how often should one sample a dataset? I have some archive data that show the variation of a certain quantity X measured over 1-year intervals.

I'm now facing the problem of understanding how X correlates with another variable Y, that I can measure much more frequently, even daily.

So my question is, is it really necessary to collect data for Y so often? This seems such a waste of resources.

So what I would do is to collect data for Y only for 10% of the days of each year and I would select those days randomly. This way I'm sure that the observations are independent because the sample size is not too large and days have been selected randomly.

What do you think of that? Is that the approach you would follow as well?
In order to show a correlation between X and Y they should be aggregated over the same time period. Otherwise, there there may be seasonality or other features in Y that may have been averaged out in X. Is it possible re-index X to get monthly aggregates? I would not sub-sample Y. Find a common time period for both X and Y to make your comparisons.