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When using an SDR (software defined radio), there is generally an error between the receiver frequency and the transmitter frequency. This results in a frequency beat that is not necessarily audible, but it will be quite apparent when viewing the IQ data on a Lissajous display. I noticed this when I added a Lissajous scope to my signal analyzer. It never dawned on me until I mentioned this on IRC (##rtlsdr), and tejeez indicated that the big circle is the result of a frequency error. This prompted me to come up with a frequency error estimator so that I can use the result (the frequency error) to drive an NCO plus phase corrector, so that I could derotate the phase velocity of the signal. And so it begins... Chris G. 08/21/2023 #**************************************************************** 09/01/2023 #**************************************************************** We now have a working phase-locked loop. It stablizes the Lissajous display nicely so that signal constellations can be viewed.