EE novice here. I have an analog synth oscillator core which produces a sync pulse each time the waveform resets. I'd like to generate a short series of pulses triggered from each sync pulse, ideally with configurable count (from, say, 2 to 5) and manually tunable rate (generally much higher than the sync pulse rate, say 500-5000Hz). The pulse sequence must start synchronized to the input pulse -- it can't be a free-running oscillator that is just gated from the input.
Needn't be a pure analog solution but I don't want to involve an MCU. I'm looking for a low part count solution for easy breadboard experimentation more than for a particular result.
The goal is to get something like VOSIM, but I don't care much about the pulse shape; square digital pulses are fine. Bonus points if the pulses in the train decay in amplitude from the first to the last, but also not a requirement. The design shown in Fig. 11 of that paper is much more complex than I'm looking for.
Can anyone offer ideas for a starting point?