Defining a white noise process in Python

Question

I need to draw samples from a white noise process in order to implement a particular integral numerically.

How do I generate this with Python (i.e., numpy, scipy, etc.)?

Answer 1

You can achieve this through the numpy.random.normal function, which draws a given number of samples from a Gaussian distribution.

import numpy
import matplotlib.pyplot as plt

mean = 0
std = 1 
num_samples = 1000
samples = numpy.random.normal(mean, std, size=num_samples)

plt.plot(samples)
plt.show()

Answer 2

Short answer is numpy.random.random(). Numpy site description

But since I find more and more answers to similar questions written as numpy.random.normal, I suspect a little description is needed. If I do understand Wikipedia (and a few lessons at the University) correctly, Gauss and White Noise are two separate things. White noise has Uniform distribution, not Normal (Gaussian).

import numpy.random as nprnd
import matplotlib.pyplot as plt

num_samples = 10000
num_bins = 200

samples = numpy.random.random(size=num_samples)

plt.hist(samples, num_bins)
plt.show()

This is my first answer, so if you correct mistakes possibly made by me here, I'll gladly update it. Thanks =)

Answer 3

Create random samples with normal distribution (Gaussian) with numpy.random.normal:

import numpy as np
import seaborn as sns

mu, sigma = 0, 1 # mean and standard deviation
s = np.random.normal(mu, sigma, size=1000) # 1000 samples with normal distribution

# seaborn histogram with Kernel Density Estimation
sns.distplot(s, bins=40, hist_kws={'edgecolor':'black'})