I would like to know and use libraries and functions, like to do a FFT, show a spectrum, start listening the microphone, etc.
About a year ago I wrote a very detailed tutorial and taught a couple hands-on workshops which included this exact subject. But I have some good news and some bad news for you.
First, the bad news: this tutorial and the library code only works on Teensy 3.x. It will not work on Arduino Due. The code makes heavy use of DMA and special peripherals not present on Due. It also uses the Cortex-M4 DSP extensions, which are not present in the Cortex-M3 processor on Arduino Due. Maybe this material can offer some very minor help even if you don't have compatible hardware, but to actually use it, you will need get a Teensy board. (full disclosure: my company makes these boards... so my opinion is biased, but I really do wish to help you if I can)
I also do not know how to use the FFT output for speech recognition. I'm writing this message for you in hopes you might share whatever you learn. I can only help with the part you asked above... how to get the audio data and perform FFTs, and do so in a way that other code can easily work with the data while more audio is captured and analyzed by the FFT without gaps.
The good news: I wrote a very detailed 31 page tutorial manual. You can get it here:
Alysia and I also went to the trouble to shoot & edit a complete 48 minute walkthrough video. It shows all the tutorial steps. Scroll down at that page for the video. Of course, actually doing the tutorial yourself with the real hardware is essential, but if you get stuck and the words & pictures of the 31 page manual aren't clear, hopefully the video helps.
Again, this code only works on Teensy 3.2, Teensy 3.5 and Teensy 3.6. The tutorials use this audio shield. There are other ways to get signals in and out, and after you've read or watched the tutorial and if you look around the options offered in the design tool (part 2 of the tutorial) you'll see other ways to input & output signals. But as a practical matter, for a microphone that shield is probably the best way to get started. Notice the part of the tutorial where the mic gain is software adjustable....
If you read or watch part 3-2 of the tutorial, hopefully you can see how this works for FFT data. The audio library takes care of acquiring the signal and computing the FFT, which you can then use in your program.
Again, how you'll use the FFT data to recognize works is beyond my knowledge. I am curious. If this info helps you get started, and if you learn anything useful that could help me or others, I sincerely hope you'll share. Maybe you'll even participate here on the forum and occasionally help them, as we're trying to help you?