Speech recognition algorithm in GNU Octave to convert speech to text (and vice versa)
Is there any possibility to implement a speech recognition integrated with google voice that converts speechs in text in GNU Octave?

Yes.
The Google Cloud command line utility returns results in JSON. Octave is working on its JSON support, but until then you can use something like this.
What we are missing now is triggering the whole process from within Octave.
This can be achieved with the Subprocess control functions.
Usually, you can redirect the stdin, stdout streams towards buffers in your application, which would get you the JSON in a local variable within Octave from which then you can call its parser to make it computable. If you cannot, you would have to create an intermediate file and read any data through that. Which might require some timing control too.
This is the general way of going about it even across languages (e.g. Python) and exchanging JSON is probably the better option than just returning some data over a stream and relying on putting it back together on the other side.
But this is also slow which your users (subjects) might find annoying. There is the overhead of starting up the process and in this case, there will be data exchanged over the network too. Besides, the free version of this google service allows a limited number of accesses per month. So, overall, it might be better to check if you can handle that recognition bit locally. You would still probably have to call an external to Octave package (...indeed, most probably Python with the same way outlined here), but the round-trip will be quicker (and cheaper).
Hope this helps.