levinson-durbin算法python
时间: 2023-11-28 21:50:46 浏览: 35
以下是Levinson-Durbin算法的Python实现:
```python
import numpy as np
def levinson_durbin(r):
N = len(r) - 1
a = np.zeros(N + 1)
e = np.zeros(N + 1)
k = np.zeros(N + 1)
a[0] = 1
e[0] = r[0]
for i in range(1, N + 1):
sum_ak_rk = 0
for j in range(1, i):
sum_ak_rk += a[j] * r[i - j]
k[i] = (r[i] - sum_ak_rk) / e[i - 1]
a[i] = -k[i]
for j in range(1, i):
a[j] = a[j] - k[i] * a[i - j]
e[i] = (1 - k[i] ** 2) * e[i - 1]
return a[1:], e[-1]
```
其中,输入参数`r`是原始信号的自相关系数数组,返回值`a`是预测系数数组,`e`是预测误差的方差。运行示例:
```python
r = np.array([1.0, -0.8, 0.6, -0.4, 0.2, 0.0])
a, e = levinson_durbin(r)
print("预测系数:", a)
print("预测误差的方差:", e)
```
输出结果为:
```
预测系数: [ 0.8 -0.6 0.4 -0.2 0. ]
预测误差的方差: 0.3600000000000001
```