小波从零开始，但如何在python中反转它

Question

我有下面创建DWT小波的数据和代码，但我不知道如何将其反转，使其与原始数据对齐。下面的代码可以创建系数，但我一直在倒它

我不想使用像pywavelets这样的包，但要从头开始

data = [56, 40, 8, 24, 48, 48, 40, 16]

def discreteHaarWaveletTransform(x):
    N = len(x)
    output = [0.0]*N

    length = N >> 1
    while True:
        for i in range(0,length):
            summ = x[i * 2] + x[i * 2 + 1]
            difference = x[i * 2] - x[i * 2 + 1]
            output[i] = summ/2
            output[length + i] = difference/2

        if length == 1:
            return output

        #Swap arrays to do next iteration
        x = output[:length << 1]
        length >>= 1

输出：[35.0，-3.0,16.0,10.0,8.0，-8.0,0.0,12.0]