ellip#

scipy.signal.ellip(N,rp,rs,Wn,btype='low',analog=False,output='ba',fs=None)[source]#

Elliptic (Cauer) digital and analog filter design.

Design an Nth-order digital or analog elliptic filter and returnthe filter coefficients.

Parameters:

Nint

The order of the filter.

rpfloat

The maximum ripple allowed below unity gain in the passband.Specified in decibels, as a positive number.

rsfloat

The minimum attenuation required in the stop band.Specified in decibels, as a positive number.

Wnarray_like

A scalar or length-2 sequence giving the critical frequencies.For elliptic filters, this is the point in the transition band atwhich the gain first drops below -rp.

For digital filters,Wn are in the same units asfs. By default,fs is 2 half-cycles/sample, so these are normalized from 0 to 1,where 1 is the Nyquist frequency. (Wn is thus inhalf-cycles / sample.)

For analog filters,Wn is an angular frequency (e.g., rad/s).

btype{‘lowpass’, ‘highpass’, ‘bandpass’, ‘bandstop’}, optional

The type of filter. Default is ‘lowpass’.

analogbool, optional

When True, return an analog filter, otherwise a digital filter isreturned.

output{‘ba’, ‘zpk’, ‘sos’}, optional

Type of output: numerator/denominator (‘ba’), pole-zero (‘zpk’), orsecond-order sections (‘sos’). Default is ‘ba’ for backwardscompatibility, but ‘sos’ should be used for general-purpose filtering.

fsfloat, optional

The sampling frequency of the digital system.

Added in version 1.2.0.

Returns:

b, andarray, ndarray

Numerator (b) and denominator (a) polynomials of the IIR filter.Only returned ifoutput='ba'.

z, p, kndarray, ndarray, float

Zeros, poles, and system gain of the IIR filter transferfunction. Only returned ifoutput='zpk'.

sosndarray

Second-order sections representation of the IIR filter.Only returned ifoutput='sos'.

See also

ellipord,ellipap

Notes

Also known as Cauer or Zolotarev filters, the elliptical filter maximizesthe rate of transition between the frequency response’s passband andstopband, at the expense of ripple in both, and increased ringing in thestep response.

Asrp approaches 0, the elliptical filter becomes a Chebyshevtype II filter (cheby2). Asrs approaches 0, it becomes a Chebyshevtype I filter (cheby1). As both approach 0, it becomes a Butterworthfilter (butter).

The equiripple passband has N maxima or minima (for example, a5th-order filter has 3 maxima and 2 minima). Consequently, the DC gain isunity for odd-order filters, or -rp dB for even-order filters.

The'sos' output parameter was added in 0.16.0.

The current behavior is forndarray outputs to have 64 bit precision(float64 orcomplex128) regardless of the dtype ofWn butoutputs may respect the dtype ofWn in a future version.

Array API Standard Support

ellip has experimental support for Python Array API Standard compatiblebackends in addition to NumPy. Please consider testing these featuresby setting an environment variableSCIPY_ARRAY_API=1 and providingCuPy, PyTorch, JAX, or Dask arrays as array arguments. The followingcombinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	⚠️ computes graph	n/a

SeeSupport for the array API standard for more information.

Examples

Try it in your browser!

Design an analog filter and plot its frequency response, showing thecritical points:

>>>fromscipyimportsignal>>>importmatplotlib.pyplotasplt>>>importnumpyasnp

>>>b,a=signal.ellip(4,5,40,100,'low',analog=True)>>>w,h=signal.freqs(b,a)>>>plt.semilogx(w,20*np.log10(abs(h)))>>>plt.title('Elliptic filter frequency response (rp=5, rs=40)')>>>plt.xlabel('Frequency [rad/s]')>>>plt.ylabel('Amplitude [dB]')>>>plt.margins(0,0.1)>>>plt.grid(which='both',axis='both')>>>plt.axvline(100,color='green')# cutoff frequency>>>plt.axhline(-40,color='green')# rs>>>plt.axhline(-5,color='green')# rp>>>plt.show()

Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz

>>>t=np.linspace(0,1,1000,False)# 1 second>>>sig=np.sin(2*np.pi*10*t)+np.sin(2*np.pi*20*t)>>>fig,(ax1,ax2)=plt.subplots(2,1,sharex=True)>>>ax1.plot(t,sig)>>>ax1.set_title('10 Hz and 20 Hz sinusoids')>>>ax1.axis([0,1,-2,2])

Design a digital high-pass filter at 17 Hz to remove the 10 Hz tone, andapply it to the signal. (It’s recommended to use second-order sectionsformat when filtering, to avoid numerical error with transfer function(ba) format):

>>>sos=signal.ellip(8,1,100,17,'hp',fs=1000,output='sos')>>>filtered=signal.sosfilt(sos,sig)>>>ax2.plot(t,filtered)>>>ax2.set_title('After 17 Hz high-pass filter')>>>ax2.axis([0,1,-2,2])>>>ax2.set_xlabel('Time [s]')>>>plt.tight_layout()>>>plt.show()

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