# Source code for deltasigma._circ_smooth

# -*- coding: utf-8 -*-
# _circ_smooth.py
# Module providing the circ_smooth function
# 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 circ_smooth() function
"""

from __future__ import division

import numpy as np

from ._ds_hann import ds_hann
from ._utils import circshift

[docs]def circ_smooth(x, n=16):
"""Smoothing of the PSD x for linear x-axis plotting.

**Parameters:**

x : 1D ndarray
The PSD to be smoothed, or equivalently

.. math::

x = \\left|\\mathrm{FFT}\\left(u(t)\\right)(f)\\right|^2

n : int, even, optional
The length of the Hann window used in the smoothing algorithm.

**Returns:**

y : 1D ndarray
The smoothed PSD

.. seealso::

:func:logsmooth, smoothing algorithm suitable for logarithmic x-axis
plotting.

For a comparison of :func:circ_smooth and :func:logsmooth (accessed
through the helper function :func:plotSpectrum) see the following plot.

.. plot::

import numpy as np
from deltasigma import *
from numpy.fft import fft
f0 = 0
osr = 32
Hinf = 1.5
order = 3
ntf = synthesizeNTF(order, osr, 0, Hinf, f0)
f1, f2 = ds_f1f2(osr, f0, quadrature)
delta = 2
Amp = undbv(-3)
f = 0.3
N = 2**12
f1_bin = np.round(f1*N)
f2_bin = np.round(f2*N)
fin = np.round(((1 - f)/2*f1 + (f + 1)/2*f2) * N)
t = np.arange(0, N)
u = Amp*np.cos((2*np.pi/N)*fin*t)
v, xn, xmax, y = simulateDSM(u, ntf, 2)
window = ds_hann(N)
NBW = 1.5/N
spec0 = fft(v * window)/(N/4)
freq = np.linspace(0, 0.5, N/2 + 1)
# plotting
plt.figure(figsize=(12, 7))
plt.subplot(211)
plt.plot(freq, dbv(spec0[:N/2 + 1]), 'c', linewidth=1, label='$S$')
plt.hold(True)
spec_smoothed = circ_smooth(np.abs(spec0)**2., 16)
plt.plot(freq, dbp(spec_smoothed[:N/2 + 1]), 'b--', linewidth=2, label='$\\\\mathrm{circ\\\\_smooth}(S)$')
plotSpectrum(spec0, fin, 'r', linewidth=2, label='$\\\\mathrm{plotSpectrum}(S)$')
Snn = np.abs(evalTF(ntf, np.exp(2j*np.pi*freq)))**2 * 2/12*(delta)**2
plt.plot(freq, dbp(Snn*NBW), 'm', linewidth=1.5, label='$\\\\mathrm{from\\\\ NTF}$')
snr = calculateSNR(spec0[f1_bin:f2_bin + 1], fin - f1_bin)
msg = 'SQNR  =  %.1fdB\\n @ A = %.1fdBFS & osr = %.0f\\n' % \\
(snr, dbv(spec0[fin]), osr)
plt.text(f0 + .45/osr, -20, msg, horizontalalignment='left',
verticalalignment='center')
plt.text(0.5, -3, 'NBW = %.1e ' % NBW, horizontalalignment='right',
verticalalignment='top')
figureMagic((0, 0.5), None, None, (-140, 0), 20, None)
plt.ylabel('Spectrum [dB]')
ax = plt.gca()
ax.set_title('Smoothing and plotting for LOG and LIN axes')
plt.legend(loc=4)
plt.subplot(212)
plt.plot(freq, dbv(spec0[:N/2 + 1]), 'c', linewidth=1, label='$S$')
plt.hold(True)
plotSpectrum(spec0, fin, '--r', linewidth=2, label='$\\\\mathrm{plotSpectrum}(S)$')
plt.plot(freq, dbp(spec_smoothed[:N/2 + 1]), 'b', linewidth=2, label='$\\\\mathrm{circ\\\\_smooth}(S)$')
plt.plot(freq, dbp(Snn*NBW), 'm', linewidth=1.5, label='$\\\\mathrm{from\\\\ NTF}$')
msg = 'SQNR  =  %.1fdB\\n @ A = %.1fdBFS & osr = %.0f\\n' % \\
(snr, dbv(spec0[fin]), osr)
plt.text(f0 + 1./osr, -20, msg, horizontalalignment='left',
verticalalignment='center')
plt.text(0.5, -3, 'NBW = %.1e ' % NBW, horizontalalignment='right',
verticalalignment='top')
figureMagic((0, 0.5), None, None, (-140, 0), 20, None)
ax = plt.gca()
ax.set_xscale('linear')
plt.ylabel('Spectrum [dB]')
plt.xlabel('Normalized frequency ($f_s \\\\rightarrow 1$)')
plt.legend(loc=4)

"""
assert len(x.shape) == 1 or 1 in x.shape
assert n % 2 == 0
nx = max(x.shape)
w = ds_hann(n)/(n/2.)
xw = np.convolve(x, w)
yp = np.hstack((xw[n - 1:nx], xw[:n - 1] + xw[nx:]))
y = circshift(yp, [int(n/2. - 1)])
return y