I am new with detrending techniques, I have a carrier phase measurements and I want to detrend it by 6th order butterworth digital filter. After creating the digital filter I get its numerator (b) and denominator (a). The filter was created by

scipy.signal.butter(N, Wn, btype='highpass', analog=False, output='ba')

In this case, do I need only to multiply the carrier phase measurements by the output of the filter which is b/a or I need to multiply it by something else?

  • $\begingroup$ Check out lfilter, you need to be using convolution. $\endgroup$
    – A_A
    Jan 13 '19 at 11:25
  • $\begingroup$ I get the first point but the second point no I did not understand what to do? $\endgroup$
    – baddy
    Jan 13 '19 at 12:05
  • $\begingroup$ Is there any particular reason you are restricted to detrending it with a butterworth digital filter? $\endgroup$ Jan 13 '19 at 12:54
  • $\begingroup$ In fact, I am trying to detrend the carrier phase of GPS signal in order to remove low-frequency contributions from satellite-receiver range variations, antenna gain patterns, background ionosphere and troposphere delays, receiver and satellite oscillator drifts, etc and I have choosen Butterworth because it was the same one used by the receiver to give the processed file while I am working with the raw data $\endgroup$
    – baddy
    Jan 13 '19 at 13:24
  • $\begingroup$ Interesting, I haven't gone through this to know all the details sufficient to confidently provide an answer below, but did find this paper of interest in case you haven't come across it: ion.org/publications/abstract.cfm?articleID=10030 That said I suspect that you are simply filtering your carrier phase measurement (or other measurements the paper may clarify that). You found the coefficients of your filter above (coeff = scipy.signal.butter), now to filter use the scipy.signal.lfilter function: out = scipy.signal.lfilter(coeff,1, phase_in). $\endgroup$ Jan 16 '19 at 13:26

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