Fourier Series Basics : Example 1

Question:

Convert the following (finite) real Fourier series

to a (finite) complex Fourier series. What are the complex Fourier coefficients Cn?

Answer:

Use Euler's standard formulas:

Line (5) is the complex Fourier series. From it we can directly read off the complex Fourier coefficients:

Recent Posts

Question: The direct stresses acting on an element of material, on orthogonal planes, are 85N/mm^2 (tensile) and 45N/mm^2 (tensile)...

Question: A thin cylinder of 3m diameter is subjected to an internal pressure of 2.5MN/m^2. Using a factor of safety of 2.2 and a yield...

Question: A hole in a pressure vessel end plate repair casting is being drilled using a radial arm drill. The distance from the drill...