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#!/usr/bin/python
# -*- coding: utf-8 -*-
"""Methods for correlated noise generation"""
from __future__ import division
from __future__ import print_function
import numpy as np
__all__ = ["noise_exponential", "noise_cross_exponential"]
def noise_exponential(N, tau=20, variance=1, deltat=1):
"""Generate exponentially correlated noise.
Parameters
----------
N : integer
Total number of samples
tau : float
Correlation time of the exponential in `deltat`
variance : float
Variance of the noise
deltat : float
Bin size of output array, defines the time scale of `tau`
Returns
-------
a : ndarray
Exponentially correlated noise.
"""
# time constant (inverse of correlationtime tau)
g = deltat / tau
# variance
s0 = variance
# normalization factor (memory of the trace)
exp_g = np.exp(-g)
one_exp_g = 1 - exp_g
z_norm_factor = np.sqrt(1 - np.exp(-2 * g)) / one_exp_g
# create random number array
# generates random numbers in interval [0,1)
randarray = np.random.random(N)
# make numbers random in interval [-1,1)
randarray = 2 * (randarray - 0.5)
# simulate exponential random behavior
a = np.zeros(N)
a[0] = one_exp_g * randarray[0]
for i in np.arange(N - 1) + 1:
a[i] = exp_g * a[i - 1] + one_exp_g * randarray[i]
# Solving the equation iteratively leads to this equation:
# j = np.arange(i)
# a[i] = a[0]*exp_g**(i) + \
# one_exp_g)*np.sum(exp_g**(i-1-j)*randarray[1:i+1])
a = a * z_norm_factor * s0
return a
def noise_cross_exponential(N, tau=20, variance=1, deltat=1):
"""Generate exponentially cross-correlated noise.
Parameters
----------
N : integer
Total number of samples
tau : float
Correlation time of the exponential in `deltat`
variance : float
Variance of the noise
deltat : float
Bin size of output array, defines the time scale of `tau`
Returns
-------
a, randarray : ndarrays
Array `a` has positive exponential correlation to the 'truly'
random array `randarray`.
"""
# time constant (inverse of correlationtime tau)
g = deltat / tau
# variance
s0 = variance
# normalization factor (memory of the trace)
exp_g = np.exp(-g)
one_exp_g = 1 - exp_g
z_norm_factor = np.sqrt(1 - np.exp(-2 * g)) / one_exp_g
# create random number array
# generates random numbers in interval [0,1)
randarray = np.random.random(N)
# make numbers random in interval [-1,1)
randarray = 2 * (randarray - 0.5)
# simulate exponential random behavior
a = np.zeros(N)
a[0] = one_exp_g * randarray[0]
b = np.zeros(N)
b[0] = one_exp_g * randarray[0]
# slow
# for i in np.arange(N-1)+1:
# for j in np.arange(i-1):
# a[i] += exp_g**j*randarray[i-j]
# a[i] += one_exp_g*randarray[i]
# faster
j = np.arange(N + 5)
for i in np.arange(N - 1) + 1:
a[i] += np.sum(exp_g**j[2:i + 1] * randarray[2:i + 1][::-1])
a[i] += one_exp_g * randarray[i]
a *= z_norm_factor * s0
randarray = randarray * z_norm_factor * s0
return a, randarray
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