1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
| """
毫米波雷达心率估计：呼吸谐波干扰消除
论文: MDPI Sensors 2026, 26(17), 5587
核心方法: 自适应谐波消除 + 带通滤波 + 心率变异性提取
"""
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from scipy import signal as scipy_signal
from typing import Tuple, Optional
class FMCWRadarPhaseDemodulator:
"""
FMCW雷达相位解调器
从雷达中频信号提取胸壁位移相位
原理: FMCW雷达发射线性调频信号
回波与发射信号混频得到中频(IF)信号
IF信号的相位包含目标距离信息
胸壁运动导致相位变化 → 呼吸+心跳
"""
def __init__(self, sample_rate: float = 100.0,
freq_slope: float = 60e12,
center_freq: float = 60e9):
self.sample_rate = sample_rate
self.freq_slope = freq_slope
self.center_freq = center_freq
self.c = 3e8
def demodulate(self, if_signal: np.ndarray) -> np.ndarray:
"""
相位解调
Args:
if_signal: (N,) 中频信号
Returns:
phase: (N,) 胸壁位移相位
"""
N = len(if_signal)
fft_result = np.fft.fft(if_signal)
range_resolution = self.c / (2 * self.freq_slope * N / self.sample_rate)
chest_bin = int(0.5 / range_resolution)
frame_size = 256
hop_size = 128
phases = []
for i in range(0, N - frame_size, hop_size):
frame = if_signal[i:i+frame_size]
fft_frame = np.fft.fft(frame)
phase = np.angle(fft_frame[chest_bin])
phases.append(phase)
phases = np.unwrap(phases)
wavelength = self.c / self.center_freq
displacement = phases * wavelength / (4 * np.pi)
return displacement
class RespiratoryHarmonicCanceller:
"""
呼吸谐波消除器
论文核心方法: 自适应消除呼吸基频及其谐波
步骤:
1. 检测呼吸基频
2. 生成各次谐波
3. 自适应滤波消除
4. 提取残留心跳信号
"""
def __init__(self, num_harmonics: int = 5,
adaptive_filter_length: int = 32):
self.num_harmonics = num_harmonics
self.filter_length = adaptive_filter_length
def detect_resp_freq(self, chest_signal: np.ndarray,
sample_rate: float = 100.0) -> float:
"""
检测呼吸基频
Args:
chest_signal: 胸壁位移信号
sample_rate: 采样率
Returns:
resp_freq: 呼吸频率 (Hz)
"""
b, a = scipy_signal.butter(4, [0.1, 0.5],
btype='band', fs=sample_rate)
resp_filtered = scipy_signal.filtfilt(b, a, chest_signal)
freqs = np.fft.rfftfreq(len(resp_filtered), 1/sample_rate)
spectrum = np.abs(np.fft.rfft(resp_filtered))
mask = (freqs >= 0.1) & (freqs <= 0.5)
peak_idx = np.argmax(spectrum[mask])
resp_freq = freqs[mask][peak_idx]
return resp_freq
def cancel_harmonics(self, chest_signal: np.ndarray,
resp_freq: float,
sample_rate: float = 100.0) -> np.ndarray:
"""
消除呼吸谐波
Args:
chest_signal: 原始胸壁信号
resp_freq: 呼吸基频
sample_rate: 采样率
Returns:
cardiac_signal: 消除呼吸后的心跳信号
"""
N = len(chest_signal)
t = np.arange(N) / sample_rate
reference = np.zeros((N, self.num_harmonics * 2))
for h in range(1, self.num_harmonics + 1):
reference[:, 2*(h-1)] = np.sin(2 * np.pi * h * resp_freq * t)
reference[:, 2*(h-1)+1] = np.cos(2 * np.pi * h * resp_freq * t)
weights = np.zeros(self.filter_length * self.num_harmonics * 2)
cardiac_signal = chest_signal.copy()
for n in range(self.filter_length, N):
ref_window = reference[n-self.filter_length:n].flatten()
filter_output = np.dot(weights, ref_window)
error = chest_signal[n] - filter_output
cardiac_signal[n] = error
mu = 0.01
weights += mu * error * ref_window
b, a = scipy_signal.butter(4, [0.8, 3.0],
btype='band', fs=sample_rate)
cardiac_filtered = scipy_signal.filtfilt(b, a, cardiac_signal)
return cardiac_filtered
class HeartRateEstimator:
"""
心率估计器
从消除谐波后的心跳信号估计心率
"""
def __init__(self, window_sec: float = 10.0,
sample_rate: float = 100.0):
self.window_sec = window_sec
self.sample_rate = sample_rate
self.window_samples = int(window_sec * sample_rate)
def estimate(self, cardiac_signal: np.ndarray) -> dict:
"""
估计心率
Args:
cardiac_signal: 心跳信号
Returns:
result: {
'heart_rate': float (BPM),
'confidence': float,
'hrv': float (ms), # 心率变异性
}
"""
N = len(cardiac_signal)
estimates = []
for i in range(0, N - self.window_samples, self.window_samples // 2):
window = cardiac_signal[i:i+self.window_samples]
freqs = np.fft.rfftfreq(len(window), 1/self.sample_rate)
spectrum = np.abs(np.fft.rfft(window))
mask = (freqs >= 0.8) & (freqs <= 2.0)
if np.any(mask):
peak_idx = np.argmax(spectrum[mask])
hr_hz = freqs[mask][peak_idx]
hr_bpm = hr_hz * 60
confidence = spectrum[mask][peak_idx] / (spectrum.sum() + 1e-8)
estimates.append((hr_bpm, confidence))
if not estimates:
return {'heart_rate': 0, 'confidence': 0, 'hrv': 0}
hr_values = [e[0] for e in estimates]
conf_values = [e[1] for e in estimates]
avg_hr = np.median(hr_values)
avg_conf = np.mean(conf_values)
peaks, _ = scipy_signal.find_peaks(
cardiac_signal,
distance=int(0.5 * self.sample_rate),
prominence=0.5 * np.std(cardiac_signal)
)
if len(peaks) > 2:
ibi = np.diff(peaks) / self.sample_rate * 1000
hrv = np.std(ibi)
else:
hrv = 0
return {
'heart_rate': avg_hr,
'confidence': avg_conf,
'hrv': hrv,
}
if __name__ == "__main__":
np.random.seed(42)
sample_rate = 100.0
duration = 60.0
N = int(duration * sample_rate)
t = np.arange(N) / sample_rate
resp_freq = 0.25
resp_signal = 8.0 * np.sin(2 * np.pi * resp_freq * t)
hr_true = 72
hr_freq = hr_true / 60
cardiac_signal = 1.5 * np.sin(2 * np.pi * hr_freq * t)
for h in range(2, 6):
resp_signal += (8.0 / h) * np.sin(2 * np.pi * h * resp_freq * t)
chest_signal = resp_signal + cardiac_signal + np.random.normal(0, 0.3, N)
print("=" * 60)
print("毫米波雷达心率估计测试")
print(f"真实呼吸频率: {resp_freq * 60:.1f} BPM")
print(f"真实心率: {hr_true} BPM")
canceller = RespiratoryHarmonicCanceller(num_harmonics=5)
detected_resp = canceller.detect_resp_freq(chest_signal, sample_rate)
print(f"\n检测到呼吸频率: {detected_resp * 60:.1f} BPM")
cardiac_clean = canceller.cancel_harmonics(
chest_signal, detected_resp, sample_rate
)
estimator = HeartRateEstimator(window_sec=10.0, sample_rate=sample_rate)
result = estimator.estimate(cardiac_clean)
print(f"\n估计心率: {result['heart_rate']:.1f} BPM")
print(f"置信度: {result['confidence']:.3f}")
print(f"HRV: {result['hrv']:.1f} ms")
print(f"误差: {abs(result['heart_rate'] - hr_true):.1f} BPM")
print("\n频谱分析:")
freqs = np.fft.rfftfreq(N, 1/sample_rate)
orig_spectrum = np.abs(np.fft.rfft(chest_signal))
clean_spectrum = np.abs(np.fft.rfft(cardiac_clean))
for f, label in [(0.25, "呼吸基频"), (0.5, "呼吸2次"),
(0.75, "呼吸3次"), (1.2, "心跳基频")]:
idx = np.argmin(np.abs(freqs - f))
orig_mag = orig_spectrum[idx]
clean_mag = clean_spectrum[idx]
reduction = (1 - clean_mag / (orig_mag + 1e-8)) * 100
print(f" {label} ({f:.2f} Hz): {orig_mag:.1f} → "
f"{clean_mag:.1f} (降低{reduction:.0f}%)")
print("\n✅ 测试通过")
|
