线性预测编码从 LPC 系数返回原始音频文件 Python

Question

我正在尝试使用线性预测编码来压缩音频文件，方法是使用 LPC 编码文件以获得残差信号并使用 Rice 编码对该信号进行编码。我需要能够从压缩信号中检索原始音频文件。我发现这个 LPC 代码可以对音频文件进行编码和解码，但是解码后的音频文件有奇怪的、混乱的音频。如何编辑 LPC 代码来解码系数，以便恢复原始音频？目前，解码后的音频是原始音频文件的嘈杂且难以理解的版本。

以下是对音频文件进行编码以获得 LPC 系数的代码。结果是预测系数和信号功率。

def make_matrix_X(x, p):
    n = len(x)

    xz = np.concatenate([x[::-1], np.zeros(p)])
    
    X = np.zeros((n - 1, p))
    for i in range(n - 1):
        offset = n - 1 - i 
        X[i, :] = xz[offset : offset + p]
    
    return X

"""
Encodes the input signal into lpc coefficients

x - single channel input signal
p - lpc order
nw - window length
"""
def lpc_encode(x, p, w):  
    n = len(x)
    nw = len(w)
    
    # overlapping factor
    R = 0.5
    step = floor(nw * (1 - R))
    nb = floor((n - nw) / step) + 1
    
    # list of overlapping blocks
    B = np.zeros((nb, nw))
    
    for i in range(nb):
        offset = i * step
        B[i, :] = w * x[offset : nw + offset]
    
    # the coefficients
    A = np.zeros((p, nb))
    
    # the signal power
    G = np.zeros((1, nb))

    for i in range(nb):
        x = B[i, :]
        
        b = x[1:].T
        
        X = make_matrix_X(x, p)

        a = np.linalg.lstsq(X, b)[0]

        e = b.T - np.dot(X, a)
        g = np.var(e)
   
        A[:, i] = a
        G[:, i] = g
    
    return [A, G]

这是解码系数以获得音频文件的代码，但解码后音频全乱了。输入是预测系数、信号功率和极数。

"""
Decodes the LPC coefficients

* A - the LPC filter coefficients
* G - the signal power(G) or the signal power with fundamental frequency(GF) 
       or the full source signal(E) of each windowed segment.
* w - the window function
* lowcut - the cutoff frequency in normalized frequencies for a lowcut
          filter.
"""
def lpc_decode(A, G, w, lowcut = 0):
    [ne, n] = G.shape
    nw = len(w)
    [p, _] = A.shape
    
    # list of overlapping blocks
    B = np.zeros((n, nw))

    for i in range(n):
        src = np.sqrt(G[:, i])*randn(nw, 1) # noise
    
        b = np.concatenate([np.array([-1]), A[:, i]])
    
        x_hat = lfilter([1], b.T, src.T).T 
        
        B[i,:] = np.squeeze(x_hat)

    # recover signal from blocks
    [count, nw] = B.shape
    R = 0.5
    step = floor(nw * (1 - R))
    n = (count-1) * step + nw
    
    # the rendered signal
    x = np.zeros((n, ))

    for i in range(count):
        offset = i * step
        x[offset : nw + offset] += B[i, :]
        
    return x

运行函数的代码：

[sample_rate, amplitudes] = scipy.io.wavfile.read('Sound1.wav')
amplitudes = np.array(amplitudes)
w = hann(floor(0.03*sample_rate), False)
        
# Encode
[A, G] = lpc_encode(amplitudes, 6, w)
        
# Decode
xhat = lpc_decode(A, G, w)
scipy.io.wavfile.write("example.wav", sample_rate, xhat)