# understanding a spectrum of a modulated signal

I plot a spectrum of a modulated signal. It is a GMSK modulated signal. My goal to find the best parameter for a realisation it.

My first spectrum with oversampling ration M = 4 and BT (the product of 3-dB bandwidth of the LPF and the desired Tb) = 0,5

and M = 8, BT =0,5

and M = 6, BT =0,5

According to figures, can I conclude M =4 is the best option for me ( ~ -60dB side lobes)?

How to analyse the spectrum of a signal?

The spectrum will be identical for all cases of oversampling. (The frequency axis just scales accordingly). Proper oversampling does not modify the spectrum in band in any way whatsoever, but on the transmit side it provides greater margin to simplify subsequent filtering: either digital filtering if later interpolation / upsampling is performed, or the analog reconstruction filter after the DAC. Higher oversampling creates more spectral space between the images in the signal and therefore relaxes the transition bands in the related filters mentioned.

A possible benefit to lower sampling ratios is that the time duration of pulse-shaping filters implemented in the waveform creation (in this case the Gaussian filter) will extend longer in time for the same filter complexity and thus have higher performance. I detail that trade further at this post.

Therefore the choice of what oversampling is best is part of a system design with consideration of all subsequent filters needed, and traded with the resource and power requirements needed to run the digital processing at a higher rate.

Below is an example demonstrating a 16-QAM Spectrum and it oversampled by 5 where we can see from the details in the plot that the spectrum in band is not modified in any way, but the oversampling gives us much more range in frequency that facilitates later filtering operations both in the digital and analog domains.

16-QAM 4 samples per symbol:

16-QAM 20 samples per symbol:

• if the factor doesnt change the spectrum, why does my spectrum change? I changed only this parameters May 3, 2022 at 14:33
• &FrHart64 Your spectrum doesn’t change (it appears to me) just the horizontal axis scales, as we would expect since the frequency range extends to plus or minus half the sampling rate May 3, 2022 at 14:46
• Unless you use different filtering in your implementation, the spectrum will be the same. May 3, 2022 at 14:48
• what is a spectrum purity? Is it a lever of side lobes? Can I compute it? May 16, 2022 at 7:18
• @FrHart64 Please post your question where you can provide more complete details of your question including context. May 16, 2022 at 8:35