So I have a signal which is caused by an impulse train. I can determine the impulse train with 500hz but sample my output signal with only 10hz. Then I want to calculate an impulse response function. So I have a binary "signal" for the impulses with 50 times more samplepoints then my actual signal. If I resample my binary signal using fourier which I would do with an ordinary signal, I get Gibbs ringing and I doubt my impulse response function would still make sense. I can choose the nearest neighbor to be 1 in my "downsampled" impulse train but then the timing is less accurate, I could divide the impulse over the two neirest neighbors bu then no single point will have the value of 1. What would be a correct way to go about this?
The usual way to do this is with a low-pass decimating FIR filter. If you are going to decimate by a factor of 50 then you will probably want to break it up into multiple LPF decimation filters. I would probably do it as /10 followed by /5.