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Beating Heisenberg

In principle, arbitrarily small frequency separations can be resolved if

In this case, the maximum likelihood estimate (MLE) will reliably find the six sinusoidal parameters (amplitude, frequency, and phase for both sinusoids). We will return to the MLE later in the quarter.

However, in practice, there is almost always some noise and/or interference, so we normally require sinusoidal frequency separation by on the order of a main-lobe width (of the asinc function in this case, or the window transform more generally) whenever possible.


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``Music 421 Overview'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
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