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_synthesizeNTF1.py
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_synthesizeNTF1.py
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# -*- coding: utf-8 -*-
# _synthesizeNTF1.py
# Module providing the synthesizeNTF1 function
# This file is distributed with python-deltasigma.
# Copyright 2013 Giuseppe Venturini
#
# 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.
#
# The following code has been taken with little modifications from pydsm,
# its original copyright notice follows:
#
# Copyright (c) 2012, Sergio Callegari
# All rights reserved.
#
# The code was ported from the MATLAB Delta Sigma toolbox, which is
# Copyright (c) 2009, Richard Schreier
#
# The three software follow the same license, known as the 2-clause BSD.
# See the LICENSE file for details.
"""
Module providing the synthesizeNTF1() function.
"""
# The following code is
# Copyright (c) 2012, Sergio Callegari
# All rights reserved.
# Portions of code ported from the DELSIG toolbox
# Copyright (c) 2009, Richard Schreier
import numpy as np
from scipy.optimize import fmin_l_bfgs_b
from warnings import warn
from ._evalTF import evalTF
from ._utils import cplxpair
from ._ds_optzeros import ds_optzeros
from ._ds_synNTFobj1 import ds_synNTFobj1
from ._padl import padl
from ._constants import eps
def synthesizeNTF1(order, osr, opt, H_inf, f0):
"""
Synthesize a noise transfer function (NTF) for a delta-sigma modulator optimizing the result.
"""
# Determine the zeros.
if f0 != 0:
# Bandpass design-- halve the order temporarily.
order = order/2
dw = np.pi/(2*osr)
else:
dw = np.pi/osr
if opt.ndim == 0:
# opt is a number
if opt == 0:
z = np.zeros(order)
else:
z = dw*ds_optzeros(order, 1 + np.fmod(opt-1, 2))
if z.size == 0:
raise ValueError('Cannot synthesize NTF zeros')
if f0 != 0:
# Bandpass design-- shift and replicate the zeros.
order = order*2
z = np.sort(z) + 2*np.pi*f0
z = np.vstack((z,-z)).transpose().flatten()
z = np.exp(1j*z)
else:
z = opt
zp = z[np.angle(z) > 0]
x0 = (np.angle(zp)-2*np.pi*f0) * osr / np.pi
if opt.size == 1 and opt == 4 and f0 != 0:
# Do not optimize the zeros at f0
x0 = np.delete(x0, np.nonzero(abs(x0) < eps))
p = np.zeros(order)
k = 1
Hinf_itn_limit = 100
fprev = 0
opt_iteration = 5 # Max number of zero-optimizing/Hinf iterations
while opt_iteration > 0:
# Iteratively determine the poles by finding the value of the x
# parameter which results in the desired H_inf
ftol = 1e-10
if f0 > 0.25:
z_inf = 1
else:
z_inf = -1
if f0 == 0:
# Lowpass design
HinfLimit = 2**order
# !!! The limit is actually lower for opt=1 and low OSR
if H_inf >= HinfLimit:
warn('Unable to achieve specified Hinf.\n'
'Setting all NTF poles to zero.')
p = np.zeros(order)
else:
x = 0.3**(order-1) # starting guess
for itn in range(1, Hinf_itn_limit+1):
me2 = -0.5*(x**(2./order))
w = (2*np.arange(1,order+1)+1)*np.pi/order
mb2 = 1+me2*np.exp(1j*w)
p = mb2 - np.sqrt(mb2**2-1)
# Reflect poles to be inside the unit circle
out = abs(p)>1
p[out] = 1/p[out]
# The following is not exactly what delsig does.
# We do not have an identical cplxpair
p = cplxpair(p)
f = np.real(evalTF((z, p, k), z_inf))-H_inf
if itn == 1:
delta_x = -f/100
else:
delta_x = -f*delta_x/(f-fprev)
xplus = x+delta_x
if xplus > 0:
x = xplus
else:
x = x*0.1
fprev = f
if abs(f) < 1e-10 or abs(delta_x) < 1e-10:
break
if x > 1e6:
warn('Unable to achieve specified Hinf.\n'
'Setting all NTF poles to zero.')
p = np.zeros(order)
break
if itn == Hinf_itn_limit:
warn('Danger! Iteration limit exceeded.')
else:
# Bandpass design
x = 0.3**(order/2-1) # starting guess (not very good for f0~0)
if f0 > 0.25:
z_inf = 1.
else:
z_inf = -1.
c2pif0 = np.cos(2*np.pi*f0)
for itn in range(1, Hinf_itn_limit+1):
e2 = 0.5*x**(2./order)
w = (2*np.arange(order)+1)*np.pi/order
mb2 = c2pif0 + e2*np.exp(1j*w)
p = mb2 - np.sqrt(mb2**2-1)
# Reflect poles to be inside the unit circle
out = abs(p)>1
p[out] = 1/p[out]
# The following is not exactly what delsig does.
p = cplxpair(p)
f = np.real(evalTF((z, p, k), z_inf))-H_inf
if itn == 1:
delta_x = -f/100
else:
delta_x = -f*delta_x/(f-fprev)
xplus = x+delta_x
if xplus > 0:
x = xplus
else:
x = x*0.1
fprev = f
if abs(f) < 1e-10 or abs(delta_x) < 1e-10:
break
if x > 1e6:
warn('Unable to achieve specified Hinf.\n'
'Setting all NTF poles to zero.')
p = np.zeros(order)
break
if itn == Hinf_itn_limit:
warn('Danger! Iteration limit exceeded.')
# ---- Zero optimization part
if (opt.size == 1 and opt < 3) or opt.size > 1:
# Do not optimize the zeros
opt_iteration = 0
else:
if f0 == 0:
ub = np.ones(x0.size)
lb = np.zeros(x0.size)
else:
ub = 0.5*np.ones(x0.size)
lb = -ub
# options = optimset('TolX',0.001, 'TolFun',0.01, 'MaxIter',100 );
# options = optimset(options,'LargeScale','off');
# options = optimset(options,'Display','off');
# %options = optimset(options,'Display','iter');
opt_result = fmin_l_bfgs_b(ds_synNTFobj1, x0, args=(p, osr, f0),
approx_grad=True, bounds=list(zip(lb,ub)))
x=opt_result[0]
x0 = x
z = np.exp(2j*np.pi*(f0+0.5/osr*x))
if f0 > 0:
z = padl(z, len(p)/2, np.exp(2j*np.pi*f0))
z = np.concatenate((z, z.conj()), axis=1)
if f0 == 0:
z = padl(z, len(p), 1)
if np.abs(np.real(evalTF((z, p, k), z_inf)) - H_inf ) < ftol:
opt_iteration = 0
else:
opt_iteration = opt_iteration - 1
z = cplxpair(z)
return (z, p, k)