| Name | Description |
|---|
| BesselAnalog | Design an analog Bessel (Thomson) lowpass prototype filter of order Order, optimised for maximally-flat group delay (linear phase) rather than a flat magnitude. Returns zero-pole-gain with all zeros at infinity (z empty); the denominator is the reverse Bessel polynomial theta_n(s): H(s)=theta_n(0)/theta_n(s), theta_n(s)=sum_(k=0)^n((2n-k)!)/(2^(n-k) k! (n-k)!) s^k, normalised so that the DC gain is 1. The phase response is approximately linear near DC; the magnitude rolls off more gently than Butterworth. Domain: 1 <= Order <= MaxIirOrder. Poles satisfy Re(p_k)<0 (stable). z and p must share precision or an exception is raised. |
| BesselFilter (3) | Design Bessel IIR filter. |
| ButterAnalog | Design an analog Butterworth lowpass prototype filter of order Order, cutoff fixed at 1 rad/s. Returns zero-pole-gain in z (zeros), p (poles), k (gain): H(s)=k/(prod_(i=1)^n(s-p_i)), p_k=exp(j(pi/2+(pi(2k-1))/2n)), k=1... n. All n poles lie on the left half of the unit circle (so the prototype is stable, Re(p_k)<0) and all zeros are at infinity (z is returned empty), giving a maximally-flat magnitude that is 3 dB down at omega=1. Domain: Order is a positive integer, 1 <= Order <= MaxIirOrder (=50). z and p must share the same precision; a precision mismatch raises an exception. No NaN is produced for valid input. |
| ButterFilter (4) | 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. |
| ButterOrder | Estimate the minimum Butterworth filter order that meets a transition-band specification, and fill CutoffFreq with the natural (3 dB) cutoff(s). BEdges holds the band edges in ascending order (passband edge then stopband edge per band); PassRipple (R_p dB) and StopRipple (R_s dB) bound the passband ripple and stopband attenuation. The returned order is n=\lceil(log_(10)(10^(R_s/10)-1)/(10^(R_p/10)-1))/(2 log_(10)(omega_s/omega_p))\rceil, capped at MaxIirOrder (=50). CutoffFreq length must be half BEdges length and match FilterType (1 value for lp/hp, 2 for bp/bs). Domain: digital edges lie in $(0,1)$ with sampling frequency 2 (Analog=False); analog edges are in rad/s (Analog=True). NOTE: the natural cutoff placement differs slightly from scipy buttord (same integer order, the 3 dB frequency may differ by under 1 percent). |
| ChebyshevIAnalog | Design an analog Chebyshev type I lowpass prototype filter of order Order with PassRipple dB of equiripple in the passband, cutoff fixed at 1 rad/s. Returns zero-pole-gain (z empty, all zeros at infinity): |H(jomega)|^2=1/(1+varepsilon^2 T_n^2(omega)), varepsilon=sqrt(10^(R_p/10)-1), where T_n is the order-n Chebyshev polynomial and R_p=PassRipple. The magnitude is equiripple in $[0,1]$ and monotone beyond; at the passband edge omega=1 it equals 10^(-R_p/20). Domain: 1 <= Order <= MaxIirOrder, PassRipple>0 dB. Poles satisfy Re(p_k)<0 (stable). z and p must share precision or an exception is raised. |
| ChebyshevIFilter (4) | Design Chebyshev type I IIR filter. |
| ChebyshevIIAnalog | Design an analog Chebyshev type II (inverse Chebyshev) lowpass prototype filter of order Order with StopRipple dB of equiripple attenuation in the stopband, cutoff fixed at 1 rad/s. Returns zero-pole-gain with finite imaginary-axis zeros: |H(jomega)|^2=1/(1+[varepsilon^2 T_n^2(1/omega)]^(-1)), varepsilon=1/(sqrt(10^(R_s/10)-1)), z_k=j/(cos((2k-1)pi)/2n). The magnitude is maximally flat in the passband and equiripple in the stopband; at the stopband edge omega=1 it equals 10^(-R_s/20) where R_s=StopRipple. Domain: 1 <= Order <= MaxIirOrder, StopRipple>0 dB. Poles satisfy Re(p_k)<0 (stable). z and p must share precision or an exception is raised. |
| ChebyshevIIFilter (4) | Design Chebyshev type II IIR filter. |
| ChebyshevIIOrder | Estimate the minimum Chebyshev type II (inverse Chebyshev) filter order that meets a transition-band specification, and fill CutoffFreq with the STOPBAND-edge cutoff(s). The order formula matches Chebyshev type I, n=\lceil(cosh^(-1)sqrt((10^(R_s/10)-1)/(10^(R_p/10)-1)))/(cosh^(-1)(omega_s/omega_p))\rceil, capped at MaxIirOrder (=50). Because the natural cutoff is the stopband edge, the returned CutoffFreq may sit just outside the passband bracket; for bandpass/bandstop the estimated order can differ from scipy cheb2ord by at most one section. Domain: digital edges in $(0,1)$ (Analog=False) or analog rad/s (Analog=True); CutoffFreq length is half BEdges length and matches FilterType. |
| ChebyshevIOrder | Estimate the minimum Chebyshev type I filter order that meets a transition-band specification, and fill CutoffFreq with the passband-edge cutoff(s). The order is n=\lceil(cosh^(-1)sqrt((10^(R_s/10)-1)/(10^(R_p/10)-1)))/(cosh^(-1)(omega_s/omega_p))\rceil, capped at MaxIirOrder (=50), where R_p=PassRipple and R_s=StopRipple in dB. BEdges holds the band edges ascending; CutoffFreq length must be half BEdges length and match FilterType. Domain: digital edges in $(0,1)$ (sampling frequency 2, Analog=False) or analog rad/s (Analog=True). The returned cutoff is the passband edge. |
| EllipticAnalog | Design an analog elliptic (Cauer) lowpass prototype filter of order Order, equiripple in BOTH bands (PassRipple dB passband, StopRipple dB stopband), cutoff fixed at 1 rad/s. Returns zero-pole-gain with finite imaginary-axis zeros: |H(jomega)|^2=1/(1+varepsilon^2 R_n^2(omega,xi)), varepsilon=sqrt(10^(R_p/10)-1), where R_n is the Chebyshev rational (elliptic) function. For a given order the elliptic design gives the narrowest transition band of the five families. At the passband edge omega=1 the magnitude equals 10^(-R_p/20). Domain: 1 <= Order <= MaxIirOrder, PassRipple>0, StopRipple>PassRipple (dB). Poles satisfy Re(p_k)<0 (stable). z and p must share precision or an exception is raised. |
| EllipticFilter (4) | Design Elliptic IIR filter. |
| EllipticOrder | Estimate the minimum elliptic (Cauer) filter order that meets a transition-band specification, and fill CutoffFreq with the passband-edge cutoff(s). Using the complete elliptic integral K( * ) and the selectivity k=omega_p/omega_s, discrimination k_1=sqrt((10^(R_p/10)-1)/(10^(R_s/10)-1)), the order is n=\lceil(K(k) K(sqrt(1-k_1^2)))/(K(sqrt(1-k^2)) K(k_1))\rceil, capped at MaxIirOrder (=50). For a given spec the elliptic order is the smallest of the five families. Domain: digital edges in $(0,1)$ (Analog=False) or analog rad/s (Analog=True); CutoffFreq length is half BEdges length and matches FilterType. |
| ExactIirZeros | Place the exact fixed zeros of a Butterworth or Chebyshev type I filter into z, given the filter Order, the bilinear-warped band-centre frequency Wc, the FilterType and the Analog flag. The locations are: DIGITAL (Analog=False) lowpass = Order zeros at $z=-1$; highpass = Order zeros at $z=+1$; bandpass = Order zeros at $z=+1$ then Order at $z=-1$; bandstop = 2Order unit-circle zeros at z=e^(+/- jtheta), theta=2arctanW_c/4. ANALOG (Analog=True) lowpass = no zeros; highpass/bandpass = Order zeros at the origin; bandstop = 2Order zeros at +/- jW_c. Domain: Order a positive integer; Wc the warped centre frequency (only used for bandstop). z is sized and overwritten; it must allow a complex result for the bandstop and analog-bandstop cases. No NaN is produced. |
| IirFilterMethodToString | Return a human-readable name for a TIirFilterMethod value: fimButter -> 'Butterworth', fimChebyshevI -> 'Chebyshev type I', fimChebyshevII -> 'Chebyshev type II', fimElliptic -> 'Elliptic filter', fimDC -> 'DC filter', fimNotch -> 'Notch filter', fimBessel -> 'Bessel filter'. Pure mapping with no numeric computation; the domain is the full TIirFilterMethod enumeration and every value yields a non-empty string (no exception, no NaN). |