# What happens when I try to resample a speech recording from 8kHz to 16kHz?

I have a question regarding resampling in the context of speech. Given a speech recording sampled at 16kHz, downsampling to 8kHz will basically remove half of the samples (each 16000 samples become 8000). Now, I'm wondering about the inverse senario, given a telephony quality speech recording (300Hz -> 3400Hz) sampled at 8kHz, what happens if I try to resample the signal to 16kHz ? How will the 8000 additional samples for each second be computed ?

I tried this using sox and a new recording has been generated with no complaints or error messages, So my question is : how is this done ? Is there some kind of standard procedure, like an interpolation used to build the missing samples ?

The new samples are generated by interpolating between the original ones. Exactly how this is done will vary by implementation, but the most typical way would be to use a linear interpolating filter. With this technique, you would interpolate by a factor of 2 by inserting zeros between each of your input samples. Assuming your input signal is $x[n]$, your expanded signal would look like:
$$x_e[n] = [ x[0], 0, x[1], 0, x[2], 0, \ldots ]$$
Finally, you then apply a lowpass filter to remove the extra copy of the spectrum above $f_s/4$ in the expanded signal. The result is an interpolated-by-2 version of your input signal that is bandlimited to the same region of frequencies as the original.