matlab中的filter函式：

y = filter(b,a,x)

python實現matlab中的filter函式

def filter_matlab(b,x):
  y = []
  y.append(b[0] * x[0])
  for i in range(1,len(x)):
    y.append(0)
    for j in range(len(b)):
      if i >= j :
        y[i] = y[i] + b[j] * x[i - j ]
        j += 1
    for l in range(len(b)-1 ):
      if i >l:
        y[i] = (y[i] - a[l+1] * y[i -l-1])
        l += 1
    i += 1
  return y

example:

取

b = [8,-3.5,0.5]
a = [1,-1.5,0.25]
x = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
y = filter_matlab(b,x)

函式的結果和matlab的filter函式結果一致，為

[8,24.5,52.25,94.75,156.5625,243.65625,363.84375,527.3515625,747.56640625,1042.01171875,1433.6259765625,1952.43603515625,2637.74755859375,3541.0123291015625,4729.581604003906,6291.619323730469,8342.533584594727,11033.395545959473,14561.959922790527,19187.090997695923]

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