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A band pass filter of the Butterworth type is an ARMA filter (product of a MA filter by an AR filter) whose
characteristics are defined by the frequency limits f1 and f2.
The slopes of the filter, expressed in logarithmic scale, are independent of the frequency limits f1 and f2,
and the phase of the filter varies linearly within the bandwidth. This follows that the form of the signal
limited by the bandwidth will be unchanged by the filter ; however the signal will be shifted in time.
In the example, the Butterworth filter is the product of a second order MA filter by an fourth order AR filter.
The coefficients of the MA filter (bo, b1=-2b0, b2=b0)
and AR filter (a0=1, a1, a2, a3, a4) depend on the
values chosen for the frequencies f1 and f2, which are expressed in reduced frequency.
