【发布时间】：2018-02-15 17:56:35
【问题描述】：
我有一个大小为120x1 的信号。我正在尝试创建一个一维高斯滤波器（G），这样当它乘以信号时，它会生成滤波后的信号。
sFilt = G*s
我知道 MATLAB filter 函数可以通过以下方式应用此转换：
i = -30:30;
sigma = 2;
gaussFilter = exp(- i.^ 2 / (2 * sigma ^ 2));
gaussFilter = gaussFilter / sum (gaussFilter); % normalize
s = rand(120,1); % Example signal
sFilt = filter(gaussFilter,1, s); % Example filtered signal
但是，我想自己找到内核矩阵，而不是 MATLAB 在内部找到并将其应用于我的信号。
这是我要查找的信号G。
s = [...
0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.930556000000000 3.38767207896461 2.96157398017693 -0.333333000000000 1.60762896805897 2.00694000000000 2.00694000000000 2.00694000000000 1.28472000000000 -1.43744631449631 0.944444000000000 2.59392295081968 2.99306000000000 2.99306000000000 2.99306000000000 2.99306000000000 2.99306000000000 2.99306000000000 2.99306000000000 2.02922488524590 -0.812570065573777 -1.18993444717445 -0.782122839475842 0.640152000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 0.909722000000000 2.01873464373465 4.49027190008191 5.18750000000000 5.18750000000000 5.18750000000000 5.18750000000000 5.18750000000000 4.59722000000000 2.59722000000000 3.97561321867322 3.21314756756758 0.604167000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.00694444000000000 0.111111000000000 0.458646085995084 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000 0.506944000000000
]';
这是添加了噪声的滤波信号。
sFilt = [...
0.0138889000000000 0.00208355909090909 -0.00329849545454587 0.201389000000000 0.861111500000000 1.86806000000000 2.44947936559843 2.52500275098103 2.15972000000000 2.04861000000000 2.14807844644317 2.16668303352412 1.78457304987735 1.27778000000000 1.00173350000000 1.57634828431373 2.33333000000000 3.21248677841374 3.55556000000000 3.64930500000000 3.71804717320261 3.81944000000000 3.49947244281046 2.76389000000000 1.65451500000000 0.470087078495503 -0.229167000000000 -0.208333000000000 0.354167000000000 0.789952043336059 1.08820161079313 1.19444000000000 1.19444000000000 1.07082559280458 1.09288587898610 1.19444000000000 1.20139000000000 1.23611000000000 1.45729755519215 2.02778000000000 3.14999395748160 4.65278000000000 5.78193152902698 6.30624161896975 6.45139000000000 6.34444931316435 5.92361000000000 5.44723022076860 4.78127380212592 4.18750000000000 3.06944000000000 1.72222000000000 0.791893542109568 0.312170886345054 0.0555556000000000 0.00694444000000000 0.0482593386437905 0.0524382556009807 -0.0647580647058824 -0.0694444000000000 0.0486111000000000 0.0249897492232223 0.0356016021241839 0.256944000000000 0.361111000000000 0.573964112019624 0.681776461161079 0.674996493049878 0.583855436631235 0.625000000000000 0.701389000000000 0.701389000000000 0.673611000000000 0.729167000000000 0.701389000000000 0.659722000000000 0.583333000000000 0.645833000000000 0.687500000000000 0.701389000000000 0.625000000000000 0.625000000000000 0.701389000000000 0.701389000000000 0.629343798855273 0.583333000000000 0.625000000000000 0.645833000000000 0.631944000000000 0.460070669664759 0.665622201962387 0.527778000000000 0.562500000000000 0.520833000000000 0.562500000000000 0.541667000000000 0.645833000000000 0.708333000000000 0.581075065359477 0.579855317512275 0.548611000000000 0.666667000000000 0.548611000000000 0.618056000000000 0.576389000000000 0.590278000000000 0.645833000000000 0.666667000000000 0.554531401639344 0.548611000000000 0.576389000000000 0.583333000000000 0.656560276422764 0.584357622950820 0.559938565573770 0.465278000000000 0.583333000000000 0.659722000000000 0.687500000000000 0.673611000000000
]';
我尝试了以下代码来获取G，但它没有生成正确的滤波信号：
G = zeros(180); % Zero padding G
i = -30:30;
sigma = 2;
gaussFilter = exp(- i.^ 2 / (2 * sigma ^ 2));
gaussFilter = gaussFilter / sum (gaussFilter); % normalize
for i = 31 : 150
G(i, i-30:i+30) = gaussFilter;
end
G = G(31:150,31:150); % Truncate to size 120x120
可以看出，G*s 与sFilt 不同，无论噪音如何。我的目标是能够找到G，使得G*s = sFilt不管噪声和滤波后的信号具有大致相同的幅度。
请问我创建G 的方式是否正确？如果没有，我应该如何为信号s 构建G？给定s和sFilt，找G = sFilt * pinv(s)是否正确，我怕得到一个奇异矩阵？
【问题讨论】：
-
我得到了完全相同的结果。你确定你对两者都使用了相同的输入
s吗？也许一个minimal reproducible example 可以澄清你的问题（包括绘图代码）。 -
s用于G*s与sFilt进行比较。当我申请G*s时，我没有得到正确的幅度。 -
我无法重现您的图表。我在他们俩之间变得完全一样。顺便说一句，我必须将
s = rand(500,1);更改为s = rand(120,1);才能使乘法起作用。 -
我只想知道如何创建
G。这些代码只是澄清我的问题的示例。