Low Pass Filter¶

The Low Pass Filter is a fundamental tool in signal processing used to remove high-frequency noise from a signal while preserving the low-frequency components. The filter is based on a recursive algorithm that continuously updates the filtered value based on the current input and the previous filtered value.

Low Pass Filter classes¶

class source.smoother.incremental.LowPassFilter(alpha: float = 0.999)¶

Bases: object

Low-Pass Filter using Exponential Moving Average.

Parameters:: alpha (float, optional) – Smoothing factor between 0 and 1.

Initialize the LowPassFilter object.

Parameters:: alpha (float, optional) – Smoothing factor between 0 and 1.

__init__(alpha: float = 0.999) → None¶

Initialize the LowPassFilter object.

Parameters:: alpha (float, optional) – Smoothing factor between 0 and 1.

fit(observations: list[ndarray]) → None¶

Fit the low-pass mean to a set of observations.

Parameters:: observations (list of np.ndarray) – List of observation vectors.
Returns:: list_smooth – List of low-pass means after each observation.
Return type:: list of np.ndarray

update(observation: ndarray) → None¶

Update the low-pass mean with a new observation.

Parameters:: observation (np.ndarray) – New observation to update the mean.

Example Usage¶

import numpy as np
import matplotlib.pyplot as plt
from source.generator.change_point_generator import ChangePointGenerator
from source.smoother.incremental import LowPassFilter

# Generate time series data with change points
generator = ChangePointGenerator(num_segments=3,
                                segment_length=1000,
                                change_point_type='sudden_shift',
                                seed=12)  # set seed for reproducibility
generator.generate_data()
observations = generator.get_data()

# create the model
model = LowPassFilter(alpha=0.99)
list_filtered = []
# update the model with each observation
for observation in observations:
    model.update(observation)
    list_filtered.append(model.lowpass_mean)

# plot the filtered values
plt.figure(figsize=(15, 4))
plt.plot(observations, label='Observations')
plt.plot(list_filtered, label='Low Pass Filtered', color='orange')
plt.legend()
plt.show()

Plotting