Remove high frequency noise

I have a highly corrupted data set (blue in attached image). How do I remove the high frequency noise and recover the original signal (red)? I want to use a low pass Butterworth filter of first order.

Answer 1

[Patrik Ek]

There is a function in matlab called "butter" that creates the coefficients to a butterworth filter of order N with cut-off frequency Wn. See MATLAB help. Then the function "filter" can be used to filter the signal. Notice however that the functions uses normalized frequencies here.

[Deepayan Bhadra]

Thank you! I eventually found out from a youtube video. But I could not understand exactly what 'normalized' here means. For e.g, say my cut-off is 5 Hz and the total f range is 500 Hz, is it 5/500?

[Patrik Ek]

It is kind of right, but not accurate enough. I am not a hundred sure of how matlab normalizes these function, but I think that matlab uses the convention,

fnorm = 2*freal/fsample

There are a difference between range, since that is specified by you. Eg you may have a valid range for some model as 0 to 20hz even though the sample rate is 100 hz