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| """ DR-MUSIC: 抑制呼吸谐波的心跳检测算法 核心:RLS自适应滤波 + 相位差分 + MUSIC频谱估计 """
import numpy as np from scipy import signal from scipy.linalg import svd from typing import Tuple, Optional
class RLSFilter: """ RLS自适应滤波器 用于自适应消除呼吸谐波干扰 """ def __init__( self, filter_order: int = 32, forgetting_factor: float = 0.99, regularization: float = 1.0 ): """ Args: filter_order: 滤波器阶数 forgetting_factor: 遗忘因子 regularization: 正则化参数 """ self.filter_order = filter_order self.forgetting_factor = forgetting_factor self.regularization = regularization self.weights = np.zeros(filter_order) self.P = np.eye(filter_order) * regularization self.x_buffer = np.zeros(filter_order) def filter( self, reference: np.ndarray, primary: np.ndarray ) -> Tuple[np.ndarray, np.ndarray]: """ RLS自适应滤波 Args: reference: 参考信号(呼吸信号) primary: 主信号(包含呼吸和心跳) Returns: output: 滤波输出 error: 误差信号(心跳成分) """ num_samples = len(primary) output = np.zeros(num_samples) error = np.zeros(num_samples) for n in range(num_samples): self.x_buffer = np.roll(self.x_buffer, 1) self.x_buffer[0] = reference[n] output[n] = np.dot(self.weights, self.x_buffer) error[n] = primary[n] - output[n] Px = self.P @ self.x_buffer k = Px / (self.forgetting_factor + self.x_buffer @ Px) self.weights = self.weights + k * error[n] self.P = (self.P - np.outer(k, self.x_buffer @ self.P)) / self.forgetting_factor return output, error
class MUSIC: """ MUSIC频谱估计算法 多信号分类算法,用于高精度频率估计 """ def __init__( self, signal_dim: int = 2, num_freqs: int = 1024 ): """ Args: signal_dim: 信号子空间维度 num_freqs: 频率点数 """ self.signal_dim = signal_dim self.num_freqs = num_freqs def estimate( self, x: np.ndarray, sample_rate: float ) -> Tuple[np.ndarray, np.ndarray]: """ MUSIC频谱估计 Args: x: 输入信号 sample_rate: 采样率 Returns: spectrum: MUSIC伪谱 frequencies: 频率轴 """ M = len(x) // 2 R = np.zeros((M, M), dtype=complex) for i in range(M): for j in range(M): if i + j < len(x): R[i, j] = x[i + j] U, s, Vh = svd(R) noise_subspace = U[:, self.signal_dim:] frequencies = np.linspace(0, sample_rate / 2, self.num_freqs) spectrum = np.zeros(self.num_freqs) for i, f in enumerate(frequencies): omega = 2 * np.pi * f / sample_rate a = np.exp(1j * omega * np.arange(M)) denominator = np.sum(np.abs(noise_subspace.conj().T @ a) ** 2) spectrum[i] = 1.0 / (denominator + 1e-10) return spectrum, frequencies
class DRMUSIC: """ DR-MUSIC算法 结合相位差分、RLS滤波和MUSIC频谱估计 用于高精度心跳检测 """ def __init__( self, rls_order: int = 32, music_signal_dim: int = 2, sample_rate: float = 20.0 ): """ Args: rls_order: RLS滤波器阶数 music_signal_dim: MUSIC信号子空间维度 sample_rate: 采样率 """ self.rls_filter = RLSFilter(filter_order=rls_order) self.music = MUSIC(signal_dim=music_signal_dim) self.sample_rate = sample_rate def process( self, phase_signal: np.ndarray ) -> Tuple[float, float, dict]: """ 完整处理流程 Args: phase_signal: 相位信号 Returns: heart_rate: 心率 (次/分) breathing_rate: 呼吸频率 (次/分) info: 中间信息 """ info = {} phase_diff = np.diff(phase_signal) phase_diff = np.concatenate([[0], phase_diff]) breathing_band = (0.1, 0.5) heartbeat_band = (0.8, 2.0) sos_breathing = signal.butter( 4, breathing_band, btype='band', fs=self.sample_rate, output='sos' ) breathing_signal = signal.sosfilt(sos_breathing, phase_signal) sos_heartbeat = signal.butter( 4, heartbeat_band, btype='band', fs=self.sample_rate, output='sos' ) mixed_signal = signal.sosfilt(sos_heartbeat, phase_diff) _, heartbeat_signal = self.rls_filter.filter( breathing_signal, mixed_signal ) info['breathing_signal'] = breathing_signal info['heartbeat_signal'] = heartbeat_signal spectrum, frequencies = self.music.estimate( heartbeat_signal, self.sample_rate ) info['spectrum'] = spectrum info['frequencies'] = frequencies heartbeat_mask = (frequencies >= 0.8) & (frequencies <= 2.0) heartbeat_spectrum = spectrum * heartbeat_mask heart_freq = frequencies[np.argmax(heartbeat_spectrum)] heart_rate = heart_freq * 60 breathing_mask = (frequencies >= 0.1) & (frequencies <= 0.5) breathing_spectrum = spectrum * breathing_mask breath_freq = frequencies[np.argmax(breathing_spectrum)] breathing_rate = breath_freq * 60 return heart_rate, breathing_rate, info
if __name__ == "__main__": np.random.seed(42) sample_rate = 20.0 duration = 60 num_samples = int(duration * sample_rate) t = np.arange(num_samples) / sample_rate breathing_freq = 0.3 breathing_amplitude = 4.0 breathing_signal = breathing_amplitude * np.sin(2 * np.pi * breathing_freq * t) heartbeat_freq = 1.2 heartbeat_amplitude = 0.5 heartbeat_signal = heartbeat_amplitude * np.sin(2 * np.pi * heartbeat_freq * t) chest_displacement = breathing_signal + heartbeat_signal wavelength = 3.75 phase_signal = 4 * np.pi * chest_displacement / wavelength noise = 0.1 * np.random.randn(num_samples) phase_signal = phase_signal + noise detector = DRMUSIC(sample_rate=sample_rate) heart_rate, breathing_rate, info = detector.process(phase_signal) print("=== DR-MUSIC 测试 ===") print(f"真实心率: {heartbeat_freq * 60:.0f} 次/分") print(f"检测心率: {heart_rate:.0f} 次/分") print(f"误差: {abs(heartbeat_freq * 60 - heart_rate):.1f} 次/分") print() print(f"真实呼吸频率: {breathing_freq * 60:.0f} 次/分") print(f"检测呼吸频率: {breathing_rate:.0f} 次/分") print(f"误差: {abs(breathing_freq * 60 - breathing_rate):.1f} 次/分")
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