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In principle, arbitrarily small frequency separations can be resolved if
- there is no noise, and
- we are sure we are looking at the sum of two ideal sinusoids under the window
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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Download Intro421.pdf
Download Intro421_2up.pdf
Download Intro421_4up.pdf
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