Impulse Pair
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
المرجع الالكتروني للمعلوماتيه
الجزء والصفحة:
...
25-5-2019
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Impulse Pair
The even impulse pair is the Fourier transform of 
,
![AdjustmentBox[I, BoxMargins -> <span style=]() {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)=1/2delta(x+1/2)+1/2delta(x-1/2). " src="http://mathworld.wolfram.com/images/equations/ImpulsePair/NumberedEquation1.gif" style="height:23px; width:190px" /> |
(1)
|
It satisfies
![AdjustmentBox[I, BoxMargins -> <span style=]() {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)*f(x)=1/2f(x+1/2)+1/2f(x-1/2), " src="http://mathworld.wolfram.com/images/equations/ImpulsePair/NumberedEquation2.gif" style="height:23px; width:234px" /> |
(2)
|
where 
denotes convolution, and
![int_(-infty)^inftyAdjustmentBox[I, BoxMargins -> <span style=]() {{0.13913, -0.13913}, {-0.5, 0.5}}]I(x)dx=1. " src="http://mathworld.wolfram.com/images/equations/ImpulsePair/NumberedEquation3.gif" style="height:35px; width:105px" /> |
(3)
|
The odd impulse pair is the Fourier transform of 
,
![AdjustmentBox[I, BoxMargins -> <span style=]() {{0.101266, -0.101266}, {0.375, -0.375}}, BoxBaselineShift -> -0.375]AdjustmentBox[I, BoxMargins -> {{0, 0}, {-0.25, 0.25}}, BoxBaselineShift -> 0.25](x)=1/2delta(x+1/2)-1/2delta(x-1/2). " src="http://mathworld.wolfram.com/images/equations/ImpulsePair/NumberedEquation4.gif" style="height:23px; width:190px" /> |
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