I am going to remove the noise from a brain recorded signal. It was a continuous recording and with sample rate=30kHz, it was digitized. So now it is a digital signal. I have written the code here for denoising this signal and I put two figures (the red one is the denoised one) including one big picture figure and the second one is by using zoom in. Below is the code.
wn=0.01 n=4 #order b, a= signal.butter(n, wn, btype='low', analog=False, output='ba') filtered = signal.lfilter(b, a, data_raw) plt.plot(data_raw, 'b', filtered,'r') plt.show()
Now I have several questions please (sorry if they are easy as I am a beginner):
1) Here we only determined the normalized frequency (wn). So if I want to know the low frequency of the filter, what is the default amount of sampling frequency for the Signal.butter function, please?
2) If I want to determine the sampling frequency of the butter filter by my self, is it the same sampling frequency as the data was digitized with? I mean the 30 kHz? If not what is the amount for this frequency, please? How should I determine it?
3) Do you have any other recommendations to filter this signal better and with less noise? Thanks a lot
Hi Zeinab,
Your question is a bit difficult to understand, and I'm not sure if it is a language problem or an understanding problem.
" Here we only determined the normalized frequency (wn). So if I want to know the low frequency of the filter, what is the default amount of sampling frequency for the Signal.butter function, please? "
Your butterworth filter does not have a sampling frequency. Only during digitization do you have a sampling frequency (i.e. how often the digitizer stores a value, in your case 30,000 times a second). A filter can have one (or many) cut off frequencies, also know as a corner frequency. You set the corner frequency with the wn paramter. There is no default value (as far as I know). The value of wn depends on whether you want to specify an "analog" or a "digital" filter, which you set with the analog parameter, which defaults to false, and returns a digital filter. In which case, as you point out, wn is normalized, between 0 and 1 in pi radians/sample.
Most physiologists wouldn't want to specify "digital" filter as they aren't used to thinking that way. In some situations, specifying a filter that way makes sense because mathematically, performing a 50 Hz low pass filter on 100 Hz digitized data, is exactly the same as performing a 200 Hz low pass filter on 400 Hz digitized data.
That said, if you want to specific a filter, and you know the cut off frequency you want, then the math is simple.
1 pi radians/sample is the same as 1/2 cycles per sample.
30 kHz = 30,000 samples per second
Multiplying them together gives you
15,000 cycles per second = 15 kHz.
So if you set Wn to 1, you would get a 15 kHz filter, either a low or high pass, depending on what you specify in the 3rd parameter.
I'll skip straight to point 3.
You want a "better" filter. What "better" is depends on what you want to measure. Your job is a physiologist is to decide what frequency ranges you data might lie in, and then filter accordingly. You can't go around filtering your data to make it look how you want, otherwise you can make your signal look like anything. Look in the literature, see what filter settings other people use, and use those. Also, for what it's worth, most physiologists would use a bessel filter, rather than a butterworth.
Finally, I wrote an article almost designed for someone like you. You can ignore the code (it's in matlab, not Python), but it's for people who aren't used to thinking about filters. I think you might find it very useful.
http://www.billconnelly.net/?p=501
Thanks a lot for the explanation. I think I got what you mean and how the data should be filtered.
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