New Sampling Techniques Make Up For Lost Data

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."

Comments

Re:So....

[pmc]

No.

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?

Some useful niche applications

[michaelmalak]

Think about computer displays. Would you ever want to have to deal with non-square pixels? Sometimes, yes, like in the CGA days where the goal was to display 80 columns while keeping memory and bandwidth costs down. In general, it's a PITA. Now multiply that pain by not only having non-square pixels but where the pixels also come in various sizes.

What's the practicality of this? Well, spiral MRIs, 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.

Nyquist, not Shannon

[s20451]

It was at Bell Labs ... but the guy who developed the Uniform Sampling Theorem was Nyquist, not Shannon.

ah, there is the problem

[markj02]

Doctor to patient, after looking at the reconstructed images: "Ah there is the problem. The cause of your headaches is that you have a bunch of inch-long bony spikes sticking out of your neck, plus a bunch of holes in your skull."

Some folks seem to be missing the point on the MRI

[fatboy-fitz]

example. It was not provided to show a compression mechanism in which the original image could be compressed. It was intended to show that if you sample randomly, then their algorithm can come up with a highly accurate representation of the original. The implication here is that given current capability to sample, if you apply the new technique, you can get a better image/audio recording using their technique, than you can using the current fixed sampling interval technique, making the image more vivid, or the musical recording more lifelike than current sampling provides.

Time vs. Frequency

[PingXao]

Classical techniques also require that the original signal be "band limited" - a technical term meaning that the signal must stay within certain, defined limits.

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:Brain scans?

[Hal-9001]

Any medical imaging technique can only be so accurate, due to either machine or physical limitations. This defines a maximal meaningful sampling rate or resolution for that imaging modality. For example, positron emission tomography (PET) has a physical resolution limit of 10mm because positrons can propagate up to 10mm from where they are generated before they decay into gamma radiation that can be detected by the machine. With this technique, a doctor can get an image with better than 10mm resolution, something that the machine by itself could never do.

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.

Both are right:

[volpe]

From Engineering Fundamentals

The sampling theorem is considered to have been articulated by Nyquist in 1928 and mathematically proven by Shannon in 1949. Some books use the term "Nyquist Sampling Theorem", and others use "Shannon Sampling Theorem". They are in fact the same sampling theorem.