Question

我有一个大小为120x1的信号。我正在尝试创建一维高斯滤波器（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，我希望自己找到内核矩阵，而不是MATLAB在内部找到并将其应用于我的信号。

这是我想要找到G的信号。

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
    ]';

这是带噪声的滤波信号。

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
      ]';

我尝试使用以下代码来获取G，但它不会生成正确的过滤信号：

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，无论噪音如何，G*s都与sFilt不同。我的目标是能够找到G，G*s = sFilt，无论噪音如何，滤波信号的幅度大致相同。

我是否也知道我创建G的方式是否正确？如果没有，我应该如何为信号G构建s？给定s和sFilt，找到G = sFilt * pinv(s)是否正确，我害怕得到奇异矩阵？

Answer 1

我认为你应该写错字，因为我获得了两种方法完全相同的结果：

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
    ];

i = -30:30;
sigma = 2;
gaussFilter = exp(- i.^ 2 / (2 * sigma ^ 2));
gaussFilter = gaussFilter / sum (gaussFilter); % normalize
sFilt = filter(gaussFilter,1, s); % Example filtered signal

G = zeros(180); % Zero padding G
for i = 31 : 150
    G(i, i-30:i+30) = gaussFilter;
end
G = G(31:150,31:150); % Truncate to size 120x120

figure
hold on
plot(s)
plot(sFilt(31:end))
plot(G*s')

为1D信号创建高斯滤波器变换矩阵

1 个答案: