in line with suggestions from Forum Members, while still having MATLAB files which reflect the Vision's current embodiment, as well as sound clips which demonstrate inputs and outputs from the MATLAB code. URL remains: https://deserdi.xyz

Thanks for working with me on this, and your tremendous patience with me.
- Winkie

[Winkie]

In the website, I couch myself as a modestly educated guess and check technician, rather than as a bonified Bohmian (or Holographic) theorist. My meager education qualifies me uniquely to have an open, dreamy mind with regards to what may be possible in the realm in physics and information processing/theory.

A few more rotations of the guess-and-check grindstone, informed by an intuitive hunch back-checked with what mathematical rigor I can manage, may have led us to a watershed moment worth mentioning. I won't yet throw up my arms and shout "Eureka!! Alchemical DSP Gold!!" without first hearing from the community.

The alchemical concepts of microcosm and macrocosm, in just one regard among many, provide a kind of peer-review that stabilizes the potential vacillations of the individual mind. As with the scientist John Lilly experimenting with hallucinogens and isolation tanks, and portrayed by William Hurt in the movie "Altered States," ballast for the potential instability of an isolated mind is found in community, in this case embodied my Lilly's wife.

The current results on the website, I have a hunch, may be "juicy," and I encourage those new and old to this discussion to revisit past posts to get a better, or renewed, understanding of some of the weirdness I have had to adopt in service of this "mission."

[BertKoor]

One of the laws in data/information processing technology states that the bandwidth or entropy of a signal cannot be extended.

I've listened to the samples, the results sound much worse than some months ago. Not much progress, we call that regression.

You write about aliasing, but there is no indication (let alone proof) that the downsampled signal contains any.

[Winkie]

Thanks to Bert for his honest, yet hard-edged feedback... you can't expect communication on the internet to be all wine and roses, and I'm grateful for what feedback I can get.

Bert's comments along with some other considerations, led me to the idea that, in order to simulate, using the DFT, certain Fourier transform properties, like the correspondence between frequency-domain dilation and time-domain contraction for purely-real time signals, one must 'open-up' the DFT at the half-way point, dispense (temporarily) with the redundant information in the upper-half of the DFT, perform necessary operations, and then 'close' the frequency-domain DFT up again to (taking the inverse DFT) yield the expected 'real' output.

The discussion on the Fourier Forecasting page of https://deserdi.xyz contains a new, more in-depth discussion of where responding to Bert's comments has brought us, along with new sound clips. MATLAB code on last page has been updated, too.

I continue to put my results 'out there' without more than an oblique (necessary but not sufficient) look at the output data to ensure that this remains a communal effort, with the psychic 'safety net' that provides. I appreciate you KVR's indulgence of me eccentricities.

Cheers...
Winkie

[Aleksey Vaneev]

Using "pattern recognition" or "AI" you can fill the gaps in the extended spectrum as much as you want. But virtual reality is not a reality. You can find restored old films on YouTube that not only try to recover color, they also fit sound to the picture.

[Winkie]

I've cried 'wolf,' or in this case, 'alchemy' so many times on this forum that I would not be surprised to have lost 95% of interested parties. Nevertheless, I felt I should report on the last six months' happenings. With regards to band-limited forecasting, the current version of the code uses the negative phantom signal of zeroed out frequencies, which appears wherever the time domain signal would otherwise have been null, combined with a simplified deconvolution technique, along with a few other little 'sleeve-tricks,' in the attempt to accomplish effective forecasting.

Further, this forecasting algorithm is used in a restorative up sampling (RUP) algorithm, wherein the original (N) signal values are laid out on the unit-circle of the complex-plane, coupled with their time-reversal representation, such that the IDFT of the combination is purely real. This IDFT is then forecast out to double length before taking the only real portion of its DFT (actually just to clean up some tiny imaginary remnants), from which the first (2N-1) signal points are harvested.

I don't have an exact feel if I may be on to something, but on the Soundcloud level-meter, and after all these convoluted steps where I could have screwed up royal, the level-image for a (16x) under-sampled signal is a near exact match with that same under-sampled signal after it has had its sampling frequency doubled three times with the restorative up-sampling algorithm. We would expect some minor differences, of course, but by and large they match.

I am looking to the community to evaluate this work, as looking too closely myself at the results has been like placing a microphone too close to the amplifier speaker, at least in my psyche. "Necessary, but not sufficient" tests have been all I can stomach and use to guide me, at least without a community to provide the buffer of communication.

Band-limited forecasting algorithms already exist in the peer-reviewed literature, and deconvolution was first used for forecasting in WWII, so I don't know why I have a bug up my butt concerning the recapitulation of this previous work, maybe because it could have the potential to add credence to the other writings on the website.

Again, the website is https://deserdi.xyz and thanks for your patience.
-Winkie

[Winkie]

Had an error in the MATLAB code concerning time-reversal and corresponding frequency-reversal in the DFT-domain. I had used a straight {fliplr} command rather than taking pains to leave the DC-spectral component where it belongs. Don't know if this made a substantive difference in the sound of the outputs, but the sound files and posted MATLAB code were updated mid-afternoon on Dec. 5 (MST).

[Winkie]

Well one, hopefully, final change was made to the MATLAB code for the Fourier Forecasting, Restorative Up-sampling, and newly minted Quantization Error and Artifact Reduction (noise reduction) algorithms - I invite you to check out the sound files. We also documented our MATLAB code, the lack of which had been criticized, and was sorely overdue. Apologies for taking so long in accomplishing this, maybe my troubleshooting would have been easier had I taken the time to document the code sooner.

As I have stated before, there seems to be some kind of positive quantum feedback loop concerning my awareness and the checking of the posted results (sound files) without the buffer of community. Therefore, for a final check I am relying on any communal interest there may be to provide a kind of make-shift peer-review, and dilute the impact of either success or failure on my psyche. This may seem weird, I know, but it's just how I have to operate for now.

Thanks,
Winkie
https://www.deserdi.xyz

[Winkie]

As reported on a couple other forums, this first part of February 2023 has served as a kind of "soft-opening" in which www.deserdi.xyz has been able to get some etheric feedback and iron out some kinks. We can only imagine the reader's frustration at our unwillingness to look directly into the mirror of our results and either confirm and report, or shut-up and continue refining our work in internet silence.

Again "necessary but not sufficient" checks of results have been used to refine our work to the utmost of tolerance for anxiety, but a final direct look into the narcissistic mirror of absolute failure or success seems unwise without a community to buffer the shock, either way. I hope a community like KVR Audio might be sensitive and receptive to both the inner-workings and potential contributions of a "gentleman amateur" who only has a B.S. in electrical engineering.

Cheers to you and your community.
-Winkie

[BertKoor]

I understand you're asking for honest feedback. Here you go.

I listened to the Fourier Forecasting example. What's with the high frequency bursts at the start and end? You get excellent results by just looping that piece of audio. No mumbo-jumbo alchemical processing is needed.

I listened to the Restorative Upsampling example. In my humble opinion nothing got really restored. I hear distortion-like noise (4-8kHz) that was not there, but also should not be there. It only distracts. It sounds like the result of sampling rate reduction done badly (without the necessary filtering above Nyquist)

I also listened to the Noise Reduction example. In my humble opinion the noise did not get reduced. High frequencies were cut off, throwing away the baby with the bath water. I'm not hearing Bono anymore, while I clearly could in the unprocessed file. What's left is the sound of the ocean, which is basically just noise. So the signal-noise ratio shifted in the wrong direction.

Then I read some text fragments. I have sincere doubts whether your understanding of things like quantization error and aliasing are the same as what the rest of the world thinks these are.

For you it's a nice and harmless way to waste time, like all of us do with our hobbies. But the results are not ground breaking or impressive.

[hugoderwolf]

I'm not really sure what you want to hear. It sounds as if you know deep inside that your research is going nowhere. And quickly judging from the sound examples and randomly skimming the text, that is very likely the case. Even adjusting for a vague probability that you might be "on to something", it is at the very least far too early to present sound examples. Especially should you - maybe - expect people on the internet to engage with your concepts and code on a less superficial level and e.g. help you figure out why your code obviously doesn't do what you would like it to do.

If you strip away the sound examples and keep the pseudoscientific text, then sell some box that just does nothing to audiophiles, you might be able to make a nice buck out of all that work though.