Delta function

𝝳(𝚝)

1

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Delta function transposed

𝝳(𝚝 - 𝚝𝟢)

𝙚(-𝘪 𝜔 𝚝𝟢)

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Step Function

𝙪(𝚝)

 1
____ + 𝜋·𝝳(𝜔)
 𝘪𝜔

𝙪(-𝚝)

 -1
____ + 𝜋·𝝳(𝜔)
 𝘪𝜔

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Sign Function

sgn(𝚝)
 = 2·(𝙪(𝚝)-0.5)

 2
____ 
 𝘪𝜔

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Constant

C𝟢

 2·𝜋·C𝟢·𝝳(𝜔)

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Exponential

C𝟢·𝙚(-𝘢·𝚝)·𝙪(𝚝)
> 𝘢 : 𝘢>0

   C𝟢
________
 𝘪𝜔 + 𝘢

C𝟢·𝚝·𝙚(-𝘢·𝚝)·𝙪(𝚝)
> 𝘢 : 𝘢>0

   C𝟢
__________
(𝘪𝜔 + 𝘢)²

𝙚(-𝘢·|𝚝|)
> 𝘢 : 𝘢>0

  2·𝘢
________
 𝜔² + 𝘢²

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Cosine

cos(𝜔𝟢·𝚝)

 𝜋·(𝝳(𝜔-𝜔𝟢) + 𝝳(𝜔+𝜔𝟢))

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Sine

sin(𝜔𝟢·𝚝)

 -𝘪𝜋·(𝝳(𝜔-𝜔𝟢) - 𝝳(𝜔+𝜔𝟢))

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Modulation

𝚡(𝚝)·cos(𝜔𝟢·𝚝)

 (𝚇(𝜔-𝜔𝟢) + 𝚇(𝜔+𝜔𝟢)) 
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