Happy Birthday, Harry Nyquist!
This morning I learned via Twitter that today is the 125th anniversary of the birth of Harry Nyquist, a physicist and electrical engineer, who was a prolific inventor who made fundamental theoretical and practical contributions to the field of telecommunications. He also gave his name to the Nyquist frequency and the Nyquist sampling theorem, now usually known as the Nyquist-Shannon sampling theorem.
Harry Nyquist (left) was born on February 7, 1889, in Nilsby, Sweden but moved to the United States in 1907. In 1917, after earning a Ph.D. in physics from Yale University, he joined the American Telephone and Telegraph Company (AT&T). There he remained until his retirement in 1954, working in the research department and then (from 1934) at Bell Laboratories. Apparently he didn’t have a beard, but he seems to have overcome this obstacle and had an illustrious career in research.
In my opinion, Harry Nyquist’s achievements are not sufficiently appreciated either by physicists or by the wider world, so here’s a quick summary of some of his greatest hits:
Some of Nyquist’s best-known work was done in the 1920s and was inspired by telegraph communication problems of the time. Because of the elegance and generality of his writings, much of it continues to be cited and used. For example, his 1928 paper Certain Topics in Telegraph Transmission Theory refined his earlier results and established the principles of sampling continuous signals to convert them to digital signals. The Nyquist sampling theorem showed that the sampling rate must be at least twice the highest frequency present in the sample in order to reconstruct the original signal. These two papers by Nyquist, along with one by R.V.L. Hartley, are cited in the first paragraph of Claude Shannon’s classic essay The Mathematical Theory of Communication (1948), where their seminal role in the development of information theory is acknowledged.
In 1927 Nyquist provided a mathematical explanation of the unexpectedly strong thermal noise studied by J.B. Johnson. The understanding of noise is of critical importance for communications systems. Thermal noise is sometimes called Johnson noise or Nyquist noise because of their pioneering work in this field.
In 1932 Nyquist discovered how to determine when negative feedback amplifiers are stable. His criterion, generally called the Nyquist stability theorem, is of great practical importance. During World War II it helped control artillery employing electromechanical feedback systems.
I think that demonstrates the tremendous debt the modern world of telecommunications owes to Harry Nyquist, and why we should remember him on his 125th birthday..
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In the Dark 
February 7, 2014 at 3:07 pm
I have a terminology question. In observational astronomy, we say we are Nyquist sampling in spatial frequency if there are two detectors per Airy disk. I wonder if this is correct use of the term?
February 10, 2014 at 11:37 pm
Indeed, it’s close, but incorrect. The formal Nyquist criterion assumes infinitesimally short sampling time, and that the highest component in the signal is sinusoidal. With a typical imager such as a CCD you have fat pixels, so you convolve in the Fourier domain, and hence you can recover the highest Fourier components in the image by dithering – even with arbitrarily fat pixels, if you have enough signal to noise.
Nyquist’s motivation was “How fast do you have to sample _to avoid aliasing_?”. In imaging, the analogy would be “If you can only sample with sparse detectors, how close do they have to be to avoid creating bogus features in your image?”
February 12, 2014 at 4:41 am
Thanks Garret. I first came across the term in the context of bolometer arrays, which indeed are sparse detectors, and so dithering was used the better sample the image plane. So, as you say, the usage of the phrase “fully Nyquist sampled” was probably close but not strictly correct.
February 10, 2014 at 12:07 pm
CDs do sound worse than vinyl, and they ruin the needles on your gramophone.
February 10, 2014 at 11:30 pm
Many of those who claim that, in the early days, CD’s sounded worse than vinyl, had a fair knowledge of DSP and knew about the bit-dropping habits of some of the early DAC chips.
Admittedly, the same people find it bemusing that today you can buy one-bit DACs with insane sampling rates for HiFi, at insane prices, where it’s really easy to show you are paying money for nothing.
February 13, 2014 at 11:21 pm
Phillip,
Don’t the cranks who make those claims about cables etc ever subject themselves to double-blind tests?
If you don’t like a CD (or if you want to definitively destroy the data on a CD-ROM), just pop it in the microwave. Watching the sparks fly under the plastic substrate is great fun. But always do it with windows wide open as the gases produced are extremely toxic.
February 14, 2014 at 5:18 pm
Don’t wrteck a good post with one passing comment Phillip! I don’t know any AGW deniers but I am a, and also know more than one, dangerous-magnitude-AGW denier. Best data show it hasn’t got warmer in 16 years although China and India continue to industrialise and increase CO2 levels, and the effect of CO2 is instantaneous.
Have you a reference to those Stradivarius tests please? Very interesting!
February 15, 2014 at 10:07 am
“At least almost all of these claims come from people whose main agenda is denying AGW”
Maybe they deny (danger-magnitude) AGW because they have seen these data; you are claiming to know which is cause and which is effect inside their heads, which of course you cannot know.
It’s based on the satellite data, not the terrestrial data which have less coverage.
“in some cases paid by the oil industry”
The US government has put huge amounts of money into funding the warmists, and arguments that are good (or bad) about sources of funding and corruption cut both ways.
Many thanks for the interesting violin test URL.
May 23, 2014 at 11:08 am
He was more than the founding father of Digital Communications. If you can understand just a little of his work then you have got the chance of breaking the communications barrier and calculating 10 times faster.
He had a vision of connecting the world, benefits of which the World is enjoying today. A visionary that the world has not seen for a long time and probably won’t again for a long time. The next leg of this journey is just commencing!