Deconvolution/1D: Difference between revisions
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(→{{header|Java}}: fixed error in deconv method where input parameters were reversed; changed array types from double[] to int[]; updated output; removed "untested" banner.) |
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:<math> G(n) = \sum_{m=-\infty}^{\infty} F(m) H(n-m) </math> |
:<math> G(n) = \sum_{m=-\infty}^{\infty} F(m) H(n-m) </math> |
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for all integers <math>\mathit{n}</math>. Assume <math>F(n)</math> can be non-zero only for <math>0</math> ≤ <math>\mathit{n}</math> ≤ <math>|\mathit{F}|</math>, where <math>|\mathit{F}|</math> is the "length" of <math>\mathit{F}</math>, and similarly for <math>\mathit{G}</math> and <math>\mathit{H}</math>, so that the functions can be modeled as finite sequences by identifying <math>f_0, f_1, f_2, \dots</math> with <math>F(0), F(1), F(2), \dots</math>, etc. |
for all integers <math>\mathit{n}</math>. Assume <math>F(n)</math> can be non-zero only for <math>0</math> ≤ <math>\mathit{n}</math> ≤ <math>|\mathit{F}|</math>, where <math>|\mathit{F}|</math> is the "length" of <math>\mathit{F}</math>, and similarly for <math>\mathit{G}</math> and <math>\mathit{H}</math>, so that the functions can be modeled as finite sequences by identifying <math>f_0, f_1, f_2, \dots</math> with <math>F(0), F(1), F(2), \dots</math>, etc. |
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Then for example, values of <math>|\mathit{F}| = 6</math> and <math>|\mathit{H}| = 5</math> would determine the following value of <math>\mathit{g}</math> by definition. |
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:<math> |
:<math> |
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NEXT |
NEXT |
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= LEFT$(LEFT$(a$))</lang> |
= LEFT$(LEFT$(a$))</lang> |
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{{out}} |
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'''Output:''' |
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<pre> |
<pre> |
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deconv(g,f) = -8, -9, -3, -1, -6, 7 |
deconv(g,f) = -8, -9, -3, -1, -6, 7 |
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for (int i = 0; i < lh; i++) printf(" %g", h2[i]); |
for (int i = 0; i < lh; i++) printf(" %g", h2[i]); |
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printf("\n"); |
printf("\n"); |
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}</lang> |
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}< |
{{out}}<pre>f[] data is : -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1 |
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deconv(g, h): -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1 |
deconv(g, h): -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1 |
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h[] data is : -8 -9 -3 -1 -6 7 |
h[] data is : -8 -9 -3 -1 -6 7 |
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deconv(g, f): -8 -9 -3 -1 -6 7</ |
deconv(g, f): -8 -9 -3 -1 -6 7</pre> |
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=={{header|Common Lisp}}== |
=={{header|Common Lisp}}== |
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return h |
return h |
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}</lang> |
}</lang> |
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{{out}} |
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Output: |
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<pre> |
<pre> |
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[-8 -9 -3 -1 -6 7] |
[-8 -9 -3 -1 -6 7] |
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[-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1] |
[-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1] |
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</pre> |
</pre> |
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{{trans|C}} |
{{trans|C}} |
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<lang go>package main |
<lang go>package main |
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} |
} |
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}</lang> |
}</lang> |
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{{out}} |
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Output: |
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<pre> |
<pre> |
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h = [-8, -9, -3, -1, -6, 7] |
h = [-8, -9, -3, -1, -6, 7] |
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deconv[f,g] |
deconv[f,g] |
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</pre> |
</pre> |
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{{out}} |
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Gives the output: |
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<pre>{-8, -9, -3, -1, -6, 7}</pre> |
<pre>{-8, -9, -3, -1, -6, 7}</pre> |
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=={{header|MATLAB}}== |
=={{header|MATLAB}}== |
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The deconvolution function is built-in to MATLAB as the "deconv(a,b)" function, where "a" and "b" are vectors storing the convolved function values and the values of one of the deconvoluted vectors of "a". |
The deconvolution function is built-in to MATLAB as the "deconv(a,b)" function, where "a" and "b" are vectors storing the convolved function values and the values of one of the deconvoluted vectors of "a". |
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To test that this operates according to the task spec we can test the criteria above: |
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<lang MATLAB>>> h = [-8,-9,-3,-1,-6,7]; |
<lang MATLAB>>> h = [-8,-9,-3,-1,-6,7]; |
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>> g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]; |
>> g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]; |
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.say for ~@f, ~deconvolve(@g, @h),'';</lang> |
.say for ~@f, ~deconvolve(@g, @h),'';</lang> |
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{{out}} |
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Output: |
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<pre> |
<pre> |
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24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7 |
24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7 |
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(deconvolve g h) |
(deconvolve g h) |
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</lang> |
</lang> |
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{{out}} |
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Output: |
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<lang racket> |
<lang racket> |
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#<array '#(6 1) #[-8 -9 -3 -1 -6 7]> |
#<array '#(6 1) #[-8 -9 -3 -1 -6 7]> |
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pp "deconv(g,h) = f" [1D deconvolve $g $h] |
pp "deconv(g,h) = f" [1D deconvolve $g $h] |
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pp " conv(f,h) = g" [1D convolve $f $h]</lang> |
pp " conv(f,h) = g" [1D convolve $f $h]</lang> |
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{{out}} |
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Output: |
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<pre> |
<pre> |
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deconv(g,f) = h = [-8,-9,-3,-1,-6,7] |
deconv(g,f) = h = [-8,-9,-3,-1,-6,7] |
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'f': deconv(g,h)> |
'f': deconv(g,h)> |
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</lang> |
</lang> |
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{{out}} |
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output: |
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<pre> |
<pre> |
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< |
< |
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