Delta Std Preprocessor¶

The delta std preprocessor function shifts the input signal by the std of the signal. This is defined as:

\[ x_{shifted_{i}} = x_{i} - \sigma_{x}, \quad \forall i \in \{1, \dots, N\} \]

For shifting signals by a custom \(\delta\), see the delta preprocessor function. For more on how we compute the std of a signal, check out std function.

Preprocess the signal x by shifting each element of x by the standard deviation of x.

Parameters:

Name	Type	Description	Default
`x`	`ndarray`	The array to shift by its standard deviation.	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
`ndarray`	The shifted signal.

Examples¶

Here we look at an example where we shift two signals by their std to demonstrate the effect of the delta std preprocessor function.

Transform Signal¶

First, we define the signals as two normal distributions with different means and standard deviations. Then, we apply the delta std preprocessor function to both signals.

A univariate normal distribution with mean \(\mu\) and std \(\sigma\) is defined as:

\[ \mathcal{N}(\mu, \sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{-\frac{(x - \mu)^{2}}{2 \sigma^{2}}} \]

import numpy as np
import autonfeat.preprocess.functional as PF

# Number of samples
n_samples = 100

# Generate sample data
x1 = np.random.normal(0, 1, n_samples)
x2 = np.random.normal(5, 5, n_samples)

shifted_x1 = PF.delta_std_tf(x1)
shifted_x2 = PF.delta_std_tf(x2)

Visualize Transform¶

Next, we visualize the effect of the transform on the signals.

import matplotlib.pyplot as plt

# Plot original data
plt.figure(figsize=(8, 4))
plt.subplot(1, 2, 1)
plt.plot(x1, 'b.', label='x1')
plt.plot(x2, 'r.', label='x2')
plt.legend()
plt.title('Original Data')

# Plot shifted data
plt.subplot(1, 2, 2)
plt.plot(shifted_x1, 'b.', label='x1 shifted')
plt.plot(shifted_x2, 'r.', label='x2 shifted')
plt.legend()
plt.title('Shifted Data')

plt.tight_layout()
plt.show()

This can be seen in the figure below.

DeltaStd

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