First I am not an electrical engineer, but I am on a mission, so please forgive my lack of resources and ability to explain my concepts.
I am designing a device for people with blindness. Currently it just blinks faster when objects are nearer, but I want to have it output a tone/frequency dependent on distance. To do that, I have to convert these short pulses into long pulses. The voltage of the long pulses must be dependent on the voltage of the short pulses. How short are the pulses? Well the speed of light short, only a few nanoseconds in duration, but still enough to light up an LED or output a beep to a speaker. Currently I am using the short pulse to charge a capacitor that triggers the next range finding sequence. When objects are near it the sequence occurs quickly and you hear many beeps, when objects are far away the beeps slow to 1hz. This method is not good for battery duration. Instead I want the range finding sequence to only sample the distance once every second and then output a specific tone based on this distance. The tones would be tuned to a persons ability to hear and thus allow them to learn to distinguish exact distances.
The first thing I tried was applying a lowpass filter, but even if I got this working correctly this just causes the tone to taper off really quickly. Hence the tone is not consistent. Here are my signals with a lowpass filter applied. The first signal is distance measuring at ~1ft (30cm), and the second is at ~7ft (2m). The maximum range will be up to 40m in the daylight.
Here is a photo of an ideal signal conversion. The short pulses converted into a long consistent voltage that I can transform into tones based on differing voltages. The bandpass of the signal doesn't have to be precise but long enough in duration for someone to hear the the unique tone. 500ms to 900ms would likely be perfect.