Always remember that whatever time interval you choose, if the "ends" don't meet, it compromises the FFT.? In other words, MUST have an exact whole number of cycles, or FFT suffers.
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Also, if the frequency varies, it needs to be stabilized and unvarying over the time interval used for the FFT.? Choose each of your time intervals carefully.
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In cases like this, applying a Window might help.
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Sndy