Recursive Average Filter

The Recursive Average Filter is a simple yet effective signal-processing technique that incrementally computes the average when the data volume is too large to process in a single pass or when data arrive as a stream.

Recursive Average Filter classes

class source.smoother.incremental.RecursiveAverage

Bases: object

Recursive Average Filter for incremental average computation.

Initialize the RecursiveAverage object.

__init__() → None

Initialize the RecursiveAverage object.

fit(observations: list[ndarray]) → None

Fit the recursive mean to a set of observations.

Parameters:

observations (list of np.ndarray) – List of observation vectors.

Returns:

list_smooth – List of recursive means after each observation.

Return type:

list of np.ndarray

update(observation: ndarray) → None

Update the recursive 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 RecursiveAverage

# 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 = RecursiveAverage()
list_means = []
# update the model with each observation
for observation in observations:
   model.update(observation)
   list_means.append(model.recursive_mean)

# verify that the final recursive mean matches the batch mean
round(model.recursive_mean, 3) == round(np.mean(observations),3)

# plot the means: batch mean vs recursive mean
plt.figure(figsize=(15, 4))
plt.plot(observations, label='Observations')
plt.plot(list_means, label='Recursive Mean', color='red')
plt.hlines(np.mean(observations), 0, len(observations), colors='green', label='Batch Mean')
plt.legend()
plt.show()

Plotting