_simulateDSM_numba.py

# -*- coding: utf-8 -*-
# _simulateDSM_numba.py
# Module providing the Numba simulateDSM function
# Copyright 2014 Giuseppe Venturini & Shayne Hodge
# 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 simulateDSM() function implemented in Numba
"""

import collections

from warnings import warn

import numpy as np

from scipy.signal import tf2zpk, zpk2ss
from scipy.linalg import orth, norm, inv
from ._utils import carray, _get_zpk

from numba import double, int32, complex64
from numba.types import pyobject
from numba.decorators import jit

# Using object mode, is nopython mode faster?  Array slicing doesn't work in it
# Input data type assumptions
# u = 2D double array
# arg2 = float tuple?
# nlev = 1D int array
# x0 = 1D double array

#@jit(arg_types=[double[:, :], complex64[:], int32[:], double[:]])
@jit()
def simulateDSM(u, arg2, nlev=2, x0=0):
    """Simulate a Delta Sigma modulator

    **Syntax:**

     * [v, xn, xmax, y] = simulateDSM(u, ABCD, nlev=2, x0=0)
     * [v, xn, xmax, y] = simulateDSM(u, ntf, nlev=2, x0=0)

    Compute the output of a general delta-sigma modulator with input u,
    a structure described by ABCD, an initial state x0 (default zero) and
    a quantizer with a number of levels specified by nlev.
    Multiple quantizers are implied by making nlev an array,
    and multiple inputs are implied by the number of rows in u.

    Alternatively, the modulator may be described by an NTF.
    The NTF is zpk object. (And the STF is assumed to be 1.)
    The structure that is simulated is the block-diagonal structure used by
    ``zpk2ss()``.

    **Example:**

    Simulate a 5th-order binary modulator with a half-scale sine-wave input and
    plot its output in the time and frequency domains.::

        import numpy as np
        from deltasigma import *
        OSR = 32
        H = synthesizeNTF(5, OSR, 1)
        N = 8192
        fB = np.ceil(N/(2*OSR))
        f = 85
        u = 0.5*np.sin(2*np.pi*f/N*np.arange(N))
        v = simulateDSM(u, H)[0]

    Graphical display of the results:

    .. plot::

        import numpy as np
        import pylab as plt
        from numpy.fft import fft
        from deltasigma import *
        OSR = 32
        H = synthesizeNTF(5, OSR, 1)
        N = 8192
        fB = np.ceil(N/(2*OSR))
        f = 85
        u = 0.5*np.sin(2*np.pi*f/N*np.arange(N))
        v = simulateDSM(u, H)[0]
        plt.figure(figsize=(10, 7))
        plt.subplot(2, 1, 1)
        t = np.arange(85)
        # the equivalent of MATLAB 'stairs' is step in matplotlib
        plt.step(t, u[t], 'g', label='u(n)')
        plt.hold(True)
        plt.step(t, v[t], 'b', label='v(n)')
        plt.axis([0, 85, -1.2, 1.2]);
        plt.ylabel('u, v');
        plt.xlabel('sample')
        plt.legend()
        plt.subplot(2, 1, 2)
        spec = fft(v*ds_hann(N))/(N/4)
        plt.plot(np.linspace(0, 0.5, N/2 + 1), dbv(spec[:N/2 + 1]))
        plt.axis([0, 0.5, -120, 0])
        plt.grid(True)
        plt.ylabel('dBFS/NBW')
        snr = calculateSNR(spec[:fB], f)
        s = 'SNR = %4.1fdB' % snr
        plt.text(0.25, -90, s)
        s =  'NBW = %7.5f' % (1.5/N)
        plt.text(0.25, -110, s)
        plt.xlabel("frequency $1 \\\\rightarrow f_s$")

    Click on "Source" above to see the source code.
    """

    #fprintf(1,'Warning: You are running the non-mex version of simulateDSM.\n');
    #fprintf(1,'Please compile the mex version with "mex simulateDSM.c"\n');

    nlev = carray(nlev)
    u = np.array(u) if not hasattr(u, 'ndim') else u
    if not max(u.shape) == np.prod(u.shape):
        warn("Multiple input delta sigma structures have had little testing.")
    if u.ndim == 1:
        u = u.reshape((1, -1))
    nu = u.shape[0]
    nq = 1 if np.isscalar(nlev) else nlev.shape[0]
    # extract poles and zeros

    # Removing type checking that is conflicting with Numba
    #if (hasattr(arg2, 'inputs') and not arg2.inputs == 1) or \
    #   (hasattr(arg2, 'outputs') and not arg2.outputs == 1):
    #        raise TypeError("The supplied TF isn't a SISO transfer function.")
    if isinstance(arg2, np.ndarray):
        ABCD = np.asarray(arg2, dtype=np.float64)
    #    if ABCD.shape[1] != ABCD.shape[0] + nu:
    #        raise ValueError('The ABCD argument does not have proper dimensions.')
        form = 1
    else:
        zeros, poles, k = _get_zpk(arg2)
        form = 2
    #raise TypeError('%s: Unknown transfer function %s' % (__name__, str(arg2)))

    # need to set order and form now.
    order = carray(zeros).shape[0] if form == 2 else ABCD.shape[0] - nq

    if not isinstance(x0, collections.Iterable):
        x0 = x0*np.ones((order, 1))
    else:
        x0 = np.array(x0).reshape((-1, 1))

    if form == 1:
        A = ABCD[:order, :order]
        B = ABCD[:order, order:order+nu+nq]
        C = ABCD[order:order+nq, :order]
        D1 = ABCD[order:order+nq, order:order+nu]
    else:
        A, B2, C, D2 = zpk2ss(poles, zeros, -1)    # A realization of 1/H
        # Transform the realization so that C = [1 0 0 ...]
        C, D2 = np.real_if_close(C), np.real_if_close(D2)
        Sinv = orth(np.hstack((np.transpose(C), np.eye(order)))) / norm(C)
        S = inv(Sinv)
        C = np.dot(C, Sinv)
        if C[0, 0] < 0:
            S = -S
            Sinv = -Sinv
        A = np.dot(np.dot(S, A), Sinv)
        B2 = np.dot(S, B2)
        C = np.hstack((np.ones((1, 1)), np.zeros((1, order-1)))) # C=C*Sinv;
        D2 = np.zeros((0,))
        # !!!! Assume stf=1
        B1 = -B2
        D1 = 1
        B = np.hstack((B1, B2))

    N = u.shape[1]
    v = np.empty((nq, N), dtype=np.float64)
    y = np.empty((nq, N), dtype=np.float64)     # to store the quantizer input
    xn = np.empty((order, N), dtype=np.float64) # to store the state information
    xmax = np.abs(x0) # to keep track of the state maxima

    for i in range(N):
        # y0 needs to be cast to real because ds_quantize needs real
        # inputs. If quantization were defined for complex numbers,
        # this cast could be removed
        y0 = np.real(np.dot(C, x0) + np.dot(D1, u[:, i]))
        y[:, i] = y0
        v[:, i] = ds_quantize(y0, nlev)
        x0 = np.dot(A, x0) + np.dot(B, np.vstack((u[:, i], v[:, i])))
        xn[:, i] = np.real_if_close(x0.T)
        xmax = np.max(np.hstack((np.abs(x0), xmax)), axis=1, keepdims=True)

    return v.squeeze(), xn.squeeze(), xmax, y.squeeze()

def ds_quantize(y, n):
    """v = ds_quantize(y,n)
    Quantize y to:

    * an odd integer in [-n+1, n-1], if n is even, or
    * an even integer in [-n, n], if n is odd.

    This definition gives the same step height for both mid-rise
    and mid-tread quantizers.
    """
    v = np.zeros(y.shape)
    for qi in range(n.shape[0]):
        if n[qi] % 2 == 0: # mid-rise quantizer
            v[qi, 0] = 2*np.floor(0.5*y[qi, 0]) + 1
        else: # mid-tread quantizer
            v[qi, 0] = 2*np.floor(0.5*(y[qi, 0] + 1))
        L = n[qi] - 1
        v[qi, 0] = np.sign(v[qi, 0])*np.min((np.abs(v[qi, 0]), L))
    return v