Basic method for 2x oversampling? I would like to know if the following method of 2x oversampling is correct:

Interpolate:


Take an original signal sampled at 44100Hz as input
Upsample by adding a zero after each original sample to get a signal twice as long
Filter the new signal using a low pass filter (cutoff of 44100Hz based on new sample rate of 88200Hz)


Use new signal:


Do some additional filtering of the the new signal at 88200Hz


Decimate:


Take the final signal at 88200Hz as input
Filter using a low pass filter (cutoff of 44100Hz based on sample rate of 88200Hz)
Downsample by removing every other (odd) sample
Now have a signal that is 44100Hz again


What I would like to check is if the method is correct and my cut off frequencies for my low pass filters are right.
Interpolation (sampling frequency 44.1 kHz ➔ 88.2 kHz)

Your original 44.1 kHz sampled signal has frequencies up to 22.05 kHz, so you should lowpass filter at 22.05 kHz after dilution with zeros. Your filter should have a gain of 2. Otherwise the signal amplitude drops to half because you set half of the samples to zero. Like Jim Clay says, you can combine these things; there will be plenty of opportunity for optimization.

Downsampling (sampling frequency 88.2 kHz ➔ 44.1 kHz)

If your 88.2 kHz sampled signal is the one you lowpass filtered at 22.05 kHz, you can simply decimate by throwing away every second sample. Otherwise, first lowpass filter at 22.05 kHz to prevent aliasing, and then decimate. If you combine lowpass filtering and decimation, you can optimize again.