{"id":1073727,"date":"2025-01-08T11:28:16","date_gmt":"2025-01-08T03:28:16","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1073727.html"},"modified":"2025-01-08T11:28:18","modified_gmt":"2025-01-08T03:28:18","slug":"python%e4%b8%8b%e5%a6%82%e4%bd%95%e5%af%b9%e6%95%b0%e6%8d%ae%e8%bf%9b%e8%a1%8c%e5%8e%bb%e8%ba%81-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1073727.html","title":{"rendered":"python\u4e0b\u5982\u4f55\u5bf9\u6570\u636e\u8fdb\u884c\u53bb\u8e81"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25103543\/8a0046ae-86a4-4792-bdfa-06437b98450a.webp\" alt=\"python\u4e0b\u5982\u4f55\u5bf9\u6570\u636e\u8fdb\u884c\u53bb\u8e81\" \/><\/p>\n<p><p> <strong>\u5728Python\u4e2d\u5bf9\u6570\u636e\u8fdb\u884c\u53bb\u566a\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u4f7f\u7528\u6ee4\u6ce2\u5668\u3001\u5e94\u7528\u79fb\u52a8\u5e73\u5747\u6cd5\u3001\u5229\u7528\u5c0f\u6ce2\u53d8\u6362\u3001\u91c7\u7528\u81ea\u9002\u5e94\u6ee4\u6ce2\u5668\u3001\u4f7f\u7528\u5085\u91cc\u53f6\u53d8\u6362\u3002<\/strong> \u5176\u4e2d\uff0c<strong>\u6ee4\u6ce2\u5668<\/strong>\u662f\u4e00\u79cd\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u5b83\u53ef\u4ee5\u901a\u8fc7\u9009\u62e9\u6027\u5730\u6d88\u9664\u7279\u5b9a\u9891\u7387\u7684\u566a\u58f0\u6765\u51c0\u5316\u6570\u636e\u3002<\/p>\n<\/p>\n<p><p>\u6ee4\u6ce2\u5668\u53ef\u4ee5\u5206\u4e3a\u4f4e\u901a\u6ee4\u6ce2\u5668\u3001\u9ad8\u901a\u6ee4\u6ce2\u5668\u3001\u5e26\u901a\u6ee4\u6ce2\u5668\u548c\u5e26\u963b\u6ee4\u6ce2\u5668\u7b49\u3002\u4f4e\u901a\u6ee4\u6ce2\u5668\u5141\u8bb8\u4f4e\u9891\u4fe1\u53f7\u901a\u8fc7\u5e76\u963b\u6b62\u9ad8\u9891\u566a\u58f0\uff0c\u4f7f\u4fe1\u53f7\u66f4\u52a0\u5e73\u6ed1\u3002\u9ad8\u901a\u6ee4\u6ce2\u5668\u5219\u76f8\u53cd\uff0c\u7528\u4e8e\u53bb\u9664\u4f4e\u9891\u566a\u58f0\u3002\u5e26\u901a\u6ee4\u6ce2\u5668\u5141\u8bb8\u7279\u5b9a\u9891\u7387\u8303\u56f4\u5185\u7684\u4fe1\u53f7\u901a\u8fc7\uff0c\u800c\u5e26\u963b\u6ee4\u6ce2\u5668\u5219\u7528\u4e8e\u963b\u6b62\u7279\u5b9a\u9891\u7387\u8303\u56f4\u5185\u7684\u4fe1\u53f7\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u4f7f\u7528\u6ee4\u6ce2\u5668\u53bb\u566a<\/h3>\n<\/p>\n<p><p>\u6ee4\u6ce2\u5668\u662f\u4fe1\u53f7\u5904\u7406\u4e2d\u7684\u91cd\u8981\u5de5\u5177\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u53bb\u9664\u566a\u58f0\u3002\u5728Python\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528SciPy\u5e93\u4e2d\u7684\u6ee4\u6ce2\u529f\u80fd\u6765\u5b9e\u73b0\u8fd9\u4e00\u70b9\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u4f4e\u901a\u6ee4\u6ce2\u5668<\/h4>\n<\/p>\n<p><p>\u4f4e\u901a\u6ee4\u6ce2\u5668\u7528\u4e8e\u5141\u8bb8\u4f4e\u9891\u4fe1\u53f7\u901a\u8fc7\uff0c\u540c\u65f6\u963b\u6b62\u9ad8\u9891\u566a\u58f0\u3002\u5b83\u5728\u53bb\u9664\u9ad8\u9891\u566a\u58f0\u7684\u540c\u65f6\u4fdd\u7559\u4e86\u4fe1\u53f7\u7684\u4e3b\u8981\u7279\u5f81\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>from scipy.signal import butter, filtfilt<\/p>\n<h2><strong>\u751f\u6210\u4e00\u4e2a\u793a\u4f8b\u4fe1\u53f7<\/strong><\/h2>\n<p>t = np.linspace(0, 1, 500, False)  # 1\u79d2\u949f\u5185\u7684\u91c7\u6837<\/p>\n<p>signal = np.sin(2 * np.pi * 7 * t) + np.random.normal(0, 0.5, t.shape)<\/p>\n<h2><strong>\u8bbe\u8ba1\u4e00\u4e2a\u4f4e\u901a\u6ee4\u6ce2\u5668<\/strong><\/h2>\n<p>def butter_lowpass(cutoff, fs, order=5):<\/p>\n<p>    nyq = 0.5 * fs<\/p>\n<p>    normal_cutoff = cutoff \/ nyq<\/p>\n<p>    b, a = butter(order, normal_cutoff, btype=&#39;low&#39;, analog=False)<\/p>\n<p>    return b, a<\/p>\n<p>def lowpass_filter(data, cutoff, fs, order=5):<\/p>\n<p>    b, a = butter_lowpass(cutoff, fs, order=order)<\/p>\n<p>    y = filtfilt(b, a, data)<\/p>\n<p>    return y<\/p>\n<h2><strong>\u5e94\u7528\u4f4e\u901a\u6ee4\u6ce2\u5668<\/strong><\/h2>\n<p>cutoff = 3.5  # \u622a\u6b62\u9891\u7387<\/p>\n<p>fs = 500  # \u91c7\u6837\u9891\u7387<\/p>\n<p>filtered_signal = lowpass_filter(signal, cutoff, fs)<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>import matplotlib.pyplot as plt<\/p>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, filtered_signal, label=&#39;Filtered signal&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001\u9ad8\u901a\u6ee4\u6ce2\u5668<\/h4>\n<\/p>\n<p><p>\u9ad8\u901a\u6ee4\u6ce2\u5668\u7528\u4e8e\u53bb\u9664\u4f4e\u9891\u566a\u58f0\uff0c\u4fdd\u7559\u9ad8\u9891\u4fe1\u53f7\u3002\u5b83\u9002\u7528\u4e8e\u90a3\u4e9b\u9ad8\u9891\u6210\u5206\u5360\u4e3b\u8981\u5730\u4f4d\u7684\u4fe1\u53f7\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>from scipy.signal import butter, filtfilt<\/p>\n<h2><strong>\u8bbe\u8ba1\u4e00\u4e2a\u9ad8\u901a\u6ee4\u6ce2\u5668<\/strong><\/h2>\n<p>def butter_highpass(cutoff, fs, order=5):<\/p>\n<p>    nyq = 0.5 * fs<\/p>\n<p>    normal_cutoff = cutoff \/ nyq<\/p>\n<p>    b, a = butter(order, normal_cutoff, btype=&#39;high&#39;, analog=False)<\/p>\n<p>    return b, a<\/p>\n<p>def highpass_filter(data, cutoff, fs, order=5):<\/p>\n<p>    b, a = butter_highpass(cutoff, fs, order=order)<\/p>\n<p>    y = filtfilt(b, a, data)<\/p>\n<p>    return y<\/p>\n<h2><strong>\u5e94\u7528\u9ad8\u901a\u6ee4\u6ce2\u5668<\/strong><\/h2>\n<p>cutoff = 3.5  # \u622a\u6b62\u9891\u7387<\/p>\n<p>fs = 500  # \u91c7\u6837\u9891\u7387<\/p>\n<p>filtered_signal = highpass_filter(signal, cutoff, fs)<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u6ee4\u6ce2\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, filtered_signal, label=&#39;Filtered signal&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e8c\u3001\u79fb\u52a8\u5e73\u5747\u6cd5\u53bb\u566a<\/h3>\n<\/p>\n<p><p>\u79fb\u52a8\u5e73\u5747\u6cd5\u662f\u4e00\u79cd\u7b80\u5355\u800c\u6709\u6548\u7684\u53bb\u566a\u65b9\u6cd5\uff0c\u901a\u8fc7\u5bf9\u6570\u636e\u8fdb\u884c\u5c40\u90e8\u5e73\u5747\u6765\u5e73\u6ed1\u4fe1\u53f7\u3002\u79fb\u52a8\u5e73\u5747\u6cd5\u7684\u57fa\u672c\u601d\u60f3\u662f\u7528\u4e00\u7ec4\u6570\u636e\u70b9\u7684\u5e73\u5747\u503c\u6765\u4ee3\u66ff\u8be5\u7ec4\u6570\u636e\u70b9\u7684\u4e2d\u5fc3\u503c\uff0c\u4ece\u800c\u51cf\u5c11\u968f\u673a\u566a\u58f0\u7684\u5f71\u54cd\u3002<\/p>\n<\/p>\n<p><h4>1\u3001\u7b80\u5355\u79fb\u52a8\u5e73\u5747\u6cd5<\/h4>\n<\/p>\n<p><p>\u7b80\u5355\u79fb\u52a8\u5e73\u5747\u6cd5\u662f\u4e00\u79cd\u6700\u57fa\u672c\u7684\u79fb\u52a8\u5e73\u5747\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u5bf9\u4e00\u6bb5\u6570\u636e\u53d6\u5e73\u5747\u503c\u6765\u5e73\u6ed1\u6570\u636e\u3002\u53ef\u4ee5\u4f7f\u7528pandas\u5e93\u4e2d\u7684rolling\u65b9\u6cd5\u6765\u5b9e\u73b0\u7b80\u5355\u79fb\u52a8\u5e73\u5747\u6cd5\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import pandas as pd<\/p>\n<h2><strong>\u751f\u6210\u4e00\u4e2a\u793a\u4f8b\u4fe1\u53f7<\/strong><\/h2>\n<p>signal = pd.Series(signal)<\/p>\n<h2><strong>\u5e94\u7528\u7b80\u5355\u79fb\u52a8\u5e73\u5747\u6cd5<\/strong><\/h2>\n<p>window_size = 5  # \u7a97\u53e3\u5927\u5c0f<\/p>\n<p>moving_average = signal.rolling(window=window_size).mean()<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u79fb\u52a8\u5e73\u5747\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, moving_average, label=&#39;Moving Average&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2\u3001\u52a0\u6743\u79fb\u52a8\u5e73\u5747\u6cd5<\/h4>\n<\/p>\n<p><p>\u52a0\u6743\u79fb\u52a8\u5e73\u5747\u6cd5\u5728\u8ba1\u7b97\u5e73\u5747\u503c\u65f6\uff0c\u5bf9\u4e0d\u540c\u7684\u6570\u636e\u70b9\u8d4b\u4e88\u4e0d\u540c\u7684\u6743\u91cd\uff0c\u901a\u5e38\u662f\u6700\u8fd1\u7684\u6570\u636e\u70b9\u6743\u91cd\u8f83\u9ad8\uff0c\u8f83\u8fdc\u7684\u6570\u636e\u70b9\u6743\u91cd\u8f83\u4f4e\u3002\u8fd9\u79cd\u65b9\u6cd5\u80fd\u591f\u66f4\u597d\u5730\u4fdd\u7559\u4fe1\u53f7\u7684\u8d8b\u52bf\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u5e94\u7528\u52a0\u6743\u79fb\u52a8\u5e73\u5747\u6cd5<\/p>\n<p>weights = np.arange(1, window_size + 1)<\/p>\n<p>weighted_moving_average = signal.rolling(window=window_size).apply(lambda x: np.dot(x, weights) \/ weights.sum(), raw=True)<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u52a0\u6743\u79fb\u52a8\u5e73\u5747\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, weighted_moving_average, label=&#39;Weighted Moving Average&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e09\u3001\u4f7f\u7528\u5c0f\u6ce2\u53d8\u6362\u53bb\u566a<\/h3>\n<\/p>\n<p><p>\u5c0f\u6ce2\u53d8\u6362\u662f\u4e00\u79cd\u9002\u7528\u4e8e\u975e\u5e73\u7a33\u4fe1\u53f7\u7684\u53bb\u566a\u65b9\u6cd5\uff0c\u5b83\u53ef\u4ee5\u901a\u8fc7\u5206\u89e3\u4fe1\u53f7\u6765\u63d0\u53d6\u4e0d\u540c\u5c3a\u5ea6\u7684\u4fe1\u606f\u3002\u5728Python\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528PyWavelets\u5e93\u6765\u5b9e\u73b0\u5c0f\u6ce2\u53d8\u6362\u53bb\u566a\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import pywt<\/p>\n<h2><strong>\u751f\u6210\u4e00\u4e2a\u793a\u4f8b\u4fe1\u53f7<\/strong><\/h2>\n<p>signal = np.sin(2 * np.pi * 7 * t) + np.random.normal(0, 0.5, t.shape)<\/p>\n<h2><strong>\u5e94\u7528\u5c0f\u6ce2\u53d8\u6362\u53bb\u566a<\/strong><\/h2>\n<p>def wavelet_denoise(data, wavelet=&#39;db1&#39;, level=1):<\/p>\n<p>    coeffs = pywt.wavedec(data, wavelet, level=level)<\/p>\n<p>    sigma = np.median(np.abs(coeffs[-1])) \/ 0.6745<\/p>\n<p>    uthresh = sigma * np.sqrt(2 * np.log(len(data)))<\/p>\n<p>    coeffs = list(map(lambda x: pywt.threshold(x, uthresh, mode=&#39;soft&#39;), coeffs))<\/p>\n<p>    return pywt.waverec(coeffs, wavelet)<\/p>\n<h2><strong>\u53bb\u566a<\/strong><\/h2>\n<p>denoised_signal = wavelet_denoise(signal, wavelet=&#39;db1&#39;, level=2)<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u53bb\u566a\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, denoised_signal, label=&#39;Denoised signal&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u56db\u3001\u81ea\u9002\u5e94\u6ee4\u6ce2\u5668\u53bb\u566a<\/h3>\n<\/p>\n<p><p>\u81ea\u9002\u5e94\u6ee4\u6ce2\u5668\u662f\u4e00\u79cd\u6839\u636e\u8f93\u5165\u4fe1\u53f7\u7684\u53d8\u5316\u81ea\u52a8\u8c03\u6574\u6ee4\u6ce2\u53c2\u6570\u7684\u6ee4\u6ce2\u5668\uff0c\u5e38\u7528\u4e8e\u5904\u7406\u975e\u5e73\u7a33\u4fe1\u53f7\u3002\u5728Python\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528NLMS\u7b97\u6cd5\u6765\u5b9e\u73b0\u81ea\u9002\u5e94\u6ee4\u6ce2\u5668\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u751f\u6210\u4e00\u4e2a\u793a\u4f8b\u4fe1\u53f7<\/strong><\/h2>\n<p>signal = np.sin(2 * np.pi * 7 * t) + np.random.normal(0, 0.5, t.shape)<\/p>\n<h2><strong>\u5e94\u7528NLMS\u7b97\u6cd5<\/strong><\/h2>\n<p>def nlms_filter(x, d, mu=0.01, M=32):<\/p>\n<p>    N = len(x)<\/p>\n<p>    w = np.zeros(M)<\/p>\n<p>    y = np.zeros(N)<\/p>\n<p>    e = np.zeros(N)<\/p>\n<p>    for n in range(M, N):<\/p>\n<p>        x_n = x[n-M:n][::-1]<\/p>\n<p>        y[n] = np.dot(w, x_n)<\/p>\n<p>        e[n] = d[n] - y[n]<\/p>\n<p>        w = w + mu * e[n] * x_n \/ (np.dot(x_n, x_n) + 1e-5)<\/p>\n<p>    return y, e<\/p>\n<h2><strong>\u53bb\u566a<\/strong><\/h2>\n<p>filtered_signal, error = nlms_filter(signal, signal)<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u53bb\u566a\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, filtered_signal, label=&#39;Filtered signal&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e94\u3001\u4f7f\u7528\u5085\u91cc\u53f6\u53d8\u6362\u53bb\u566a<\/h3>\n<\/p>\n<p><p>\u5085\u91cc\u53f6\u53d8\u6362\u7528\u4e8e\u5c06\u4fe1\u53f7\u4ece\u65f6\u57df\u8f6c\u6362\u5230\u9891\u57df\uff0c\u901a\u8fc7\u5206\u6790\u4fe1\u53f7\u7684\u9891\u7387\u6210\u5206\u6765\u53bb\u9664\u566a\u58f0\u3002\u5728Python\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u4e2d\u7684FFT\u51fd\u6570\u6765\u5b9e\u73b0\u5085\u91cc\u53f6\u53d8\u6362\u53bb\u566a\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u751f\u6210\u4e00\u4e2a\u793a\u4f8b\u4fe1\u53f7<\/strong><\/h2>\n<p>signal = np.sin(2 * np.pi * 7 * t) + np.random.normal(0, 0.5, t.shape)<\/p>\n<h2><strong>\u5e94\u7528\u5085\u91cc\u53f6\u53d8\u6362\u53bb\u566a<\/strong><\/h2>\n<p>def fft_denoise(data, threshold=50):<\/p>\n<p>    fft_coeffs = np.fft.fft(data)<\/p>\n<p>    fft_coeffs[np.abs(fft_coeffs) &lt; threshold] = 0<\/p>\n<p>    return np.fft.ifft(fft_coeffs)<\/p>\n<h2><strong>\u53bb\u566a<\/strong><\/h2>\n<p>denoised_signal = fft_denoise(signal)<\/p>\n<h2><strong>\u7ed8\u5236\u539f\u59cb\u4fe1\u53f7\u548c\u53bb\u566a\u540e\u7684\u4fe1\u53f7<\/strong><\/h2>\n<p>plt.plot(t, signal, label=&#39;Noisy signal&#39;)<\/p>\n<p>plt.plot(t, denoised_signal, label=&#39;Denoised signal&#39;, linewidth=2)<\/p>\n<p>plt.legend()<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u901a\u8fc7\u4e0a\u8ff0\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u5728Python\u4e2d\u4f7f\u7528\u591a\u79cd\u6280\u672f\u5bf9\u6570\u636e\u8fdb\u884c\u53bb\u566a\u3002\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u53d6\u51b3\u4e8e\u4fe1\u53f7\u7684\u7279\u6027\u548c\u5177\u4f53\u7684\u5e94\u7528\u573a\u666f\u3002\u5e0c\u671b\u8fd9\u4e9b\u65b9\u6cd5\u80fd\u591f\u5e2e\u52a9\u60a8\u6709\u6548\u5730\u53bb\u9664\u6570\u636e\u4e2d\u7684\u566a\u58f0\uff0c\u63d0\u9ad8\u6570\u636e\u5206\u6790\u548c\u5904\u7406\u7684\u51c6\u786e\u6027\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5728Python\u4e2d\uff0c\u54ea\u4e9b\u5e38\u7528\u5e93\u53ef\u4ee5\u5e2e\u52a9\u6211\u8fdb\u884c\u6570\u636e\u53bb\u566a\uff1f<\/strong><br 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