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Standard Deviation Transform

The standard deviation transform computes the standard deviation of a window. When combined with the SlidingWindow abstraction, the standard deviation transform can be used to compute the std feature of a time series. The standard deviation is defined as:

\[ \sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2} \]

where \(x_i\) is the \(i\)-th element of the window, \(n\) is the number of elements in the window, and \(\mu\) is the mean of the window.

Bases: Transform

Compute the standard deviation of the values in x.

__call__(signal_window, ddof=0, where=lambda : not np.isnan(x))

Compute the standard deviation of the signal window provided.

Parameters:

Name Type Description Default
signal_window ndarray

The signal window to find the standard deviation of.

 required
ddof Union[int, int_]

The delta degrees of freedom. Default is 0. See numpy.std for more information.

 0
where Callable[[Union[int, float, int_, float_]], Union[bool, bool_]]

A function that takes a value and returns True or False. Default is lambda x: not np.isnan(x) i.e. a measurement is valid if it is not a NaN value.

 lambda : not numpy.isnan(x)

Returns:

Type Description
Union[float_, int_]

A scalar value representing the standard deviation of the signal.

Examples

import numpy as np
import autonfeat as aft

# Random data
n_samples = 100
x = np.random.rand(n_samples)

# Create sliding window
ws = 10
ss = 10
window = aft.SlidingWindow(window_size=ws, step_size=ss)

# Create transform
tf = aft.StdTransform()

# Get featurizer
featurizer = window.use(tf)

# Get features
features = featurizer(x)

# Print features
print(window)
print(tf)
print(features)

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