Source code for deltasigma._infnorm

# -*- coding: utf-8 -*-
# This module provides the infnorm 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
# LICENSE file for the licensing terms.

"""This module provides the infnorm() function, which finds the infinity
norm of a z-domain transfer function.

from __future__ import division

from warnings import warn

import numpy as np
from scipy.optimize import fminbound

from ._evalTF import evalTF
from ._nabsH import nabsH

[docs]def infnorm(H): """Find the infinity norm of a z-domain transfer function. **Parameters:** H : object the LTI description of the DT system, which can be in one of the following forms: * an LTI object, * a zpk tuple, * a (num, den) tuple, * an ABCD matrix (internally converted to zpk representation), * a list-like containing the A, B, C, D matrices (also internally converted to zpk representation). **Returns:** Hinf : float The infinity norm of ``H``. fmax : float The frequency to which Hinf corresponds. """ # Get a rough idea of the location of the maximum. N = 129 w = np.linspace(0, 2*np.pi, num=N, endpoint=True) dw = 2*np.pi/(N-1) Hval = evalTF(H, np.exp(1j*w)) Hinf = np.max(np.abs(Hval)) wi = np.where(np.abs(Hval) == Hinf)[0] # Home in using the scipy "fminbound" function. # original MATLAB code: # wmax = fminbnd(nabsH, w(wi)-dw, w(wi)+dw, options, H); wmax = fminbound(nabsH, w[wi]-dw, w[wi]+dw, args=(H,), \ xtol=1e-08, maxfun=5000, full_output=0) if wmax is None: warn('Hinf: scipy.optimize.fminbound() failed.' + ' The result returned may not be very accurate.') wmax = w[wi] Hinf = -nabsH(wmax, H); fmax = wmax/(2*np.pi); # in the original Toolbox, wmax is returned (seems to be never used though) # rep? We return fmax. return Hinf, fmax