"""
Advanced Computation Module for Physiological Signal Processing
This module provides comprehensive capabilities for physiological
signal processing including ECG, PPG, EEG, and other vital signs.
Author: vitalDSP Team
Date: 2025-01-27
Version: 1.0.0
Key Features:
- Object-oriented design with comprehensive classes
- Multiple processing methods and functions
- NumPy integration for numerical computations
Examples:
---------
Basic usage:
>>> import numpy as np
>>> from vitalDSP.advanced_computation.generative_signal_synthesis import GenerativeSignalSynthesis
>>> signal = np.random.randn(1000)
>>> gen = GenerativeSignalSynthesis()
>>> signal = gen.generate()
"""
import numpy as np
[docs]
class GenerativeSignalSynthesis:
"""
Generative Signal Synthesis for creating synthetic signal data using various methods.
This class provides methods to generate synthetic signals using techniques such as random noise, Gaussian processes,
autoregressive (AR) models, Markov chains, and custom-defined functions.
Methods
-------
generate(method="random_noise", length=100, **kwargs) :
Generates synthetic signals using the specified method.
Example Usage
-------------
signal_synthesizer = GenerativeSignalSynthesis()
# Generate random noise
random_signal = signal_synthesizer.generate(method="random_noise", length=100)
print("Random Noise Signal:", random_signal)
# Generate Gaussian process
gp_signal = signal_synthesizer.generate(method="gaussian_process", length=100, mean=0, std_dev=1, correlation=0.9)
print("Gaussian Process Signal:", gp_signal)
# Generate AR model signal
ar_signal = signal_synthesizer.generate(method="autoregressive", length=100, coeffs=[0.9, -0.5])
print("AR Model Signal:", ar_signal)
# Generate Markov chain signal
markov_signal = signal_synthesizer.generate(method="markov_chain", length=100, states=[-1, 1], transition_matrix=[[0.9, 0.1], [0.1, 0.9]])
print("Markov Chain Signal:", markov_signal)
# Generate custom function signal
custom_signal = signal_synthesizer.generate(method="custom_function", length=100, func=lambda x: np.sin(x))
print("Custom Function Signal:", custom_signal)
"""
def __init__(self):
"""Initialize the GenerativeSignalSynthesis class."""
pass
[docs]
def generate(self, method="random_noise", length=100, **kwargs):
"""
Generate synthetic signals.
Parameters
----------
method : str, optional
The method to use for generating the signal. Options include "random_noise", "gaussian_process",
"autoregressive", "markov_chain", "custom_function". Default is "random_noise".
length : int, optional
The length of the generated signal. Default is 100.
kwargs : dict
Additional parameters depending on the generation method. These include:
- mean (float): Mean of the noise or process (for "random_noise" and "gaussian_process").
- std_dev (float): Standard deviation (for "random_noise" and "gaussian_process").
- correlation (float): Correlation coefficient between successive points (for "gaussian_process").
- coeffs (list of float): Coefficients for the AR model (for "autoregressive").
- states (list): Possible states of the Markov chain (for "markov_chain").
- transition_matrix (list of list of float): State transition matrix (for "markov_chain").
- func (callable): Function to generate the signal (for "custom_function").
Returns
-------
numpy.ndarray
The generated synthetic signal.
Raises
------
ValueError
If the specified generation method is unknown.
"""
if method == "random_noise":
return self._generate_random_noise(length, **kwargs)
elif method == "gaussian_process":
return self._generate_gaussian_process(length, **kwargs)
elif method == "autoregressive":
return self._generate_autoregressive(length, **kwargs)
elif method == "markov_chain":
return self._generate_markov_chain(length, **kwargs)
elif method == "custom_function":
return self._generate_custom_function(length, **kwargs)
else:
raise ValueError(f"Unknown generation method: {method}")
def _generate_random_noise(self, length, mean=0, std_dev=1):
"""
Generate a random noise signal.
Parameters
----------
length : int
Length of the generated signal.
mean : float, optional
Mean of the noise. Default is 0.
std_dev : float, optional
Standard deviation of the noise. Default is 1.
Returns
-------
numpy.ndarray
The generated random noise signal.
Examples
--------
>>> signal_synthesizer = GenerativeSignalSynthesis()
>>> random_signal = signal_synthesizer._generate_random_noise(length=100, mean=0, std_dev=1)
>>> print(random_signal)
"""
return np.random.normal(mean, std_dev, length)
def _generate_gaussian_process(self, length, mean=0, std_dev=1, correlation=0.9):
"""
Generate a synthetic signal using a Gaussian process.
Parameters
----------
length : int
The length of the generated signal.
mean : float, optional
Mean of the Gaussian process. Default is 0.
std_dev : float, optional
Standard deviation of the Gaussian process. Default is 1.
correlation : float, optional
Correlation coefficient between successive points. Default is 0.9.
Returns
-------
numpy.ndarray
The generated Gaussian process signal.
Examples
--------
>>> signal_synthesizer = GenerativeSignalSynthesis()
>>> gp_signal = signal_synthesizer._generate_gaussian_process(length=100, mean=0, std_dev=1, correlation=0.9)
>>> print(gp_signal)
"""
signal = np.zeros(length)
signal[0] = np.random.normal(mean, std_dev)
for i in range(1, length):
signal[i] = correlation * signal[i - 1] + np.random.normal(mean, std_dev)
return signal
def _generate_autoregressive(self, length, coeffs):
"""
Generate a synthetic signal using an autoregressive (AR) model.
Parameters
----------
length : int
Length of the generated signal.
coeffs : list of float
Coefficients for the AR model.
Returns
-------
numpy.ndarray
The generated AR model signal.
Examples
--------
>>> signal_synthesizer = GenerativeSignalSynthesis()
>>> ar_signal = signal_synthesizer._generate_autoregressive(length=100, coeffs=[0.9, -0.5])
>>> print(ar_signal)
"""
signal = np.zeros(length)
p = len(coeffs)
# Initialize the signal with random noise
signal[:p] = np.random.normal(0, 1, p)
for i in range(p, length):
signal[i] = np.sum(
[coeffs[j] * signal[i - j - 1] for j in range(p)]
) + np.random.normal(0, 1)
return signal
def _generate_markov_chain(self, length, states, transition_matrix):
"""
Generate a synthetic signal using a Markov chain.
Parameters
----------
length : int
Length of the generated signal.
states : list
Possible states of the Markov chain.
transition_matrix : list of list of float
State transition matrix.
Returns
-------
numpy.ndarray
The generated Markov chain signal.
Examples
--------
>>> signal_synthesizer = GenerativeSignalSynthesis()
>>> markov_signal = signal_synthesizer._generate_markov_chain(length=100, states=[-1, 1], transition_matrix=[[0.9, 0.1], [0.1, 0.9]])
>>> print(markov_signal)
"""
n_states = len(states)
signal = np.zeros(length, dtype=int)
signal[0] = np.random.choice(n_states)
for i in range(1, length):
signal[i] = np.random.choice(n_states, p=transition_matrix[signal[i - 1]])
return np.array([states[s] for s in signal])
def _generate_custom_function(self, length, func):
"""
Generate a synthetic signal using a custom function.
Parameters
----------
length : int
Length of the generated signal.
func : callable
Function to generate the signal.
Returns
-------
numpy.ndarray
The generated signal.
Examples
--------
>>> signal_synthesizer = GenerativeSignalSynthesis()
>>> custom_signal = signal_synthesizer._generate_custom_function(length=100, func=lambda x: np.sin(x))
>>> print(custom_signal)
"""
return np.array([func(x) for x in range(length)])