2014 radio reception problem

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2007 CX-7 Turbo AWD, 2010 Mazda3 Hatchback
I just bought my wife a used 2014 cx5 with 13k miles. We are having a strange problem with the radio. About 50% of the time the radio has a very high pitched whine and very bad reception on all stations. The high pitched whine goes away whenever it picks up an HD signal. The other 50% of the time it sounds great, even when no HD signal is available. Has anyone else had this problem? Is there anything I should check?
 
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