Fourier transform of cos(wt) and cos(t).

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Homework Help Overview

The discussion revolves around the Fourier transform of cosine functions, specifically comparing cos(w0t) and cos(t). Participants are exploring the differences in their transforms and the implications of the frequency variable ω0.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the Fourier transforms of cos(w0t) and cos(t), with some attempting to clarify the expected results and the role of the frequency variable. There is a suggestion to use the exponential form of cosine to derive the transform.

Discussion Status

The discussion is active, with participants offering different perspectives on the transforms. Some guidance has been provided regarding the use of the exponential form of cosine, but there is no explicit consensus on the transforms or any scaling factors involved.

Contextual Notes

There is mention of inconsistent notes and a lack of clarity regarding the presence of the frequency variable ω0 in the functions being discussed. Participants are also considering the implications of scaling factors in the Fourier transform of cos(t).

thomas49th
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Is there a difference? My notes are inconsistent and very poor. Google search doesn't seem to be having much use.

Which one transforms into pi(dirac(w+w0) + dirac(w-w0))?

Thanks
Thomas
 
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Neither since ω0 doesn't appear in either function.
 
Okay Fourier transform of cos(w0t) and cos(t).

What do they transform into? I presume cos(w0t) is pi(dirac(w+w0) + dirac(w-w0))?

but what about cos(t). I'm guessing somewhere like pi(dirac(w+t) + dirac(w-t)) but is there some scaling factor?
 
Use cos(t)=(e^(it)+e^(-it))/2. You know the Fourier transform of e^(it) is a delta function, right?
 

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