如何获取信号的高和低包络？

Python中是否有类似的功能可以做到这一点？

据我所知，在Numpy / Scipy / Python中没有这样的功能。但是，创建一个并不是很困难。总体思路如下：

给定值的向量：

1. 找到（s）的峰值位置。我们称他们为（u）
2. 找到s的槽的位置。我们称它们为（l）。
3. 将模型拟合到（u）个值对。叫它（u_p）
4. 将模型拟合到（l）个值对。叫它（l_p）
5. 在（s）的范围内求值（u_p），以获得上包络线的插值。（给他们打电话（q_u））
6. 在（s）的域上评估（l_p），以获得较低包络线的插值。（我们称它们为（q_l））。

如您所见，它是三个步骤的顺序（查找位置，拟合模型，评估模型），但是应用了两次，一次用于信封的上部，一次用于下部。

要收集（s）的“峰值”，您需要找到（s）的斜率从正变为负的点，并且要收集（s）的“波谷”，您需要找到（s）的斜率的点）从负数变为正数。

一个峰值示例：s = [4,5,4] 5-4为正4-5为负

一个低谷的例子：s = [5,4,5] 4-5为负5-4为正

这是一个示例脚本，可让您开始使用大量内联注释：

from numpy import array, sign, zeros
from scipy.interpolate import interp1d
from matplotlib.pyplot import plot,show,hold,grid

s = array([1,4,3,5,3,2,4,3,4,5,4,3,2,5,6,7,8,7,8]) #This is your noisy vector of values.

q_u = zeros(s.shape)
q_l = zeros(s.shape)

#Prepend the first value of (s) to the interpolating values. This forces the model to use the same starting point for both the upper and lower envelope models.

u_x = [0,]
u_y = [s[0],]

l_x = [0,]
l_y = [s[0],]

#Detect peaks and troughs and mark their location in u_x,u_y,l_x,l_y respectively.

for k in xrange(1,len(s)-1):
    if (sign(s[k]-s[k-1])==1) and (sign(s[k]-s[k+1])==1):
        u_x.append(k)
        u_y.append(s[k])

    if (sign(s[k]-s[k-1])==-1) and ((sign(s[k]-s[k+1]))==-1):
        l_x.append(k)
        l_y.append(s[k])

#Append the last value of (s) to the interpolating values. This forces the model to use the same ending point for both the upper and lower envelope models.

u_x.append(len(s)-1)
u_y.append(s[-1])

l_x.append(len(s)-1)
l_y.append(s[-1])

#Fit suitable models to the data. Here I am using cubic splines, similarly to the MATLAB example given in the question.

u_p = interp1d(u_x,u_y, kind = 'cubic',bounds_error = False, fill_value=0.0)
l_p = interp1d(l_x,l_y,kind = 'cubic',bounds_error = False, fill_value=0.0)

#Evaluate each model over the domain of (s)
for k in xrange(0,len(s)):
    q_u[k] = u_p(k)
    q_l[k] = l_p(k)

#Plot everything
plot(s);hold(True);plot(q_u,'r');plot(q_l,'g');grid(True);show()

这将产生以下输出：

进一步改进的要点：

1. 上面的代码不过滤可能比某个阈值“距离”（T1）（例如时间）更近的峰值或谷值。这类似于的第二个参数envelope。通过检查的连续值之间的差异，很容易添加它u_x,u_y。

2. However, a quick improvement over the point mentioned previously is to lowpass filter your data with a moving average filter BEFORE interpolating an upper and lower envelope functions. You can do this easily by convolving your (s) with a suitable moving average filter. Without going to a great detail here (can do if required), to produce a moving average filter that operates over N consecutive samples, you would do something like this: s_filtered = numpy.convolve(s, numpy.ones((1,N))/float(N). The higher the (N) the smoother your data will appear. Please note however that this will shift your (s) values (N/2) samples to the right (in s_filtered) due to something that is called group delay of the smoothing filter. For more information about the moving average, please see this link.

Hope this helps.

（如果提供了有关原始应用程序的更多信息，请高兴地回应一下。也许可以用更合适的方式对数据进行预处理（？））