Matlab过滤器与Python lfilter不兼容 [英] Matlab filter not compatible with Python lfilter

问题描述

美好的一天，

我一直在摆弄将matlab代码移植到python的问题，遇到了这个奇怪的问题.我在Google上搜索了一下，但没有发现任何信息表明我做错了事.

I have been fiddling around porting matlab code to python and I ran into this weird issue. I googled around a bit but found no information that indicates I am doing something wrong.

问题的核心是Matlab的filter(b，a，data)(内置在matlab中)与Python的scipy.signal.lfilter相比产生了不同的输出

The core of the issue is Matlab's filter(b, a, data) (which is built-in into matlab) is generating a different output when comparing to Python's scipy.signal.lfilter

这是问题，是在任意的粉红噪声信号上执行的

This is the issue, performed on an arbitrary pink noise signal

我有第三方给我的滤波器系数，它们如下:

I have filter coefficients given to me by a third party and they are as follows:

a0 = 1
a1 = -1.69065929318241
a2 = 0.73248077421585
b0 = 1.53512485958697
b1 = -2.69169618940638
b2 = 1.19839281085285

在matlab中，我按以下方式初始化分子/分母:

In matlab I initialize the numerator/denominator as follows:

a = [a0 a1 a2];
b = [b0 b1 b2];

在python中，我是这样的:

In python I do it like this:

a = np.array([a0, a1, a2])
b = np.array([b0, b1, b2])

在两个matlab/python中读取信号后，我打印出前15个样本，以确保你们知道输入是相同的

After reading in the signal in both matlab/python I print out the first 15 samples to make sure that you guys know the input is the same

Matlab:

   0.061920166015625
  -0.050170898437500
  -0.117370605468750
  -0.065979003906250
  -0.013854980468750
  -0.042663574218750
   0.107452392578125
  -0.044006347656250
   0.115112304687500
  -0.043457031250000
  -0.028778076171875
  -0.128234863281250
   0.045227050781250
  -0.091796875000000
   0.315063476562500

Python:

[[ 0.06192017]
 [-0.0501709 ]
 [-0.11737061]
 [-0.065979  ]
 [-0.01385498]
 [-0.04266357]
 [ 0.10745239]
 [-0.04400635]
 [ 0.1151123 ]
 [-0.04345703]
 [-0.02877808]
 [-0.12823486]
 [ 0.04522705]
 [-0.09179688]]

然后我调用过滤器功能

Matlab:

out = filter(b,a,data);
out(1:15)

ans =

   0.095055186160338
  -0.082982934483728
  -0.180851002009017
  -0.090458464750796
  -0.004794343459254
  -0.049115794227541
   0.183660200687651
  -0.061428954478571
   0.185550654888710
  -0.070597744360580
  -0.044524076275862
  -0.195036835228527
   0.082983215098531
  -0.133175807494538
   0.499012320158226

Python:

out = lfilter(b,a,data)
print out[0:14]

[[ 0.09505519]
 [-0.07701859]
 [-0.18017853]
 [-0.10128601]
 [-0.02126912]
 [-0.06549391]
 [ 0.16495284]
 [-0.06755524]
 [ 0.17671176]
 [-0.06671197]
 [-0.04417794]
 [-0.19685653]
 [ 0.06942917]
 [-0.14091966]]

其他信息:

Matlab R2012a

Matlab R2012a

2.7.3(默认值，2012年4月10日，23:31:26)[MSC v.1500 32位(英特尔)]-> python

2.7.3 (default, Apr 10 2012, 23:31:26) [MSC v.1500 32 bit (Intel)] -> python

1.6.2-> numpy

1.6.2 -> numpy

我的问题是这样的: 我是在做错什么还是在scipy软件包的基本功能中发现了错误?

My question is this: Am I doing something wrong or did I just find a bug in an essential and basic function in the scipy package?

国王的问候，

K

在下面的评论中，建议给它以冲动(我保留了系数) Matlab:

below in comments it was suggest to feed it with an impulse (I kept the coeffs) Matlab:

   1.535124676585826
  -0.096323067867721
  -0.088906133468550
  -0.079755185442926
  -0.069716811972987
  -0.059448236072219
  -0.049440488368964
  -0.040042331136521
  -0.031483732058538
  -0.023898026476545
  -0.017342192117849
  -0.011814893332425
  -0.007272136901341
  -0.003640523618135
  -0.000828184619352

Python:

[[ 1.53512468]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]
 [ 0.        ]]

这里肯定有问题，这根本看起来不像是过滤器...

There is definitely something going wrong here, this doesn't look like a filter at all...

推荐答案

这不是错误. Matlab的filter作用于数组的 first 维度，而scipy.signal.lfilter默认作用于 last 维度.

This is not a bug. Matlab's filter operates on the first dimension of the array, while scipy.signal.lfilter by default operates on the the last dimension.

从您的问题中我看到您的data数组具有第二个维度(也许为空?).当您使用lfilter时，它默认为axis=-1，这将为您提供python的答案.如果要获得与matlab相同的行为，则需要指定第一个轴或挤压数组(如果第二个维度的大小为1):

From your question I see that your data array has a second dimension (perhaps empty?). When you use lfilter it defaults to axis=-1, which will give the answer you got for python. If you want the same behaviour of matlab you need to specify the first axis or squeeze the array (if the second dimension has a size of 1):

out = lfilter(b, a, data, axis=0)
out = lfilter(b, a, np.squeeze(data))

这两个都返回以下内容:

Both of these return the following:

[ 0.09505519
 -0.08298293
 -0.180851
 -0.09045846
 -0.00479434
 -0.04911579
  0.1836602
 -0.06142895
  0.18555065
 -0.07059774
 -0.04452408
 -0.19503684
  0.08298322
 -0.13317581
  0.49901232]

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