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Thanks for this simple UWB pulses demonstration with pulse position modulation (PPM).
I use your doublets (second derivative Gaussian pulse) with and without pulses train and then we can see periodic variations on frequencies display - fine.
The very simple correlation separate correctly single pulses from delay pulses like PPM must do !
I was excited about the result and delighted by the simplicity.
You write the equations completely so that we can change at will by mastering what we do well.
Congratulations and thank you.