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## Homework Statement

The problem/question is attached in the file called "homework". In the third signal (the peridic rectangular wave), I am requested (sub-question b) to find the Fourier series of the wave.

## Homework Equations

The file called "solution" presents a detailed solution to the problem. What I don't understand is why the phase (page 2 in that "solution" document) [itex]\phi_{n}[/itex] equals [itex]-\pi[/itex] for even values of [itex]n[/itex]. What I know is that when the argument of the arctan function is undefined (since it's divided by 0), it means that the angle is [itex]\pi/2[/itex], because only then the tan would be undefind! So why [itex]\phi_{n} = -\pi[/itex] then? does someone have an idea?

I do understand the [itex]\pm\pi[/itex] addition for the odd values of [itex]n[/itex] (i.e [itex]n=3,7,11,...[/itex]), but that [itex]\phi_{n} = -\pi[/itex] is not completely clear to me (and quite annoying to be honest...:uhh:).

## The Attempt at a Solution

Couple of hours of thinking, going back to the basics of polar representation of numbers in the x-y plane (in fact, it's the [itex] a_{n}-b_{n}[/itex] plane here) but nothing practical really... any suggestions?

Thanks! :tongue:

#### Attachments

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