Also known as: Harry Nyquist, Nyquist
Harry Nyquist (1889–1976) was a Swedish-American engineer at Bell Labs whose work on the maximum signalling rate of a channel underlies the sampling theorem at the heart of digital radio.1 The rule that a signal must be sampled at more than twice its highest frequency — the boundary every ADC in an SDR respects — carries his name.
Life and work
Nyquist was born in 1889 in Nilsby, in the Swedish province of Värmland, one of eight children in a poor farming family. He emigrated to the United States in 1907 at eighteen, worked and studied his way through the University of North Dakota, earning bachelor’s and master’s degrees in electrical engineering, and then completed a PhD in physics at Yale in
- He joined the American Telephone and Telegraph Company that year and moved to Bell Telephone Laboratories when it was formed in 1925, remaining there until his retirement in
- Over that career he accumulated some 138 patents and a reputation, among colleagues, as the quiet source of the good ideas other people developed. Shannon himself later remarked that Nyquist and Ralph Hartley were the two people whose work most influenced his own.
Contribution
Nyquist’s two most cited papers came in the 1920s. In “Certain Factors Affecting Telegraph Speed” (1924) and “Certain Topics in Telegraph Transmission Theory” (1928) he analysed how fast independent pulses could be pushed through a channel of a given bandwidth without them smearing into one another — what is now called intersymbol interference. He established that a channel of bandwidth B can carry about 2B independent symbols per second, and, read in reverse, that a signal containing no frequency above B is fully captured by samples taken at rate 2B. This is the sampling theorem in embryo; Claude Shannon later stated and proved it in full generality, which is why it is often called the Nyquist–Shannon theorem. Sample too slowly and high frequencies fold down into the passband as false low-frequency artefacts — aliasing — which is why every SDR front end pairs its ADC with an anti-alias filter.2
In 1928 Nyquist also derived, independently of and simultaneously with John B. Johnson, the formula for thermal (Johnson–Nyquist) noise, showing that the noise power available from a resistor depends only on its temperature and the bandwidth. That result sets the fundamental thermal noise floor of every receiver. A decade later, in 1932, he produced the Nyquist stability criterion, a graphical test that tells engineers whether a feedback amplifier or control loop will be stable — still taught in every controls course and directly relevant to the phase-locked loops inside a demodulator.
Legacy
Three quite different “Nyquist” concepts — the sampling rate, the thermal-noise floor, and the stability criterion — each anchor a corner of modern electronics, an unusually broad legacy for one engineer. For software radio the first is inescapable: the choice of sample rate, the design of decimation filters, and the very notion of a usable bandwidth all follow directly from his 1928 analysis. GopherTrunk lives inside those limits every time it selects a capture rate wide enough to hold a trunking system’s channels while staying above twice their highest frequency, and its decode chain is deliberately built to be well-behaved with respect to the Nyquist boundary so that no signal energy folds back to corrupt a channel.
Sources
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Harry Nyquist — Wikipedia, for biography and his work on sampling and signalling theory. ↩
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Harry Nyquist — Encyclopædia Britannica, for his telegraph-transmission analysis and the sampling and thermal-noise results. ↩