Removing noise from audio using Fourier transform in Matlab I'm trying to remove noise from an audio file. This audio file contains speech as well as constant pink noise. I know that I have to use the Fourier transform to convert to the frequency domain then use a filter to filter out the frequencies of the pink noise, but I really don't know where to start with that. It also seems that the noise covers many more frequencies than the speech file (I have the speech and noise files separately) by looking at the plots in the frequency domain.

Doesn't that mean that if I filter out the frequencies of the noise it'll remove all the speech as well?

The plot of the speech audio in the frequency domain displays that the frequencies are mostly between -450 and 450.

The plot of the noise alone in the frequency domain displays that the frequencies are between -2000 and 2000. This clearly covers a much wider range of frequencies than the speech audio. 

Does this mean I can't remove it from the noisy speech audio without removing the speech too? Or can I remove the frequencies outside of -450 and 450 and that would remove much of the noise? If so, how do I compute the range of frequencies instead of looking at plots myself to see the range?
From my experience, your best bet is spectral subtraction. You can find a lot of literature about it on the web. Here just a quick overview of what you need to do. You take overlapping windowed blocks of your time domain signal and transform them to the frequency domain using an FFT. Then for each frequency bin you need to estimate the signal-to-noise ratio. There are several simple noise tracking algorithms that perform well if the noise is relatively stationary. Based on the estimated SNR per frequency bin you mulitply each bin with a gain constant between 0 (terrible SNR) and 1 (no noise). Note that you only deal with magnitudes, the phase of the FFT is left unchanged. After modifying the FFT bins with the gain factors, you combine the processed bins back to the time domain using the phase of the original noisy signal.

Here is a classic paper on this subject. It goes a bit further than pure spectral subtraction but the overall system is the same. Don't worry too much about the math involved to derive the optimal gain function.