3) Fourier Decomposition: Most sounds are not pure (single frequency) tones but combinations of many harmonics. Consider a triangle-shaped wave, which approximates the shape of a string plucked at the center. For a triangular wave defined by the piecewise function:

Y(x) = -pi < x < 0 and Y(x) = pi x for 0 < x < 2pi

calculate the corresponding Fourier series representation. Write a small program in python to test your result for various numbers of terms in the series representation.