Lag Preprocessor¶

This preprocessor computes the lag transform of the input signal. This is shifts the signal elements by some an integer value to a new index. The lag transform is defined as:

\[ x_{t, \tau} = x_{t - \tau} \]

where \(x_{t, \tau}\) is the lag transform of \(x_t\) by some integer amount \(\tau\).

The lag transform is useful for:

Identifying periodicity in the signal.

Identifying trends in the signal.

Limitations¶

When the signal is lagged, the first \(\tau\) elements are set to np.nan values. This is because the lag transform is undefined for these elements. Therefore, when being used the user must ensure that these values are handled appropriately.

Only arrays of floats are supported. If passed an array of another type, it will be cast to float. If this fails, the function will raise an exception.

Bases: Preprocess

Preprocess the signal by shifting the signal by some delta value.

`call(signal, lag, where=lambda : not np.isnan(x))` ¶

Roll the signal by a lag where where is True. This pads the shifted signal with NaN values.

Parameters:

Name	Type	Description	Default
`signal`	`ndarray`	The array to roll.	required
`lag`	`Union[int, float, int_, float_]`	The lag to apply to the signal.	required
`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¶

Consider the following discrete 1D signal:

\[ x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] \]

Transform Signal¶

import numpy as np
import autonfeat as aft

# Define signal
num_samples = 10
signal = np.arange(1, num_samples + 1)

lag = 2

# Preprocess and transform signal
transformed_signal = preprocessor(signal, lag=lag)

Visualize Transform¶

We then visualize the signal and the transformed signal. The transformed signal is shifted by some integer amount \(\tau = 2\). For visualization, we convert any np.nan values to 0.

import matplotlib.pyplot as plt

transformed_signal = np.nan_to_num(transformed_signal)

# Plot results
fig, ax = plt.subplots(1, 1, figsize=(10, 5))
ax.plot(signal, label='Original Signal')
ax.plot(transformed_signal, label='Lag Transformed Signal')
ax.set_xlabel('Time')
ax.set_ylabel('Signal')
ax.set_title('Lag Preprocessor')
ax.legend()
ax.grid()
plt.show()

Lag

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