Death of the sampling theorem?


A team from Columbia University led by Ken Shepard and Rafa Yuste claims to beat the 100 year old Sampling Theorem [1,2]. Apparently anti-aliasing filters are superfluous now because one can reconstruct the aliased noise after sampling. Sounds crazy? Yes it is. I offer $1000 to the first person who proves otherwise. To collect your cool cash be sure to read to the end.

“Filter before sampling!”

This mantra has been drilled into generations of engineering students. “Sampling” here refers to the conversion of a continuous function of time into a series of discrete samples, a process that happens wherever a computer digitizes a measurement from the world. “Filter” means the removal of high-frequency components from the signal. That filtering process, because it happens in the analog world, requires real analog hardware: so-called “anti-aliasing” circuits made of resistors, capacitors, and amplifiers. That can be tedious, for example because there isn’t enough space on the electronic chips in question. This is the constraint considered by Shepard’s team, in the context of a device for recording signals from nerve cells [2].

Now these authors declare that they have invented an “acquisition paradigm that negates the requirement for per-channel anti-aliasing filters, thereby overcoming scaling limitations faced by existing systems” [2]. Effectively they can replace the anti-aliasing hardware with software that operates on the digital side after the sampling step. “Another advantage of this data acquisition approach is that the signal processing steps (channel separation and aliased noise removal) are all implemented in the digital domain” [2].

This would be a momentous development. Not only does it overturn almost a century of conventional wisdom. It also makes obsolete a mountain of electronic hardware. Anti-alias filters are ubiquitous in electronics. Your cell phone contains multiple digital radios and an audio digitizer, which between them may account for half a dozen anti-alias circuits. If given a chance today to replace all those electronic components with a few lines of code, manufacturers would jump on it. So this is potentially a billion dollar idea.

Unfortunately it is also a big mistake. I will show that these papers do nothing to rattle the sampling theorem. They do not undo aliasing via post-hoc processing. They do not obviate analog filters prior to digitizing. And they do not even come close to the state of the art for extracting neural signals from noise. Continue reading “Death of the sampling theorem?”