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_dsclansNTF.py
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_dsclansNTF.py
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# -*- coding: utf-8 -*-
# _dsclansNTF.py
# Module providing the dsclansNTF function
# Copyright 2013 Giuseppe Venturini
# This file is part of python-deltasigma.
#
# python-deltasigma is a 1:1 Python replacement of Richard Schreier's
# MATLAB delta sigma toolbox (aka "delsigma"), upon which it is heavily based.
# The delta sigma toolbox is (c) 2009, Richard Schreier.
#
# python-deltasigma is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# LICENSE file for the licensing terms.
"""Module providing the dsclansNTF() function
"""
import numpy as np
from ._utils import carray, zpk
def dsclansNTF(x, order, rmax, Hz):
""" Conversion of clans parameters into a NTF.
Translate x into H.
I've changed the relationships between (zeta, wn) and x
in order to guarantee LHP roots of the s-polynomial.
Returns the NTF, a (simplified) zpk object.
"""
x = x.squeeze()
Hz = carray(Hz)
Hz = Hz.reshape((-1,))
Hp = np.zeros((1,), dtype=np.complex128)
odd = (order % 2 == 1)
if odd:
s = -x[0]**2.
Hp[0] = rmax*(1. + s)/(1. - s)
for i in range(0+1*odd, order, 2):
Hp = np.hstack((Hp, np.zeros((2,))))
zeta = x[i]**2
wn = x[i + 1]**2
s = np.roots(np.array((1, 2*zeta*wn, wn**2)))
Hp[i:i+2] = rmax*(1. + s)/(1. - s)
H = (Hz, Hp, 1.)
return H
def test_dsclansNTF():
"""Test function for dsclansNTF()
"""
x = dsclansNTF(np.arange(1, 100.001, .001), 3, .5, 100)
rt = np.array(x[1][:])
rt.sort()
rp = np.array([0, -0.016805373426715, 0.014809370415763])
rp.sort()
rz = (100., )
assert np.allclose(rp, rt, rtol=1e-5, atol=1e-6)
assert np.allclose(rz, x[0], rtol=1e-5, atol=1e-8)
rp = np.array([0.35378443+0.j, 0.34187718+0.22831019j,
0.34187718-0.22831019j, 0.32978826+0.59355161j,
0.32978826-0.59355161j])
x = np.array([0.67623674, 0.9277613 , 0.70365961, 0.60374009, 0.78008118])
Hz = np.array([0.99604531 - 0.08884669j, 0.99604531 +0.08884669j,
0.99860302 - 0.05283948j, 0.99860302 +0.05283948j, 1.00000000 +0.j])
tp = dsclansNTF(x, order=5, rmax=.95, Hz=Hz)[1]
assert np.allclose(rp, tp, rtol=1e-5, atol=1e-6)