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    Fourier series expansion - calculus

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    A function is defined as followed:

    see attachment

    Where f(t+2)=f(t) that is, f(t) has period 2.
    i) Draw a plot of the function f(t). Comment fully on whether the function is even or odd or none of these.
    ii) Find the first four non-zero coefficients for the Fourier series expansion of the function f(t)
    iii) Using eg. excel, draw a plot of the partial sum of the Fourier series which uses just there first four non-zero terms and comment on it in relation to your plot (i)

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    Solution Preview

    The function looks like:

    This function is neither even function since , nor it is an odd function since
    For example, while
    However we can write the function as:
    And is an odd function and it looks like

    The general expansion of a function over the symmetric interval is given by:

    Solution Summary

    The solution shows how to utilize parity to simplify the calculations of Fourier series coefficients.