Delta Max Preprocessor¶

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

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

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

Preprocess the signal x by shifting each element of x by the maximum of x.

Parameters:

Name	Type	Description	Default
`x`	`ndarray`	The array to compute the difference from its maximum.	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)`
`initial`	`Union[int, float, int_, float_]`	The initial value for the maximum. Default is `-np.inf`.	`-inf`

Returns:

Type	Description
`ndarray`	The shifted signal.

Examples¶

Consider the following example. We generate a sound wave with a frequencey of 500Hz. The sound wave may contain magnitudes that are not safe for the human ear. We can apply the delta max preprocessor function to shift the signal such that it falls within a safe range.

Transform Signal¶

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

# Create a random signal
time = np.linspace(0, 10, 1000)
frequency = 500  # Frequency of the signal in Hz
sound_wave = np.sin(2 * np.pi * frequency * time) + 0.5 * np.sin(2 * np.pi * 2 * frequency * time) + 0.25 * np.sin(2 * np.pi * 3 * frequency * time)

# Shift the sound wave by the peak value to ensure safe listening levels
# if we define a safe listening level as 0.5
safe_level = 0.5
safe_sound = PF.delta_max_tf(sound_wave) + safe_level

Visualize Transform¶

import matplotlib.pyplot as plt

# Plot the original signal and the shifted signal
fig, ax = plt.subplots(figsize=(10, 5))
ax.plot(time, sound_wave, label='Original Signal')
ax.plot(time, safe_sound, label='Shifted Signal')
ax.axhline(y=safe_level, color='red', linestyle='--', linewidth=2)
ax.annotate('Safe Listening Level', xy=(0, safe_level), xytext=(0.5, safe_level + 0.1), arrowprops=dict(facecolor='black', shrink=0.05))
ax.set_xlabel('Time (s)')
ax.set_ylabel('Amplitude')
ax.set_title('Sound Wave')
ax.legend()
plt.tight_layout()
plt.show()

This can be seen in the figure below.

DeltaMax

If you enjoy using AutonFeat, please consider starring the repository ⭐️.