Delta Median Preprocessor Transform¶
The Delta Median Preprocessor Transform shifts the input signal by the median of the signal. The is defined as:
For shifting signals by a custom \(\delta\), see the Delta Transform Preprocessor. For more on how we compute the median of a signal, check out median function.
Bases: Preprocess
Preprocess the signal by shifting the signal up by the median value.
__call__(signal, method='linear', where=lambda : not np.isnan(x)) ¶
Compute the difference between the values in signal and median where where is True.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
signal | ndarray | The array to compute the delta with. | required |
method | str | The method to use when computing the quantile. Default is 'linear'. See | 'linear' |
where | Callable[[Union[int, float, int_, float_]], Union[bool, bool_]] | A function that takes a value and returns | lambda : not numpy.isnan(x) |
Returns:
| Type | Description |
|---|---|
ndarray | The shifted signal. |
Examples¶
Signal equilization is a common problem in signal processing. The Delta Median Preprocessor Transform can be used to equilize signals by shifting them by their median. This can be useful for removing the effect of a constant bias in the signal. This is often done in sound engineering when equilizing the sound of different instruments. In the example below, we generate three signals, a guitar signal, a piano signal, and a drums signal. We then apply the Delta Median Preprocessor Transform to each signal.
Transform Signal¶
We first generate the signals. Then we perform the equilization by applying the transform to each signal.
import numpy as np
import autonfeat as aft
# Generating example signals for each instrument
num_samples = 100
time = np.linspace(0, 1, num_samples)
guitar_signal = np.sin(2 * np.pi * 10 * time) # Guitar signal (higher frequency sine wave)
piano_signal = np.cos(2 * np.pi * 2 * time) # Piano signal (cosine wave)
drums_signal = np.random.normal(2, 0.5, num_samples) # Drums signal (random noise with higher mean)
# Defining the transform
preprocessor = aft.preprocess.DeltaMedianPreprocessor()
# Applying the transform to each signal
guitar_eq = preprocessor(guitar_signal)
piano_eq = preprocessor(piano_signal)
drums_eq = preprocessor(drums_signal)
Visualize Transform¶
We can visualize the effect of the transform by plotting the original signals and the shifted signals on the same plot. We can see that the median of each signal is shifted to zero.
import matplotlib.pyplot as plt
# Set up custom line styles
line_styles = ['-', '--', '-.']
# Set up custom color palette
colors = ['#1f77b4', '#ff7f0e', '#2ca02c']
# Plotting all original signals on one subplot
plt.figure(figsize=(10, 10))
plt.subplot(2, 1, 1)
for i, signal in enumerate([guitar_signal, piano_signal, drums_signal]):
plt.plot(time, signal, color=colors[i], linestyle=line_styles[i])
plt.title('Original Signals')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.legend(['Guitar', 'Piano', 'Drums'])
plt.grid(True)
# Plotting all shifted signals on another subplot
plt.subplot(2, 1, 2)
for i, signal in enumerate([guitar_eq, piano_eq, drums_eq]):
plt.plot(time, signal, color=colors[i], linestyle=line_styles[i])
plt.title('Shifted Signals')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.legend(['Guitar', 'Piano', 'Drums'])
plt.grid(True)
plt.tight_layout()
plt.show()
As seen in the figure, the drums signal which had a higher mean than the other signals is shifted down by a larger amount than the other signals. In doing so, we have equilized the signals.
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