Can Active Noise Canceling be implemented with Arduino or other programs?
If possible, could you tell me the code? I'm still a beginner, so fft is hard 
Not with the small, slow Arduinos.
Noise cancellation is hard for experts, using larger, faster microprocessors, too. As a beginner, you should pick beginner projects to get started.
I believe noise-cancellation is normally done in analog. An inverting amplifier (or inverting buffer) is easy to make with an op-amp.
With headphones it's pretty easy to invert the sound hitting your ear and then the soundwaves cancel.
With headphones, you can pick-up the noise on the outside of the headphone and invert-it on the inside. The microphone picks-up almost exactly what's leaking-through and hitting your ear (but the sound leaking-through is attenuated mechanically).
When you don't have headphones it's hard for the microphone to pick-the noise without also picking-up the inverted signal.
It's also difficult if the noise and inverted signal are not in the same spot because sound does not travel at infinite speed and any distance can end-up putting the soundwaves back in-phase, reinforcing instead of canceling.
...If you reverse the connections to one of your stereo speakers the bass will be pretty-effectively canceled. The bass is usually identical in both channels and the long wavelengths prevent any "unusual" phase differences. The rest of the audio range will just sound "spacey" and "phasey" If you play a mono-file with one speaker reversed (both channels completely identical) you'll get more cancellation but it's not very effective except for the bass. If you put the speakers close together it works better but you'll still hear the sound,
My five cents when you want to design an active noise cancellation:
You had to convert from analog to digital (to have it as I2S, SAI, from an ADC).
You do it from the MIC measuring the noise.
You do the noise cancellation: here you had to invert the phase of the signal and add it to the signal.
Convert the digital processed signal back (via a DAC, or I2S, SAI with external DAC).
The problem is not just the performance (speed) of the MCU, esp. for this anti-phase signal addition: bear in mind: these conversions from analog to digital and back from digital to analog is based on samples, e.g. 32bit stereo. And it will come via a buffer, e.g. 256 samples.
This is a huge delay - independent of the MCU speed. It is based on the digital audio signal (I2C, SAI).
It will be so large that you are not in sync with the real analog audio, e.g. in MIC and headset.
Bear in mind: if you want to compensate for audio with 20 KHz max. upper frequency, all has to be done within a half-cycle (at least), so in a period of 40 KHz all the audio samples must be processed.
Almost impossible w/o any hardware (e.g. FPGAs). Even an MCU and using ARM DSP (which you would consider to use), even very fast - the entire audio conversion and handling in buffered (packetized) samples is the limitation.
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