Fourier coefficients of sums of sinusoids by inspection

Question

Assignment:

Find the Fourier coefficients of sums of sinusoids by inspection. This involves first finding the fundmental period p of the sum, or equivalently finding the fundamental ω_o. All the radian frequencies in the sum must be integer multiples of this ω₀. For example, suppose that some radian frequency is such that to = 3ω_o. The sine or cosine at this frequency is then associated with index n = 3 in the Fourier series summation.

Find the first 7 Fourier coefficients {a_o,a₁ , b₁, a₂, b₂, a₃, b₃} of the function

f (x) = 14 - cosπx/10) + 3 sin(πx/10) + 0.5 cos(πx/5) + 5 sin(3πx/10) by inspection. Note that some will be zero.

Provide complete and step by step solution for the question and show calculations and use formulas.