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__extrema(signal) + + max_env = np.interp(range(len(signal)), max_peaks, [signal[i] for i in max_peaks]) + min_env = np.interp(range(len(signal)), min_peaks, [signal[i] for i in min_peaks]) + + return (max_env + min_env) / 2 + + def __IMF(signal): + + resdiual = signal + + while True: + + imf = signal - __mean_env(resdiual) + resdiual = signal - imf + + if np.mean(imf) < tolerance: + break + + return imf, resdiual + + + mean = np.mean(signal) + std = np.std(signal) + + signal = (signal - mean) / std + + imfss = [] + signals = [] + min_imf = max_imf + tmp_imf = max_imf + + for index in range(iterations): + + imfs = [] + + noise = np.random.randn(len(signal)) + noise = noise * 0.1 + + new_signal = signal + noise + signals.append(new_signal) + + tmp_imf = max_imf + + while True: + + imf, residual = __IMF(new_signal) + + imfs.append(imf) + + max_peaks, min_peaks = __extrema(residual) + + if len(max_peaks) < 2 or len(min_peaks) < 2: + + tmp_min = len(imfs) + if tmp_min < min_imf: + min_imf = tmp_min + + break + + if np.abs(np.std(residual)) < tolerance or tmp_imf == 0: + + tmp_min = len(imfs) + if tmp_min < min_imf: + min_imf = tmp_min + + break + + new_signal = residual + tmp_imf -= 1 + + imfss.append(imfs) + + imf_ans = [] + + for i in range(min_imf): + + imf = 0 + + for j in range(iterations): + imf += imfss[j][i] + + imf = imf / iterations + imf_ans.append(imf) + + signal_ans = 0 + + for signal in signals: + signal_ans += signal + + signal_ans = signal_ans / iterations + + residual_ans = signal_ans + + for imf in imf_ans: + + residual_ans = residual_ans - imf + + imf_ans = [imf * std + mean for imf in imf_ans] + residual_ans = residual_ans * std + mean + signal_ans = signal_ans * std + mean + + return imf_ans, residual_ans, signal_ans +``` + + +## Results + +通过EEMD,结果如下: + +![](signal_processing/algorithm/EMD/attachments/Figure_1%201.png) + +![](signal_processing/algorithm/EMD/attachments/Figure_2%201.png) + +![](signal_processing/algorithm/EMD/attachments/Figure_3%201.png) + +EEMD的前几个IMF将高频噪声和白噪声过滤,在IMF7显示了信号原有的模态 +# Reference + +* https://zhuanlan.zhihu.com/p/205345681 +* https://blog.csdn.net/weixin_45317919/article/details/109850346 \ No newline at end of file diff --git a/content/signal_processing/signal_processing_MOC.md b/content/signal_processing/signal_processing_MOC.md index 93a843503..00bfac9b2 100644 --- a/content/signal_processing/signal_processing_MOC.md +++ b/content/signal_processing/signal_processing_MOC.md @@ -53,6 +53,7 @@ date: 2024-03-18 ## Empirical Mode Decomposition * [EMD Basic](signal_processing/algorithm/EMD/basic.md) +* [EEMD](signal_processing/algorithm/EMD/eemd.md) # Software