scipy.signal.firwin 低通滤波器的作用类似于高通滤波器

Question

在设计 low/high/bandpass 过滤器时，我遇到了它们无法按预期工作的问题（请参阅代码和输出）。我想隔离三个频率峰值之一（具有低通滤波器等的最低频率的峰值）。但是，错误的峰是孤立的...有谁知道我的错误是什么？

    import numpy as np
    from scipy import signal
    import matplotlib.pyplot as plt

    def create_single_freq_state(N, w):
        """
        Creates a state that only contains the frequencies in w. Outputs array with N entries.
        """
        res = np.exp(2.0*np.pi*w[:,np.newaxis]*np.arange(N)/N*1j)
        return np.sum(res, axis=0)

    def band_pass_filter(f1, f2, numtaps, window="hamming"):

        fil = signal.firwin(numtaps, [f1, f2], pass_zero=False, fs=2*numtaps, window=window, scale=False)
        return fil

    def high_pass_filter(f, numtaps, window="hamming"):

        fil = signal.firwin(numtaps, f, pass_zero=False, fs=2*numtaps, window=window, scale=False)
        return fil

    def low_pass_filter(f, numtaps, window="hamming"):

        fil = signal.firwin(numtaps, f, pass_zero=True, fs=2*numtaps, window=window, scale=False)
        return fil

    def plot_freq_response(fil):

        fs = 2*len(fil)
        w, h = signal.freqz(fil, 1, worN=2000)
        plt.plot((fs * 0.5 / np.pi) * w, abs(h), label="Hamming window")
        plt.show()

    def plot_func(f):

        x = np.arange(1, len(f)+1)  
        plt.plot(x, f, color ="red")  
        plt.show()

    #create state with several frequencies (those contained in the variable ws)
    N = 60
    ws = np.array([15, 30, 50])
    f = create_single_freq_state(N, ws)


    numtaps = 60-1
    freq1 = 19.9
    freq2 = 40.0

    #choose filter
    fil = low_pass_filter(freq1, numtaps)
    #fil = band_pass_filter(freq1, freq2, numtaps)
    #fil = high_pass_filter(freq2, numtaps)

    #plot signal in fourierspace
    plot_func(np.fft.fft(f))
    #plot frequency response
    plot_freq_response(fil)
    #plot result of the application of the filter
    plot_func(np.absolute(np.fft.fft(np.convolve(fil, f, mode="same"))))

输出：The output of my code. The wrong frequency is isolated.

Answer 1

您的两个频率如此之高，以至于它们显示为直流和低频（这称为混叠，是奈奎斯特采样定理的结果）。事实上，您正在处理一个复杂的输入信号，并且您的信号相对于您的滤波器而言较短，因此很难看到这一点。

我把ws改成了ws = np.array([7.5, 15, 25])，把你第一次调用plot_func改成了plot_func(np.abs(np.fft.fft(f)))（因为其中一个峰完全在复数部分的变换）。现在输入和输出图如下所示：

scipy.signal.firwin 低通滤波器的作用类似于高通滤波器

scipy.signal.firwin lowpass filter acts like highpass filter

python

scipy

filtering

signal-processing

lowpass-filter