# Is it possible to do deconvolution with two data sets that have different sampling rates?

I have some terahertz spectroscopy time series data, a reference set with 2048 data points taken every 0.0521 picoseconds, and the sample data set with 544 data points taken every 0.0781 picoseconds. I'm using Matlab to take a FFT of both sets, with zero padding on the sample set up to 2048 points, and I'm supposed to do a deconvolution on those transformed sets on a specific range of frequencies, but because the sampling rate is different for the two, these correspond to different starting points in the data sets, and the lengths won't match up either. When plotting the two DFTs, they only line up properly when accounting for the different sampling rates when spacing the frequency axis.

Is there something I'm doing wrong, or how should I do the deconvolution?

Resample your data to be close to the same rate. Note that the ratio between the time samples is 1.4990403.... if you resampled the 0.0781 data by a frequency ratio of 3/2, you would result with a time error of 0.000033 ps per cycle. From your sampling rate and block length you can determine how much of an impact this would have to see if that scale is sufficient: 0.0521/.000033 = 157.9 samples to slip $2 \pi$ radians. Resampling with higher ratios to support larger data block sizes: For instance 9369/6250 will get you to 1.49904 with a resulting time error of 3.07E-7 ps per cycle, with a block length of .0521/3.07E-7 = 169,650.6 to slip $2 \pi$ radians.