How To Find The Odd Extension Of A Function In Fourier Series

In Mathematics, when a function is defined over the interval of 0 to L, when it was supposed to be from -L to L, we tend to not have any information of the function’s value from -L to 0, hence, there are two ways to get its Fourier series.

We either extend the function as an even function by reflecting it on the y axis or extend it as an odd function by reflecting it on the origin. When we get an even extension, the Fourier series will contain only the constant term and the cosine term, hence, it is called half range cosine series. When we get an odd extension, the Fourier series will contain only the sine term, hence, it is called half range sine series.

Problems of this nature can be presented to students as questions and they have to solve the questions of Fourier series very fast. This video will guide all students taking courses in engineering mathematics, systems and signals, electronics, advanced calculus etc.

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