从数据中过滤正确的频率

Question

我正在尝试使用Butterworth函数从某些数据中滤除信号。信号相当干净，但我似乎无法正确滤除它。

我尝试使用不同的频率范围而没有运气（频率介于1Hz和1.3Hz之间）。我也尝试过使用不同的订单，但实际上并不能找到一个好的

data = [351.1475409836066,351.1475409836066,351.1475409836066,350.93877551020404,350.93877551020404,350.93877551020404,350.93877551020404,351.1475409836066,351.1475409836066,351.18367346938777,351.1475409836066,351.1475409836066,351.1475409836066,351.1475409836066,351.5702479338843,351.1475409836066,351.1475409836066,351.1475409836066,350.69387755102036,350.2834008097166,350.2834008097166,350.2834008097166,350.2834008097166,350.3225806451613,350.3225806451613,350.3225806451613,350.3225806451613,350.3225806451613,350.08064516129036,350.08064516129036,350.08064516129036,350.08064516129036,350.4878048780488,350.5263157894737,350.5263157894737,350.5263157894737,350.5263157894737,350.93877551020404,350.93877551020404,350.93877551020404,351.1475409836066,351.1475409836066,351.18367346938777,351.18367346938777,351.1475409836066,351.1475409836066,350.93877551020404,350.93877551020404,350.93877551020404,350.93877551020404,350.93877551020404,350.93877551020404,350.93877551020404,351.1475409836066,351.1475409836066,351.1475409836066,351.1475409836066,351.1475409836066,351.1475409836066,351.1475409836066,351.1475409836066,351.5702479338843,351.6049382716049,351.6049382716049,351.6049382716049,351.8181818181818,352.06611570247935,352.3140495867769,352.06611570247935,352.06611570247935,352.75,352.5,352.75,352.5,352.0331950207469,352.06611570247935,352.06611570247935,352.06611570247935,352.06611570247935,352.06611570247935,352.09876543209873,352.09876543209873,352.3140495867769,352.0331950207469,352.28215767634856,352.06611570247935,352.06611570247935,352.06611570247935,352.06611570247935,352.3140495867769,352.3140495867769,352.3140495867769,352.3140495867769,352.3140495867769,352.3140495867769,352.75,352.75,352.75,352.75,353.2217573221758,353.2217573221758,353.2217573221758,353.0,352.5311203319502,352.3140495867769,352.3140495867769,352.34567901234567,352.34567901234567,352.34567901234567,352.5619834710744,352.3140495867769,352.3140495867769,352.5619834710744,352.3140495867769,352.3140495867769,352.5619834710744,352.3140495867769,352.5619834710744,352.3140495867769,352.75,352.75,352.75,352.97071129707115,353.0,353.0,353.2217573221758,353.2217573221758,353.67088607594934,353.67088607594934,353.9240506329114,353.9240506329114,354.1525423728814,354.1525423728814,354.1525423728814,353.9240506329114,353.25,353.02904564315355,353.02904564315355,353.02904564315355,353.02904564315355,353.02904564315355,353.25,353.25,353.4728033472803,353.4728033472803,353.25,353.25,353.4728033472803,353.4728033472803,353.9240506329114,353.9240506329114,354.1525423728814,353.8983050847458,354.1276595744681,354.1276595744681,354.61538461538464,354.84978540772534,354.59227467811155,355.0862068965517,355.0862068965517,355.0862068965517,355.0862068965517,354.84978540772534,354.1525423728814,353.4728033472803,353.02904564315355,353.02904564315355,353.02904564315355,353.02904564315355,352.7800829875519,353.0,353.0,353.0,352.7800829875519,352.7800829875519,352.7800829875519,352.7800829875519,352.7800829875519,352.7800829875519,352.7800829875519,352.7800829875519,353.0,353.0,353.0,353.0,353.2217573221758,353.2217573221758,353.2217573221758,353.2217573221758,353.2217573221758,352.75,352.09876543209873,352.34567901234567,352.34567901234567,351.91836734693874,351.6734693877551,352.09876543209873,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,352.06611570247935,352.09876543209873,352.09876543209873,352.09876543209873,352.5311203319502,352.5311203319502,352.5311203319502,352.75,353.0,352.7800829875519,352.7800829875519,352.09876543209873,351.6734693877551,351.6734693877551,351.4634146341463,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,352.06611570247935,352.06611570247935,352.09876543209873,352.09876543209873,352.09876543209873,352.06611570247935,351.85185185185185,351.42857142857144,351.2195121951219,351.2195121951219,351.2195121951219,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.42857142857144,351.2195121951219,351.42857142857144,351.42857142857144,351.42857142857144,351.85185185185185,351.85185185185185,351.85185185185185,352.06611570247935,352.06611570247935,352.06611570247935,352.06611570247935,352.06611570247935,352.09876543209873,352.5311203319502,352.5311203319502,352.5311203319502,352.5,351.85185185185185,351.85185185185185,351.42857142857144,351.6734693877551,351.6734693877551,351.42857142857144,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,351.85185185185185,352.06611570247935,352.06611570247935,352.09876543209873,352.09876543209873,352.5311203319502,352.5311203319502,352.5311203319502,352.5311203319502,352.5311203319502,352.7800829875519,353.0,353.25,352.75,352.5619834710744,352.34567901234567,351.91836734693874]





from scipy.signal import butter, lfilter
import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import freqz

def butter_bandpass(lowcut, highcut, fs, order=5):
    nyq = 0.5 * fs
    low = lowcut / nyq
    high = highcut / nyq
    b, a = butter(order, [low, high], btype='band')
    return b, a


def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
    b, a = butter_bandpass(lowcut, highcut, fs, order=order)
    y = lfilter(b, a, data)
    return y


def run():


    # Sample rate and desired cutoff frequencies (in Hz).
    fs = 30.0
    lowcut = .9
    highcut = 1.5

    # Plot the frequency response for a few different orders.
    plt.figure(1)
    plt.clf()
    for order in [3,4,5]:
        b, a = butter_bandpass(lowcut, highcut, fs, order=order)
        w, h = freqz(b, a, worN=2000)
        plt.plot((fs * 0.5 / np.pi) * w, abs(h), label="order = %d" % order)

    plt.plot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)],
             '--', label='sqrt(0.5)')
    plt.xlabel('Frequency (Hz)')
    plt.ylabel('Gain')
    plt.xlim((0,2)) 
    plt.legend(loc='best')

    # Filter a noisy signal.
    T = 10.266666666666667
    nsamples = T * fs
    t = np.linspace(0, T, nsamples, endpoint=False)
    a = 0.02
    f0 = .8

    plt.figure(2)
    plt.clf()
    plt.plot(t, data, label='Noisy signal')


    y = butter_bandpass_filter(data, lowcut, highcut, fs, order=5)
    plt.plot(t, y, label='Filtered signal (%g Hz)' % f0)
    plt.xlabel('time (seconds)')
    plt.hlines([-a, a], 0, T, linestyles='--')
    plt.grid(True)
    plt.axis('tight')
    plt.legend(loc='lower left')
    plt.ylim((-40,40))   # set the ylim to bottom, top
    plt.show()


run()

过滤后的数据的峰明显与数据的峰不匹配，我不确定为什么。在我看来，原始数据相当干净（如果将其绘制出来，则可以直观地看到峰值）。

这可能是一个单独的问题，但是我知道我的峰值频率不是规则的并且是可变的（可能在.2Hz以内），但是因为它占实际Hz的很大比例，所以我担心这是一个问题。频率变化会导致此问题吗？

谢谢！

所以我对原始数据的采样率为30Hz，因此为什么x轴比例乘以30。