Phase invariant detection of low frequency spikes
I would use a band-pass filter centred at the frequency of the peaks (10ns period?). That should give you more of a peak in the second signal.
Use a quadrature filter pair (band-pass filter and its Hilbert transform) to gain phase invariance. The output is called the analytic signal. Its amplitude is a local phase-invariant energy measure.


In MATLAB this would be

f_a = hilbert(conv(f,g,'same'));
amplitude = abs(f_a);
phase = angle(f_a);


where f is the signal and g is the band-pass filter.