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Module « scipy.signal »

Fonction besselap - module scipy.signal

Signature de la fonction besselap

def besselap(N, norm='phase') 

Description

help(scipy.signal.besselap)

Return (z,p,k) for analog prototype of an Nth-order Bessel filter.

Parameters
----------
N : int
    The order of the filter.
norm : {'phase', 'delay', 'mag'}, optional
    Frequency normalization:

    ``phase``
        The filter is normalized such that the phase response reaches its
        midpoint at an angular (e.g., rad/s) cutoff frequency of 1. This
        happens for both low-pass and high-pass filters, so this is the
        "phase-matched" case. [6]_

        The magnitude response asymptotes are the same as a Butterworth
        filter of the same order with a cutoff of `Wn`.

        This is the default, and matches MATLAB's implementation.

    ``delay``
        The filter is normalized such that the group delay in the passband
        is 1 (e.g., 1 second). This is the "natural" type obtained by
        solving Bessel polynomials

    ``mag``
        The filter is normalized such that the gain magnitude is -3 dB at
        angular frequency 1. This is called "frequency normalization" by
        Bond. [1]_

    .. versionadded:: 0.18.0

Returns
-------
z : ndarray
    Zeros of the transfer function. Is always an empty array.
p : ndarray
    Poles of the transfer function.
k : scalar
    Gain of the transfer function. For phase-normalized, this is always 1.

See Also
--------
bessel : Filter design function using this prototype

Notes
-----
To find the pole locations, approximate starting points are generated [2]_
for the zeros of the ordinary Bessel polynomial [3]_, then the
Aberth-Ehrlich method [4]_ [5]_ is used on the Kv(x) Bessel function to
calculate more accurate zeros, and these locations are then inverted about
the unit circle.

References
----------
.. [1] C.R. Bond, "Bessel Filter Constants",
       http://www.crbond.com/papers/bsf.pdf
.. [2] Campos and Calderon, "Approximate closed-form formulas for the
       zeros of the Bessel Polynomials", :arXiv:`1105.0957`.
.. [3] Thomson, W.E., "Delay Networks having Maximally Flat Frequency
       Characteristics", Proceedings of the Institution of Electrical
       Engineers, Part III, November 1949, Vol. 96, No. 44, pp. 487-490.
.. [4] Aberth, "Iteration Methods for Finding all Zeros of a Polynomial
       Simultaneously", Mathematics of Computation, Vol. 27, No. 122,
       April 1973
.. [5] Ehrlich, "A modified Newton method for polynomials", Communications
       of the ACM, Vol. 10, Issue 2, pp. 107-108, Feb. 1967,
       :DOI:`10.1145/363067.363115`
.. [6] Miller and Bohn, "A Bessel Filter Crossover, and Its Relation to
       Others", RaneNote 147, 1998,
       https://www.ranecommercial.com/legacy/note147.html

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