# General setting

I'm playing around with an RTL-SDR and recently captured some FM spectrum in Hannover, Germany. I want to undersand what's going on, so I've read a lot about FM and its spectra, but I can't completely make sense out of it.

# Problem

At the moment of taking the samples, the channel at 98.7 MHz must have been silent (at least, the pattern looks like what the real-time spectrum shows me when nobody is talking). It looks like only the stereo pilot tone at 19 kHz is being transmitted at that time. This would make sense with the spacing of the lines, being approximately 20 kHz apart from each other.

# Things I've tried unsuccessfully

However, I'm still confused. As I understand it, the amplitude of the spectral lines should be given by the Bessel function of first order with respect to the modulation index (frequency deviation is 75 kHz). Performing abs(besselj(-4:4,75/19)) in Matlab gives me

[0.2732 0.4277 0.3769 0.0458 0.4001 0.0458 0.3769 0.4277 0.2732]

20*log10(abs(besselj(-4:4,75/19))) gives

[-11.2692 -7.3769 -8.4757 -26.7828 -7.9567 -26.7828 -8.4757 -7.3769 -11.2692]

This appears to be congruent with the Bessel diagrams I've seen. However, this is not what I see in the spectrum. I've also tried different modulating frequencies, but nothing seems to give those amplitudes. Can anyone point me to why this is?

I've tried to simulate a frequency modulation of the pilot tone and a single tone at 57 kHz (approximating) RDS. However, this only makes things worse, and looks even more different from the recorded spectrum.

# Summary of questions

1. What is being modulated (what does the MPX spectrum look like during silence)?
2. How to explain those spectral amplitudes (as you can see, for other channels, the amplitude relations and line spacings look similar during silence, just not visible as nicely because of low power level)?
3. What happened to the RDS carrier? Why does the spectrum resemble the one of a single-tone modulating signal?
• How are you normalizing your DFT to generate the plot? Your signal seems to have > -10 dBFS power the peak power frequency, which might indicate you're driving your receiver into nonlinearities, in which you'd get intermodulation products between that strongest tone and a lot of other tones, with typically unforeseeable effects. When you plot a histogram of abs() of the time domain signal, how "safely" are we away from clipping? Commented Aug 20, 2018 at 18:56
• Oh, and are you sure you've got RDS on that channel at that time? Have you checked (e.g. by demodulating the FM stereo audio + RDS part e.g. with gr-rds)? Commented Aug 20, 2018 at 19:19
• I'm normalizing the DFT by making sure I never have a time sample that is greater than 0.5 (-6 dBFS) by adjusting the gain. I've checked that this works correctly. So non-linearities because of overdriving shouldn't be a big problem, right? Commented Aug 22, 2018 at 11:34
• I'm not sure about RDS. Normally, there is one on that channel, but theoretically, it could be gone during silence (I assume silence has no influence on RDS, but I could be wrong). To be sure about the baseband signal, I should probably keep the original samples, instead of just the spectrum, and demodulate to get the baseband signal. I might try that later (or try to use SDR#, which shows the baseband spectrum) and then ask agagin. Commented Aug 22, 2018 at 11:37
• You don't need to ask again, just edit your question to contain the new info :) Commented Aug 22, 2018 at 12:53