New Sampling Techniques Make Up For Lost Data 162
An unnamed reader writes: "Professors at Vanderbilt and the University of Connneticut have published a non-uniform sampling theory that could yield better quality digital signals than the standard Uniform sampling techniques pioneered by Shannon at Bell Labs.
The Vanderbilt press release and link to the published paper can be found here."
So.... (Score:1, Insightful)
Re:So.... (Score:5, Informative)
As the abstract says
"The new theory, however, handles situations where the sampling is non-uniform and the signal is not band-limited."
So it isn't applicable to digital music (as this is band-limited by our hearing, and we can pick the sampling interval) but other signals that cannot be sampled well by regular sampling (either in time or in space). Examples given are seismic surveys and MRI scans. But you knew this as you'd have taken the time to read the linked article first, wouldn't you?
Re:So.... (Score:1)
Re:So.... (Score:2)
Re:So.... (Score:1)
As an alternative, I could say that the music will usually be between 0 Hz and 10KHz. Now my sampling rate is cut in half, and if I'm wrong, I can iteratively adjust upward to recover the higher frequency information (if I'm understanding the basics of the paper correctly). This seems attractive to me, at least. Obviously it's too late to change the CD or DVD standards, but maybe some new music format for 3G cell phones, for instance?
Or am I misunderstanding something here?
adéu,
Mateu
Re:So.... (Score:2)
A low-frequency note is shaped by high-frequency components. If a difference in shape of the lower-frequency can somehow be detected, then inaudible frequences still make a difference.
Normal telephone IIRC cuts off about 3.5kHz.
Brain scans? (Score:1)
Okay
Re:Brain scans? (Score:5, Insightful)
BTW, sampling doesn't mean that you're guessing. The sampled data points are the actual measured values of the signal at specified points in time or space. You have to sample because there is no way that you could collect all values for the signal for all points in time or space, and there is usually a sampling rate at which point you're collecting more data than you need to accurately represent the signal.
Re:Brain scans? (Score:2, Informative)
First ... (Score:1)
Not that ground-breaking... (Score:1, Interesting)
Re:Not that ground-breaking... (Score:1)
old news! (Score:1)
New data compression or is it too inaccurate? (Score:1)
Well.. one thing's for sure, if I ever have a doctor reading my brain MRI I sure as hell don't want half of it removed (neither my brain, nor the scan).
Re:New data compression or is it too inaccurate? (Score:1)
Are you even familiar with how JPEG works? It's already half-detail, half-math... JPEG images involve a significant amount of math and statistical trickery (in throwing away data). However, all the math used in standard signal processing (image and audio compression fall in this category) make the basic assumption that the signal is sampled at a uniform rate... a lot of the current techniques wouldn't apply without tweaking...
Fractal compression is pure math (Score:4, Informative)
Along your point, there's actually a technique that uses the self similarity of images to help you compress themselves. For example, you might have seen the "Sierpinsky Triangle." [rice.edu] You can generate this image with a few very simple recursive move/resize/draw operations.
Fractal compression uses this technique on abstract images. It aims to find a set of operations (sometimes very large) to generate any given input picture. It's very cool, and you can get more information (including example pictures) at this page. [rasip.fer.hr]
The "state of the art" of fractal compression beats JPEG compression at some compression ratios, but looses at others. It's also interesting that a fractally-compressed image has no implicit size (ie: 640x460), so it enlarges MUCH better than simple image enlargement.
Re:Fractal compression is pure math (Score:2, Interesting)
One main problem has been that no one has found an efficient way to create the PIFS functions for an arbitrary image. So fractal compression can take a long time and is non-deterministic (i.e. you can't tell ahead of time how long it will take).
Another problem is that Barnsley et al. hold patents on many of the techniques used. Until its performance makes it a clear winner, why pay royalties.
It's been a couple of years since I paid close attention fo fractal compression, but I haven't heard of anything that changes the above problems.
Some useful niche applications (Score:5, Insightful)
What's the practicality of this? Well, spiral MRIs [umd.edu], for example, where for mechanical reasons you don't want to have to stop-and-start the very heavy "scanner", wasting time and jarring sensitive equipment. As I said, niche applications.
As for compressing audio, there are already plenty of other psychoacoustic compression schemes -- whether non-uniform sampling is better or worse will likely depend on the application.
Re:Some useful niche applications (Score:2, Informative)
And, I'm still trying to figure out by what you mean by non-square pixels. Are you trying to say the physical size on the screen, or how they are stored in memory on the graphics adaptor?
If these guys have the ability to return useful data from non reporting areas I can see a whole range of non niche applications - and real word applications where data recovery would be useful.
Re:Some useful niche applications (Score:3, Informative)
Re:Some useful niche applications (Score:1)
Re:Some useful niche applications (Score:2)
Hmm... you're right. The "spiral" in Spiral MRI evidently refers [wisc.edu] to frequency/amplitude space rather than physical space.
Re:Some useful niche applications (Score:2)
PAL DV has pixels slightly taller than square, and NTSC DV has pixels slightly shorter than square. It makes editing on a square-pixel PC monitor a bit wierd, because the images look stretched or squashed.
I had to recode an NTSC DV tape for PAL once, which was a total PITA. Different frame rate, different resolution, horrible smeary colour... Never again.
A Pixel Is Not A Little Square (Score:2, Informative)
Here's a good paper on why it's important to keep in mind the true nature of pixels (by Alvy Ray Smith):
A Pixel Is Not A Little Square, A Pixel Is Not A Little Square, A Pixel Is Not A Little Square! (And a Voxel is Not a Little Cube) [alvyray.com]
Nyquist, not Shannon (Score:5, Informative)
Nyquist conjectured it; Shannon proved it (Score:1)
the guy who developed the Uniform Sampling Theorem [wolfram.com] was Nyquist, not Shannon.
Nyquist conjectured it in 1928; Shannon proved it in 1949 [efunda.com]. Many texts split the credit, calling it the "Nyquist-Shannon sampling theorem."
Re:Nyquist, not Shannon (Score:2, Redundant)
Both are right: (Score:5, Informative)
Re:Both are right: (Score:1)
As a CpE (or ECE, or Comp. Eng.) this screws up... (Score:1)
Anybody understand what's new? (Score:3, Interesting)
In fact, you're not limited by the Nyquist frequency when you are sampling non-uniformly, so it has some strengths in that respect. However, it has to be more to it than this for it to be news. Can anybody who understands this better than I provide any insights?
Re:Anybody understand what's new? (Score:1)
So this is a classical expansion on the variable bit rate sampling as is done on MP3 files now. The only difference is that this is done on bitmap files in place of sound files.
Not like Variable bit-rate (Score:2, Informative)
alter the amount of time between each sample. In
terms of sampling frequency MP3, even VBR is still
uniform, uniform as in time. VBR changes how many
bits are in a sample, not the time between samples.
Re:Anybody understand what's new? (Score:2)
Variable bit-rate, if I have understood it correctly, is about say that you have a period in the sound file that is very quiet, then you don't need many bits to represent it well. Therefore, you don't use many bits per sample, and you save some space.
You still sample regularily, for example, if you sample with a 44.1 kHz sampling frequency, then you take a sample every 0.023 milliseconds, exactly.
This stuff is different. Instead of taking a sample with exactly the same interval, you sample at random, or you sample every now and then. The number of bits you have for each sample is a completely different matter, that may or may not be variable.
The funny thing is that you can actually use this to reconstruct the signal much better in many cases, which is pretty counterintuitive when you think about it! (until you've thought much about it, because then it makes a lot of sense... :-) )
Re:Anybody understand what's new? (Score:2)
We have a lot of powerful tools (such as Fourier transforms) for analizing precisely sampled data. For example sound is often sampled at a precise frequency - about 44khz.
The problem is that sometimes the data available isn't spaced regularly. This makes most analysis techniques throw fits. He's come up with tools to ues here that do a good job of taking irregular data and returning a very good estimation of the values everywhere.
If you're familiar with Fourier transforms, this is a more generalized version.
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Re:Anybody understand what's new? (Score:2)
I'm not an expert in the field, so I just did a google search [google.com], and as far as I can tell, all of the first 30 links state uniform sample spacing and/or specificlly say that irregular sample spacing is a problem.
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Re:Anybody understand what's new? (Score:2)
Anyway, try a better search [google.com].
But of course, it depends on what you mean by "problem".
medical imaging and compression? (Score:4, Interesting)
We found that jpeg compression of images made medical diagnosis unreliable. Hairline fractures in x-rays are exactly the kind of small details that tend to get washed away in 'lossy' compression, and the banding caused can lead to false assumptions as well.
The article suggests that this is still a lossy compression with small amounts of data loss. I know Doctors that would take that admission as a condemnation of the technique.
Re:medical imaging and compression? (Score:1)
From what I read, the paper does not represent a compression technique, but a better way to fill in the missing data between samples, especially when the samples are nonuniform, or samples are missing. This would allow you to remove data for storage/transport and recover a similar image later, or as it would probably be used with medical imaging, to recover data lost during the imaging process due to sampling and quantizing error. In the second case, the fracture shouldn't be lost if done correctly.
Re:medical imaging and compression? (Score:2)
Nope. Re-read the article. It's not a compression scheme. If anything, it's the reverse, and expansion scheme. It takes all the available data and does a good job of filling in the gaps. It even works when the available data isn't arranged nice and neatly.
Used in the right context it would make things like hairline fractures MORE visible. You wouldn't usually use it in video teleconferencing though.
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new 1000:1 compression scheme (Score:3, Funny)
Hereby I donate the following algorithm to the public. It's called GNU-squat.
Step 1:
Non-uniformly sample your favorite music using just 1 bit. This will ofcourse take up at least 8 bits on your harddisk but let's not nitpick. The good part is you don't even need special hardware to sample the music, just enter if the music is loud (1) or soft (0).
Step 2:
Use the Vanderbilt mathematical routines to extrapolate the rest of the data, and presto: the complete song re-appears from just one bit of data.
Re:new 1000:1 compression scheme (Score:2, Funny)
ah, there is the problem (Score:5, Funny)
I noticed that too. Potential downsides? (Score:1)
However, in some other image settings this might not be the case. For example, where there are a lot of linear-dimensioned information that tends to go by the same grain as the pixels.
They might be pulling some wool over our eyes by picking samples that minimize the downsides of their algorithms.
Perhaps they should focus on esthetics improvement, such as music and clipart and not on domains where you can get your ess sued off if somebody dies from a misleading image.
(troll mode on)
This kind of reminds me of the OOP books which tend to show change patterns that OOP seems to benefit, but completely ignores change patterns which tend to get messy under OOP.
(troll mode off)
Some folks seem to be missing the point on the MRI (Score:5, Informative)
Re:Some folks seem to be missing the point on the (Score:1)
However, I suspect their point is that they can reconstruct the original at all with non-uniform sampling. This is useful in cases when it is not feasible to obtain fixed samples.
Re:Some folks seem to be missing the point on the (Score:1)
48kHz 24 bit is all you need to generate a perfect reproduction of audio as far as the human ear is concerned. These days, audio in the pre-amplified stage is about as good as it's going to get, because it's already as good as the human ear.
Non-uniform sampling, if it really improves matters (which I doubt in the case of audio), can't improve on what's already perfect.
Just to emphasise: by perfect I mean the theory says that none of the distortions generated are even close to what a human ear can hear. This is also true in practice.
Re:Some folks seem to be missing the point on the (Score:2)
Non-skipping CD players.
De-scratching old LP records.
Reconstructing old photographs.
near-perfect zooming (Score:1, Interesting)
On a side note, you could apply random color-relative noise on to the entire zoomed image before you save the random parts, then it might pick up the slack of the algorithm placing the same bordering colors over the unknown pixels.
If they consider digital music captured with this set of algorithms near-perfect, then near-perfect zooming is just around the corner.
PhotoCD/ FlashPix does that (Score:2)
PhotoCD works with a differential 'error' image that was created by comparing the resampled to the original, and then that was compressed. Effect? Take a small image, blow it up by a factor of 2x, apply this itty bitty 'error' transform, and you have a nearly perfect 'fixed' image for the cost of some small change on disk space
Then there is the 'much better clarity' etc statement- there's 'inverse point transform' for getting out defects.. they used that on the Hubble Telescope. Looked pretty good for being wildly out of focus.
Everything you've mentioned is already available... the technique looks interesting but it's all data dependent
gives you an answer, not necessarily the right one (Score:2, Interesting)
There are already many other methods for reconstructing functions from sparse, non-uniformly sampled data, so this paper doesn't solve an unsolved problem. Rather, it provides one more solution under a set of assumptions that are mathematically a bit more like those of the original sampling theorem.
Will it be useful? That's hard to tell at this point. I think it will take a lot more work to figure out whether this method is any better than existing methods on real-world problems, whether its application can be justified in real problems, and whether it leads to algorithms that are practical. It may also turn out that the method is closely related to methods already in use in other fields; for example, the kinds of function spaces they study have received some attention in neural networks, but the authors cite no papers from that work and may not be aware of it.
Time vs. Frequency (Score:5, Informative)
This is not quite accurate. The original signal is not "required" to be band-limited. Rather, it is accepted that frequencies outside of your design bandwidth will not be captured. The signal can stray outside of the "defined limits", but should it do so that information will be lost. Furthermore, Fourier's math tells us that a signal that is limited in time is unlimited in frequency, and a signal that is limited in frequency is unlimited in time. This has important ramifications. The biggest - and most obvious - is that all man-made signals are limited in time and therefore unlimited in frequency. Ergo there will ALWAYS be information lost no matter what bandwidth you design for.
Now to read the rest of the article - it sounds intriguing...
Re:Time vs. Frequency (Score:2)
The original signal is not "required" to be band-limited. Rather, it is accepted that frequencies outside of your design bandwidth will not be captured.
Well, that's not entirely accurate either. The presence of frequencies outside of the design bandwidth will lead to aliasing. The reconstructed signal will have additional low-frequency energy that should not be there.
In practice, we often use analog "anti-aliasing" lowpass filters to band-limit the signal before sampling.
Re:Time vs. Frequency (Score:3, Informative)
But I think you misunderstood the "band limited" thing.
When you sample you have to the filter out frequencies above the Nyquist-freq., if you want to avoid aliasing-problems.
Aliasing comes from the mirroring of the spectrum around n*Fsample. So if you don't want your original signal to get distorted when sampling, one have to use an anti-aliasing filter, that "band-limits" the signal to below Fsample/2.
Does this new technique mean, you can skip anti-aliasing filters?
Re:Time vs. Frequency (Score:2)
I'm not sure if this is new at all. Some digital scopes will attempt to hit higher effective bandwidths by shifting the time of starting sampling at each sweep, so as to fill in between the dots of the first sweep. This only works if the signal you are measuring is absolutely regular, and the triggering (detection of the start point in the signal) is perfect...
Re:Time vs. Frequency (Score:2, Interesting)
Two of the other replies point out that this isn't quite right - the frequencies outside of nyquist just alias. However, this can actually be used to your advantage if you know that a signal lies within a narrow band of frequencies centered around a high frequency.
For example, you can perfectly sample a signal confined to 1.0-1.1MHz using a sampling rate of just 200kHz, instead of 2.2MHz. What's even more interesting is that you can play this 200kHz sample back and get the same signal in the 1.0-1.1MHz band you had originally, but along with aliases all over the rest of the spectrum. In this case, you need bandpass anti-aliasing filters and not lowpass bandlimiting ones.
Nothing new here. (Score:2, Insightful)
News article was, as usual, totally lacking in technical details. But they did link to technical articles at the bottom of the story.
NON-UNIFORM SAMPLING AND RECONSTRUCTION IN SHIFT-INVARIANT SPACES.
I skimmed the technical article (heavy math alert), and the results seem to be along the lines that: given an irregular (and possibly noisy) sample of data, reconstruct a
function that gives smoothed (continuous, not discrete) approximation for entire data set.
There is some nice mathematics that make it suitable for such purposes. The algorithms are selected to limit number of terms and guarantee convergance, and are computationally efficient. If you think of it as fancy interpolation, you are not far off the mark from what I saw.
This is not to disparage the efforts here (it looks to be quite useful in several domains), but it is a technique for generate a smooth, continuous function to represent a set of non-uniform samples. It cannot magically find missing results not were not evident in the limited sample data.
The author
Ah, good! (Score:1)
Some Clarifications (Score:3, Interesting)
This, my friends, is complete nonsense. You cannot zoom in on an image and accurately reconstruct further details. To imply that this is possible is to imply that you can add accurately representative data where there was none before.
As for "zooming technology" it is possible to better reconstruct a zoomed-in image, though not any more accurately. For example, when I go into MS Paint and zoom in, it simply blows up all the pixels as larger blocks. This clearly is not good. You could create some kind of algorithm to determine the "shapes" of sharp edges, as well as where gradients where, and scale those up when zooming in...for example, small a circle can be composed of four pixels -- such a technology would scale this up, not as four very large blocks, but as a circle.
But this involves assumptions about what the original pattern was representative of? Was it representative of a circle, or of four large blocks seen from a distance? So you're not really adding data, but just attempting to "zoom in" on an image "better" based on a set of good assumptions which generally work.
Such a thing could be accomplished. Indeed, it already has been accomplished -- in us. When we look at a small photograph and want to draw a poster from it, we don't draw a large, blocky, pixelated image. We are able to tell what things -- such as frecles -- are details to be scaled up in our drawing; what things are gradients -- such as a dark to light gradient going from the near to the far side of a forehead -- to be scaled up and gradiated; and what are sharp borders, to kept sharp -- such as the sides of one's face.
However, even this amazing system we have of reconstructing larger images from smaller one's cannot add detail where there is none. If a woman is freckled with tiny freckles, they won't be visible from 10 feet away; a picture taken from that distance won't show them, and if we wanted to make a portrait of her head based on that picture, we wouldn't know to add freckles.
Maybe this should be combined... (Score:1)
If you use a classic technique like interpolation through splines, diff the images and remove the gross errors created by this new method, the result might be quite convincing.
Short on any real details... boo! (Score:1)
How will a "new and improved" method of sampling help me hear audio I can't hear anyways?
Nyquist proved that with uniform sampling at 2/T you will lose no spectral information between DC and 1/T.
Somehow I think this is more "Magic Ph.D" material than real science.
Tom
Re:Short on any real details... boo! (Score:1)
Now, 44.1 KHz / 16-bit is just fine for me, but I can at least consider the idea that there are things happening in the frequencies above 22.05 KHz (the top frequency 44.1 can record) that have some affect on us even if we can't consciously hear them. Well, fine, but I'm not going to record everything at 96 KHz and increase all my audio file sizes to 218% of their current size just so that SuperAudioFileMan can hear the dog whistle in the background. But if I can get a variable sampling scheme that will grab some extra frequencies when the source material's spectral content warrants it, and maybe even sample below 44.1 when the tympani solo comes along, that works for me and is at least an improvement for the hypertreble freaks.
Re:Short on any real details... boo! (Score:2, Interesting)
CD's sampled at 44khz miss some of these sounds and that is what audiophiles complain about when they say digital audio sounds flat.
Re:Short on any real details... boo! (Score:1)
Re:Short on any real details... boo! (Score:3, Insightful)
If you are sampling audio at 44100 Hz, then an 8000 Hz tone will only be sampled at about 5 spots in its cycle. Although the frequency information of that 8000 Hz tone is retained, the actual waveform is lost. Exactly what the reconstructed waveform will look like is up to the DAC.
Whether the human ear can hear the difference at higher sampling rates is another question, however.
Re:Short on any real details... boo! (Score:2)
The point is, the Nyquist rate tells you the highest spectral component that can be sampled without aliasing. But a triangular wave has frequency components higher than this threshold. These components will be lost in the sampling, and the waveform will not be preserved, although its spectrum will be -- up to the Nyquist rate.
Re:Short on any real details... boo! (Score:1)
Despite what they think if your source is of low quality no amount of math will increase the accuracy/resolution. You can only make it more visually appealing.
Well are there any papers to read on the subject online? Anyone have citeceer links they want to lend me?
Tom
Varying audio sample rates (Score:4, Interesting)
Re:Varying audio sample rates (Score:1)
Re:Varying audio sample rates (Score:1)
interesting idea. The reason that we use 44kHz as the standard sampling rate is that most people's hearing ferequency cutoff is at about 20kHz, and hence the Nyquist sampling theorem shows that we need to sample at 40kHz. add a little bit to account for the fact that anti-aliasing filters aren't infinitely steep and we get 44kHz. So the real question is, in music are there blocks in which the highest frequency is below 20kHz? Then ask whether the reduced quantization brought by using higher sample sizes audible?
and audiophiles care to comment?
Re:Varying audio sample rates (Score:1)
While decreasing the sample rate would give you some savings, if you tried to get a smaller file size than an MP3, your maximum frequency response would probably be less than 3000Hz.
Re:Varying audio sample rates (Score:2, Informative)
That's not true. The whole point is that if a signal is sampled at frequency f, then it can be reconstructed perfectly if its bandwidth is less than f/2. Go learn the maths [berkeley.edu] instead of making vague statements that you think must be right intuitively, but which you actually don't know about.
Re:Varying audio sample rates (Score:1)
And my point about resampling vs. MP3 still stands, regardless.
Re:Varying audio sample rates (Score:2)
now if you sample it at frequency 2, you will get a great reconstruction if you sample at time 0.25 and 0.75. However, you will get a much worse reconstruction if you sample at time 0 and 0.5. The phase interaction between the samples and the signal become more noticiable the closer the signal is to the nyquist frequency.
Now I think you owe the previous poster an apology. A little humilty wouldn't be out of place.
Re:Varying audio sample rates (Score:2)
For an extreme example, consider a 21.9KHz tone that only goes for 1 cycle. The sample received may be to points at the top and bottom, in which case reconstruction will be pretty close. Or it may be two points at (almost) the zero crossing, so it appears that there is almost no sound.
Re:Varying audio sample rates (Score:3, Informative)
Regarding 16 bit vs 24 bit "samples", note that there's a difference between sampling accuracy and the number of bits to store your quantized samples. The two are only the same if you're using linear quantization and thus, for example, storing your 24-bit accuracy sample "itself" (i.e. linearly quantized into 2**24 discrete steps). Linear quantization is rather wasteful as the human hearing system does not have equal discrimination at all volume levels, so you might want to quantize more roughly at higher volume levels something like this:
(0) (1) (2)
So you could sample at 24 bits to capture additional detail at low volume and yet non-linearly quantize to store your samples in 16 bits wihtout losing that detail.
Re:Varying audio sample rates (Score:1, Interesting)
Re:Varying audio sample rates (Score:3, Insightful)
This is why ADCs do not just sample the incoming voltage -- they integrate over a period of time, to "boil down" the voltage over that time period to an average value, that best represents what the signal was doing during that sampling period.
Now, moving on to your point, which is to vary the sampling rate according to the characteristics of the source; this is somewhat a wasted effort, since in order to determine the source characteristics, you must perform some type of frequency analysis, or autoregression. This is intensive computation, and you would be better off spending that time doing some real compression, such as spectral quantization, or perceptual coding.
Varying the sampling rate from sample-to-sample would be the ultimate, if it were possible to gain anything from it. Unfortunately, if you vary the sampling rate at each sample, then in order to transmit the sampled stream you must transmit not only the samples, but the duration between samples as well. In the worst case you have doubled your data rate, not compressed it.
However, as you say, this could work wonders for the fidelity of the sampled signal. Instead of sampling at regular time intervals, we could build a predictive ADC that samples only when the predicted signal value becomes different from the actual by some predetermined amount. Then, send two values: the sample itself, and the duration since the last sample. This works because the DAC which converts the signal also does interpolation. It would be possible to keep the error arbitrarily small, no matter what the characteristics of the signal, up to the limits of the ADC chip itself.
Re:Varying audio sample rates (Score:2)
No, no, no. A sample is an instantanuous value, not an integration. The reason why sampling is not sensitive to very short (compared to sampling frequency) is that there is normally a (anti-aliasing) low-pass filter before the sampling operation.
As for transmitting the value and "time it stays the same", I'd suggest you first get more familiar with the sampling theory before innovating...
Re:Varying audio sample rates (Score:2)
I wasn't talking about "the time the signal stays the same," I was talking about the time period over which the prediction error reaches some threshold value. For example if I am using a first-order linear predictor for digital-to-analog conversion, and the signal changes linearly from 0 to 1 over a period of 1 second, then I only have to send two samples during that one second period in order to completely describe the behavior of the signal.
Re:Varying audio sample rates (Score:2)
As for using a "first-order linear predictor for digital-to-analog conversion", the cost/complexity of building a good analog linear predictor would far exceed any gain you'd otherwise have...
Re:Varying audio sample rates (Score:2)
Re:Varying audio sample rates (Score:2)
A sampled signal is represented by equally-spaces impulses (delta) of various amplitudes, which is the same as multiplying the low-passed signal by an impulse train.
Re:Varying audio sample rates (Score:2)
Also 16 bits is quite enough, although not very well used. Nowadays most CDs are published with high average volume to have sort of an upper hand in broadcasts (check classic music titles for comparison), a better approach is maintaining only the peaks of music near to highest representable number, the high-average volume approach severly limits dynamic range. 65535 different volume steps is quite enough for human ear, you are not supposed to hear any difference beyond that for processed music (for raw recordings, it is better to have higher resolution.)
Re:Varying audio sample rates (Score:1)
Hey! I know that guy... (Score:1)
Choosing the perfect sampling method (Score:2, Interesting)
Integrating a function f(x) from a to b means measuring the area below the graph. So the first estimation would be to split the interval from a to b into equidistant parts and sum up the area of the rectangles below or over the graph (that would be about f(x_n)*h, where h is the width). This method is called Riemann-Sums or iterated Trapezodial-Rule.
But you could also try to plot piece-wise polynomials through these equidistant points and calculate the areas below. This would yield better (order) results; these methods are then called iterated simpsons or millne rules. But if you go higher than polynomials of 4th degree, you will get to methods that could compute negative integrals of positive functions, which does not make sense. The reason is that high order polynomials tend to "oszillate" or "run out of bonds" at the end of the intervals. Thus these "Newton-Cotes" methods of equidistant sampling points are of limited capabilites...
But if you drop the assumption that you need to take equidistant (uniform) sampling points, you will get to far better methods: With Gaussian Quadratures the sampling points are far more dense at start and end of the intervals and thus the interpolating polynomials yield far better order results!
Thus if you know what you are going to use your data for, then you can always find better sampling methods to optimize for your needs- IMO it really doesn't make sense to simply sample the voltage of the signal at equidistant time frames when trying to digitally represent sound! Where as "lossy compressions" like ogg or mp3 drop information that is less interesting, this equidistant 44kHz sampling just drops anything that does not fit into this sampling; it's kind of a "brute-force" method. And if you then compress to ogg or mp3 it's the same problem like why you should never convert mp3s to ogg... It can (and will) only get worse.
If you are interested in that quadrature methods then read "Numerical Analysis" by "Kendall E. Atkinson" Chapter 5.
Re:Choosing the perfect sampling method (Score:1)
but unless you first oversample and then selectively reduce the sample rate you do not know which are the "detailed" parts, which warrant a higher sampling frequency and which aren't. Secondly, since you refer to music, human hearing is bandlimited anyhow, so there is no point reconstructing freequencies outside of our perceptual range.
Is it just me... (Score:2, Insightful)
They then remove 50% of the data in the second picture, and proceed to mathematically reconstruct it in the third. In my mind, this would be a great feat, except for two things:
- More than 50% of the data was unnecessary to present the data in the first place. The original is quite obviously scaled up from its native size.
- The mathematical reconstruction introduces artifacts that were not even present in the random image, such as huge horizontal pixel smears.
Can someone point to a better demo of this set of algorithms?
Justin
nothing new... (Score:2)
It was shown in the 70's or early 80's by A. Ahumada that the human eye uses a non-uniform distribution of rods and cones (outside the fovea) because it can give better frequency response than a uniform grid (given the same number of cones over a given area).
In short, while this paper makes good reading, don't think that it represent a breakthrough in the field.
Re:nothing new... (Score:1)
I dreamt some college lectures (=sad). I would have sworn that nonlinear sampling was part of some courses at college.
Luckily, I can now rest in peace knowing that I was just a regular student who sometimes was not entirely sober enough to remember all details...
I love articles about advanced math... (Score:1)
Impressive, but... (Score:2, Insightful)
A better article (Score:2)
This will usually give results similar to scanning at the maximum sample rate, then "compressing" by throwing out data points where the values are not changing much -- you need less RAM, but the maximum digitizer speed is the same, and you have to replay the analog data somehow. For instance, in an MRI, the multiple scans might mean holding the patient in the machine longer. That's not good, and enough RAM to hold everything isn't going to add much to the cost of the machine. Also, there is one condition where the results could be different -- if a detail such as a hairline fracture is so fine that it might be entirely missed between the points on the first coarse scan. If you scan at maximum resolution first, you won't miss that.
Re:Better Compression (Score:1, Interesting)
Could we use non-uniform sampling techniques for these forms of media in the first place? Could be interesting. Jittered sampling tends to mask visual artifacts (anti-aliasing); same could be true for audio. Their techniques are supported by wavelet transforms, which can get some great compression anyways. Maybe Creative will bring us the SBLiveNU, with on-the-fly variable sample rates from 1-96 khz?
Re:Better Compression (Score:1)
There are lots of comression applications for this research. (Although who knows how they would compare to current methods). Let's say I have an image I want to compress. I look at this image and notice that there are areas with high detail and areas with low detail. To the best of my understanding, the transforms used in JPEG compression require me to sample uniformly, so I have to throw out the same amount of information throughout the image. Since the transforms presented in the paper allow for non-uniform samples, I can pick and choose how many samples I throw out, and from where. This might allow me to keep most of the samples from the high-detail areas of the image, and throw out most of the samples from the low-detail areas of the image. Whether this would improve size/quality compared to current methods is unclear.
Re:Who gets rights to the technology (Score:1, Funny)
Maybe a compromise is possible: "We hereby publish our research with half of the data removed randomly, see if you can recover what's missing."
Idiot (Score:1)
We have enzymes called nucleases whose job is to repair specific types of DNA damage. We have nucleases that repair uv damage (in the form of thymine dymers) to our DNA for example. Anyhow, before you complain about human biology, I suggest you RTFM and take a Bio course beyond highschool level.
Why compression research continues (Score:2)
(Side note: It seems ironic that as storage space grows, this becomes less and less necessary.)
Compression research continues because in the domain where latency is less than one minute (that is, not FedEx), data communication throughput does not increase nearly as quickly as storage space. Sure, you have 100 GB to store uncompressed images and audio, but how are you going to transfer the information to another computer?
Re:Decompression? (Score:1)