What Role Do Ck and k=1 Play in Fourier Series?

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Homework Help Overview

The discussion revolves around the Fourier series representation of a function, specifically focusing on the terms Ck and the significance of the k=1 term within the series. Participants are examining the roles these components play in shaping the overall function.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the meaning of the Fourier coefficients Ck and their impact on the shape of the final wave. There is a question regarding the role of the k=1 term and its distinction from the k=0 term, with some confusion about its significance compared to other terms.

Discussion Status

The discussion is ongoing, with participants providing insights into the definitions and roles of the terms in question. Some guidance has been offered regarding the distinction between the k=1 term and the k=0 term, but there is still uncertainty about the implications of the k=1 term.

Contextual Notes

There is a mention of the k=0 term being associated with the constant or mean value of the series, which is currently zero in this context. Participants are also considering the potential for C1 to be zero, which could affect its significance.

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Homework Statement


Consider the following equation for the Fourier series:
f(t) = SUM k=1->infinity (Ck * sin(k*pi*t)

What is the meaning of the Ck terms?
What is the importance of the K=1 term?

Homework Equations





The Attempt at a Solution


Ck = Fourier Coefficents. They are the amplitudes of each term of the series, they will determine the shape of the final wave?

The k = 1 term is the "DC" or constant/mean of the series?
 
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The k=1 term is clearly not the constant/mean, because it is associated with [itex]\sin(\pi t)[/itex]. The k=0 term is the constant/mean. In your case the k=0 term is 0.
 
I'm lost as to what the significance of the n=1 term could be over any other term then, other than the most dominant?
 

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