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I used the FM 25 and the analyzer to demonstrate the occupied bandwidth of a FM signal. When a sine wave audio signal is applied there is a predictable spectrum found by using the modulation index, the audio frequency, and Bessel Functions. The calculated and measured components were very close to agreement and I don’t recall seeing anything near the displayed spectrum.
All transmitters produce harmonics and it is a matter of keeping them below legal limits so I would expect to see harmonics unless they are below the analyzer noise floor. Unfortunately, I do not recall measuring harmonics but I also do not recall seeing any and I wish I could be more certain of this.