如何在Python中平滑曲线

Question

我有一条熵曲线（就是一个一维的numpy数组），但是这条曲线里面有很多噪声。我想通过平滑处理来去掉这些噪声。

这是我的曲线图：

我尝试用凯瑟-贝塞尔滤波器做卷积运算来解决这个问题：

gaussian_curve = window_kaiser(windowLength, beta=20)  # kaiser filter
gaussian_curve = gaussian_curve / sum(gaussian_curve)

for i in range(0, windows_number):
     start = (i * step) + 1
     end = (i * step) + windowLength
     convolution[i] = (np.convolve(entropy[start:end + 1], gaussian_curve, mode='valid'))
     entropy[i] = convolution[i][0]

但是这段代码返回了一个错误：

File "/usr/lib/python2.7/dist-packages/numpy/core/numeric.py", line 822, in convolve
    raise ValueError('v cannot be empty')
ValueError: v cannot be empty

使用numpy.convolve这个操作符，并选择'valid'模式时，它会返回重叠部分的中心元素，但在这种情况下却返回了一个空元素。

有没有简单的方法可以进行平滑处理呢？

谢谢！

Answer 1

好的，我解决了这个问题。
我用了另一种方法：Savitzky-Golay滤波器

代码如下：

def savitzky_golay(y, window_size, order, deriv=0, rate=1):

    import numpy as np
    from math import factorial

    try:
        window_size = np.abs(np.int(window_size))
        order = np.abs(np.int(order))
    except ValueError, msg:
        raise ValueError("window_size and order have to be of type int")
    if window_size % 2 != 1 or window_size < 1:
        raise TypeError("window_size size must be a positive odd number")
    if window_size < order + 2:
        raise TypeError("window_size is too small for the polynomials order")
    order_range = range(order+1)
    half_window = (window_size -1) // 2
    # precompute coefficients
    b = np.mat([[k**i for i in order_range] for k in range(-half_window, half_window+1)])
    m = np.linalg.pinv(b).A[deriv] * rate**deriv * factorial(deriv)
    # pad the signal at the extremes with
    # values taken from the signal itself
    firstvals = y[0] - np.abs( y[1:half_window+1][::-1] - y[0] )
    lastvals = y[-1] + np.abs(y[-half_window-1:-1][::-1] - y[-1])
    y = np.concatenate((firstvals, y, lastvals))
    return np.convolve( m[::-1], y, mode='valid')

现在，我可以输入：

entropy = np.array(entropy)
entropy = savitzky_golay(entropy, 51, 3) # window size 51, polynomial order 3

结果是这样的：