AllPass Reverberator的lowpass反馈环路代码实现方法

问题背景 #

正在开发全通混响器（AllPass Reverberator），已掌握三级级联全通滤波器实现原理，但不清楚如何编写低通滤波器所在反馈环路的代码逻辑，需要实现完整的目标混响结构。

当前代码问题 #

现有代码仅实现了三级全通的块级联逻辑，无法支持反馈环路：

• 现有逻辑是整段音频一次性通过单级全通再传入下一级，属于离线块处理
• 反馈环路需要逐样本迭代计算：每个时刻的输出样本会按衰减系数回灌到环路输入端，块处理无法获取实时反馈状态

现有未完成代码如下：

def allpassfb(DataIn, sr, Mix, Spread, Diffusion = 0.7):
    delayAllPassMs = [23.8, 7.6, 2.6] 
    print('lista delay AllPass ms', delayAllPassMs) 
    # 延迟扰动最大比例为基准延迟的10%
    SpreadPerc = 0.1
    # 初始化最大延迟长度
    delayMaxMs = delayAllPassMs[-3] * (1 + Spread * SpreadPerc)
    pAllPass = np.zeros(len(delayAllPassMs))

    # 计算各全通级的延迟扰动量
    for i in range(len(delayAllPassMs)):
        pAllPass[i] = delayAllPassMs[i] * Spread * SpreadPerc
    
    # 逐次处理三级全通级联
    for i in range(len(delayAllPassMs)):
       
       delayAllPassL = delayAllPassMs[i]
       delayAllPassR = delayAllPassMs[i] + pAllPass[i]
       
       if isStereo:
           InL = DataIn[:, 0]
           InR = DataIn[:, 1]
           Y0 = np.zeros(len(InL))
           Y1 = np.zeros(len(InR))
           Y0 = allpassSch2(InL, sr, delayAllPassL, Diffusion, delayMaxMs)
           Y1 = allpassSch2(InR, sr, delayAllPassR, Diffusion, delayMaxMs)
           
       else:
           In = DataIn
           Y0 = np.zeros(len(In))
           Y1 = np.zeros(len(In))
           Y0 = allpassSch2(In, sr, delayAllPassL, Diffusion, delayMaxMs)
          
           Y1 = allpassSch2(In, sr, delayAllPassR, Diffusion, delayMaxMs)
           
           
    # 干湿信号混合
    if isStereo:
       DataOut0 = Y0 * Mix + InL * (1.0 - Mix)
       DataOut1 = Y1 * Mix + InR * (1.0 - Mix)
       
    else: 
       DataOut0 = Y0 * Mix + In * (1.0 - Mix)
       DataOut1 = Y1 * Mix + In * (1.0 - Mix)
       
    return(np.column_stack((DataOut0, DataOut1)))

实现方法 #

核心信号流逻辑 #

带低通的反馈全通级（单通道单级）计算顺序：

1. 环路输入 = 当前输入样本 + 反馈增益 * 低通上一时刻输出
2. 环路输入送入全通滤波器，得到全通输出
3. 全通输出送入低通滤波器，得到当前时刻反馈值，存入延迟线供下一时刻迭代使用
4. 三级结构按顺序级联，前一级全通输出作为后一级的环路输入

代码修改要点 #

• 提前将毫秒级延迟转换为采样点长度，初始化每一级全通的延迟缓冲区、读写指针、低通滤波器的状态寄存器
• 外层遍历所有音频样本，内层按顺序遍历三级全通，逐样本计算反馈值，禁止整段数组批量处理
• 立体声通道独立维护各自的延迟缓冲区与滤波器状态，右通道延迟长度叠加Spread对应的采样点偏移即可

核心逐样本处理参考代码（单通道）：

import numpy as np

def one_pole_lp(x, prev_y, cutoff, sr):
    """一阶低通滤波器，用于反馈环路阻尼控制"""
    g = np.exp(-2*np.pi*cutoff/sr)
    y = x*(1-g) + prev_y*g
    return y, y

def allpassfb(DataIn, sr, Mix, Spread, Diffusion=0.7, lp_cutoff=2000, feedback_gain=0.5):
    # 基础参数初始化
    delayAllPassMs = [23.8, 7.6, 2.6]
    SpreadPerc = 0.1
    n_samples = len(DataIn)
    DataOut = np.zeros(n_samples)
    
    # 延迟转换为采样点，初始化每级全通的延迟缓冲、读写指针、低通状态
    ap_delays = [int(m * sr / 1000) for m in delayAllPassMs]
    ap_buffers = [np.zeros(d + 2) for d in ap_delays]
    ap_read_ptr = [0 for _ in ap_delays]
    ap_write_ptr = [d for d in ap_delays]
    lp_states = [0.0 for _ in ap_delays]

    # 逐样本处理全通级联与反馈环路
    for n in range(n_samples):
        stage_in = DataIn[n]
        for stage in range(3):
            # 计算反馈环路输入
            fb = feedback_gain * lp_states[stage]
            stage_in = stage_in + fb
            # 读取延迟线历史样本
            delayed_sample = ap_buffers[stage][ap_read_ptr[stage]]
            # 全通滤波计算
            ap_out = delayed_sample*(-Diffusion) + stage_in
            ap_buffers[stage][ap_write_ptr[stage]] = stage_in + delayed_sample*Diffusion
            # 更新环形缓冲读写指针
            ap_read_ptr[stage] = (ap_read_ptr[stage] + 1) % len(ap_buffers[stage])
            ap_write_ptr[stage] = (ap_write_ptr[stage] + 1) % len(ap_buffers[stage])
            # 低通处理更新反馈状态
            _, lp_states[stage] = one_pole_lp(ap_out, lp_states[stage], lp_cutoff, sr)
            # 本级输出作为下一级输入
            stage_in = ap_out
        # 干湿信号混合
        DataOut[n] = stage_in * Mix + DataIn[n] * (1-Mix)
    return DataOut

立体声实现只需复制一套单通道状态变量，右通道延迟长度叠加Spread对应的采样点偏移即可。

内容的提问来源于stack exchange，提问作者Gherardo Vitali