Source code for deltasigma._mapRtoQ
# -*- coding: utf-8 -*-
# _mapRtoQ.py
# Module providing the mapRtoQ 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 mapRtoQ() function
"""
from __future__ import division
import numpy as np
[docs]def mapRtoQ(ABCDr):
"""Map a real ABCD matrix to a quadrature one.
**Parameters:**
ABCDr : ndarray
A real matrix describing a quadrature system.
``ABCDr`` has its states paired (real, imaginary).
**Returns:**
(ABCDq, ABCDp) : tuple
Where:
ABCDq : ndarray
is the quadrature (complex) version of ABCDr.
ABCDp : ndarray
is the mirror-image system matrix.
.. note:: ``ABCDp`` is zero if ``ABCDr`` has no quadrature errors.
"""
ABCD11 = ABCDr[::2, ::2]
ABCD12 = ABCDr[::2, 1::2]
ABCD21 = ABCDr[1::2, ::2]
ABCD22 = ABCDr[1::2, 1::2]
ABCDq = 0.5*(ABCD11 + ABCD22) + 0.5j*(ABCD21 - ABCD12);
ABCDp = 0.5*(ABCD11 - ABCD22) + 0.5j*(ABCD21 + ABCD12);
return ABCDq, ABCDp