How Does the Fourier Transform Relate to f(t-a) and Its Calculation?

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Homework Help Overview

The discussion revolves around the relationship between the Fourier transform and the function f(t-a), specifically how to express the Fourier transform of this shifted function in terms of its original transform F(w).

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the application of substitution in the Fourier transform integral and question the implications of this substitution on the resulting transform.

Discussion Status

The conversation is ongoing, with participants offering suggestions for approaches while also expressing uncertainty about the implications of the substitution on the Fourier transform. There is a request for further calculations to clarify the situation.

Contextual Notes

There appears to be some confusion regarding the definitions and transformations involved, particularly how the shift affects the Fourier transform. No explicit consensus has been reached on the correct interpretation or calculation.

spaghetti3451
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I have to show that the Fourier transform of f(t-a) is exp(-iwa)*F(w).

Any headstart?
 
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Hi failexam! :smile:

Apply substitution u=t-a in the integral.
 
I see, but then F(w) is not the Fourier transform of f(t), but of f(t-a) !
 
I don't see that, can you make the calculation? It'll turn out nicely...
 

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