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Value of Impulse function

  • Thread starter clw
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  • #1
clw
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Homework Statement


I am confused with the idea that the value of a delta function is infinity but when given a graph why is there an amplitude/magnitude value for the delta function. I have attached a graph. Assuming the phase is zero I'm trying to write a fourier transform for it.

Homework Equations



G(f) = |G(f)| [itex]e^{j\vartheta}[/itex]

The Attempt at a Solution


I know that it is a shifted impulse function so would it just be 3δ(f-5)+3δ(f+5)? Any help would be very much appreciated I'm just having a hard time grasping the idea of impulse function having an infinite value but there's an amplitude of 3?
 

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  • #2
rude man
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Homework Statement


I am confused with the idea that the value of a delta function is infinity but when given a graph why is there an amplitude/magnitude value for the delta function. I have attached a graph. Assuming the phase is zero I'm trying to write a fourier transform for it.

Homework Equations



G(f) = |G(f)| [itex]e^{j\vartheta}[/itex]

The Attempt at a Solution


I know that it is a shifted impulse function so would it just be 3δ(f-5)+3δ(f+5)? 3?
Your expression is correct.

The delta function has arbitrarily high amplitude but also arbitrarily small spread. The area is what matters.

If you take the inverse Fourier transform of your expression you would get 6cos[2π(5)t]. So what you are displaying is the Fourier transform of a cosine wave with frequency = 5 Hz and amplitute = 6.
 

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