How to filter a signal sampled at different frequencies I have a signal which was sampled using different frequencies. The 3 regions are:


0-10 ms: 10000 Hz
10-50 ms: 1000 Hz
50-200 ms: 100 Hz


The signal is very noisy, so I thought about smoothing it with a low pass filter. I worked with each of the 3 regions independently:


Apply window in time domain (Hann window)
FFT
Apply half Hann window, to remove high frequencies
IFFT


Each of my regions looks better now but I am having problems stitching them back together, due to the beginning and end of each stage deviating considerably from the original values.

What is the standard procedure of applying a low pass filter to a signal sampled at different frequencies during several stages?

Edit:

In case it might be relevant, this is the half Hann window used as a low-pass filter. The window length (in the example, 50) is different for every region. I am not interested in a specific cut-off frequency; the filter is used to remove noise and I am evaluating the output visually.
If I were you I would define my sampling period as the period present in the interval with the highest sampling frequency. Then I would try to interpolate the sections of the signal that were originally sampled at a lower sampling frequency to obtain a uniform signal of the same sampling frequency. 

Then I would filter the whole signal with the same filter. 

This procedure is often used when you have non-uniform sampling intervals but it might work for you. 

As you say that the signal is very noisy maybe interpolating is not good but you can try to and see how it works.

If you can be 100% sure that decimating the intervals with higher sampling frequency is not going to introduce aliasing you can try to decimate all the intervals to the lowest sampling frequency and avoid interpolating noisy samples.

Maybe even an intermediate solution would be the best. Take every interval to the intermediate sampling frequency, decimating the one with higher sampling frequency (if you are sure there's no aliasing) and interpolating the one with lower sampling frequency.

Since your 3 sampling frequencies are integer multiples of each other you can easily decimate or interpolate from any one to get any other