I have the following problem statement which I have no idea how to approach,
I have a IR depth sensor, that produces a distribution for it's depth value. So it kind of looks something like this:
As you can see, it shows that there are two possibilities, one at 10 and one at 20. Taking the expectation of this will give me the real depth.
What i want to do is apply some signal processing to model the motion of this camera in the Z axis. Basically i want it to shift say 5m and spread out to represent the increasing uncertainity. Hopefully to look something like this
I guess for the spreading out part, applying a 1D gaussian convolution would work, but i am not sure about the timeshifting part. Can i convolve the signal below with another signal to actual timeshift it somehow?