Convolving signals with very unequal sampling frequencies

I need to convolve two discrete signals. They were measured using very different sampling frequencies, a factor of more than 10 different. Let's call the signal with the shorter sampling period A and the signal with the longer sampling period B. I tried re-interpolating B using A's sampling period, which greatly increased the number of samples in B. As you can guess, it greatly increased my computation time too, which is the problem.

I've searched the literature for an alternative approach and come up empty. I've considered using Monte Carlo, but I'm not sure this will help at all.

Has anyone faced a problem like this in the past? Are there good solutions out there for convolving signals with very unequal sampling frequencies?

Here's where I ended up.

There's no mechanism for combining two series with different sampling intervals. Theory requires the same interval.

Re-sampling is fraught with problems, not least of which is adding artifacts. Re-sampling needs to be done very, very carefully.

In the end, I did some conditional re-sampling:

• If the series with the smaller interval has a range less than the interval of the larger series, I approximated the smaller series as a delta function
• If the series with the smaller interval has a range equal to the larger interval or more, I upsampled the larger interval to the smaller. It's not a great a solution, but ti works.