IIRFilters::ButterFilter Function

Design a complete Butterworth IIR filter of the given Order, cutoff(s) CutoffFreq and band type FilterType, returning the transfer function in zero-pole form (z, p, k): H(z)=k (prod_i (z-z_i))/(prod_i (z-p_i)). Set Analog=True for an s-plane design or Analog=False for a z-plane (digital) design; for a digital design CutoffFreq lies in $(0,1)$ with sampling frequency 2 (so 1 = Nyquist). FilterType is lp/hp (1 cutoff) or bp/bs (2 cutoffs); a bandpass/bandstop design has twice the prototype order. IirFrequencyTransform selects when the frequency-band transform is applied (state-space-analog, zero-pole-analog or zero-pole-discrete). Digital poles satisfy |p_i|<1 (stable). The function result is the natural 3 dB cutoff W_c. The other overloads return the same filter as num/den (ba), second-order sections (sos) or state space (A,B,C,D). NOTE: a digital cutoff outside $(0,1)$ is NOT range-checked and yields a degenerate filter.

Design Butterworth filter of Order with CutoffFreq frequencies and of FilterType type. Set Analog to True, to request and analog filter design in s-plane or set it to false to obtain a digital filter design in z-plane. The CutoffFreq must be in range between 0 and 1 (Sampling frequency = 2) in case of a digital filter design.

IIrFrequencyTransform specifies when and how will the frequency band transformation be applied. The resulting transfer function is returned in the zero-pole form, with z,p,k variables.

The resulting transfer function is returned in the numerator/denumerator form with num and den.

The resulting transfer function is returned in the second order section form stored in the sos variable.

The sos variable can be passed directly to the IirInitBQ filter initialization routine. Second order section form delivers substantially higher numerical stability and range than filtering with num/den form which is used by the IirInit routine.

The resulting transfer function is returned in the state-space form with A,B,C,D variables.