Gammatone滤波器组归一化代码

以下是Python代码实现Gammatone滤波器组归一化：

import numpy as np

def gammatone_filterbank(fs, num_bands, freq_range):
    """Calculate the center frequencies of the gammatone filterbank.

    Args:
        fs (float): The sampling rate.
        num_bands (int): The number of filterbanks.
        freq_range (tuple): The frequency range of the filterbank.

    Returns:
        array: The center frequencies of the filterbank.

    """
    # Get the lower and upper frequency.
    f_low, f_high = freq_range

    # Calculate the equivalent rectangular bandwidth (ERB) per band.
    erb_per_band = (f_high - f_low) / num_bands

    # Calculate the center frequencies of the filterbank using the ERB scale.
    erb = lambda x: 24.7 * (4.37 * x / 1000 + 1)
    center_freqs_erb = np.arange(1, num_bands + 1) * erb(erb_per_band)
    center_freqs_hz = (center_freqs_erb / 0.00437 - 1.0) * 1000.0

    return center_freqs_hz


def gammatone_filter(fs, freq, b=1.019, q=1.0):
    """Calculate the coefficients of a gammatone filter.

    Args:
        fs (float): The sampling rate.
        freq (float): The center frequency of the filter.
        b (float): The bandwidth of the filter.
        q (float): The Q factor of the filter.

    Returns:
        tuple: The coefficients of the filter.

    """
    # Calculate the filter coefficients.
    t = 1.0 / fs
    a0 = 1.0
    a1 = -2.0 * np.cos(2.0 * np.pi * freq * t) / np.exp(b * t)
    a2 = np.exp(-2.0 * b * t)
    b0 = q * np.exp(b / 2.0) * t ** (q - 1.0)
    b1 = 0.0
    b2 = -q * np.exp(-b / 2.0) * t ** (q - 1.0)

    return a0, a1, a2, b0, b1, b2


def gammatone_filterbank_matrix(fs, num_bands, freq_range, b=1.019, q=1.0):
    """Calculate the filterbank matrix for the gammatone filterbank.

    Args:
        fs (float): The sampling rate.
        num_bands (int): The number of filterbanks.
        freq_range (tuple): The frequency range of the filterbank.
        b (float): The bandwidth of the filter.
        q (float): The Q factor of the filter.

    Returns:
        array: The filterbank matrix.

    """
    # Calculate the center frequencies of the filterbank.
    center_freqs = gammatone_filterbank(fs, num_bands, freq_range)

    # Calculate the filter coefficients for each band.
    filters = [gammatone_filter(fs, freq, b, q) for freq in center_freqs]

    # Calculate the filterbank matrix.
    filterbank = np.zeros((num_bands, int(fs / 2)))
    for i, (a0, a1, a2, b0, b1, b2) in enumerate(filters):
        h = np.zeros(int(fs / 2))
        for n in range(int(fs / 2)):
            t = n / fs
            h[n] = b0 * t ** (q - 1.0) * np.exp(b * t) * np.cos(2.0 * np.pi * center_freqs[i] * t)
        h /= np.linalg.norm(h)
        filterbank[i, :] = np.fft.fft(h)

    return filterbank

其中，`gammatone_filterbank()`函数用于计算Gammatone滤波器组的中心频率，`gammatone_filter()`函数用于计算单个Gammatone滤波器的系数，`gammatone_filterbank_matrix()`函数用于计算Gammatone滤波器组的滤波矩阵。在计算滤波矩阵时，我们对每个滤波器的频率响应进行了归一化，以避免能量放大或缩小的问题。