all digital way
Try this way. Use a high speed ADC that samples frequently enough to get at least one sample time at the top of your waveform. Put the output to a digital magnitude comparator which compares the number to one in a latch. If the new ADC value is higher, load the value into the latch. This will then find the peak. The magnitude comparator can also sense when lets say two samples following the peak are smaller. When this happens, the latch value is loaded out to some other part of your circuit and the same circuit is used to find the lowest signal level by using the less than output of the magnitude comparator. Once the dip is found and the next two samples are higher the magnitude comparator circuit is switched to the peak finding mode again.
Alternately, if you know the voltage input will go below the 100 mV when there are no pulses, you can use the adc output going below say 50 mV as the condition to clear the latch and start the peak finding again.
If you want an analog out, the other part of your circuit can be a high speed DAC.