The data file doesn’t exist. At least it’s not available to me. It’s bettter to attach it here, anyway. If it has an excluded exttension, use the zip function to enclose it in a .zip file that you can upload here (providing it’s within the size limitts).
You can make things easier for yourself (since you obviously have the Signal Processing Toolbox) by using the highpass, bandstop, and bandpass functions. Use the 'ImpulseResponse','iir' name-value pair in each function call to force them to design a very efficientt elliptic filter. There are other name-value pair arguments to those functions that can allow you to modify the filter design, however I usually go with the default values. (An order 1 Butterworth filter isn’t going to do much actual filtering. Use the freqz function to view their Bode plots.)
Implementing the fft function is straightforward, and there are several examples in the documentation and in Answers. (I wrote several of them here, using essentially the same code, and most recently a function I created.)
Your approach is correct. The Fourier transform will demonstrate the frequency components of the signal. Frequency-selective filters will be useful for band-limited noise, including mains/powerline noise, however broadband noise will be difficult to deal with. There is no best solution for that, however wavelet denoising and the Savitzky-Golay filter are commonly used to reduce or eliminate broadband noise. The tradeoff is in reducing the noise without compromising the signal morphology. Badly designed filters that eliminate most of the noise can render the resulting filtered signal clinically useless.
