Since we know the frequency of each component, we can design filters to smooth out the jumps and protect sensitive components. 2. Electromagnetics and Periodic Media
Even with jumps, the Fourier coefficients (\varepsilon_m) decay as (1/m) (for a step change). Meanwhile, the electric field or pressure wave is assumed to follow Bloch’s theorem: Since we know the frequency of each component,
The use of Fourier series in analyzing discontinuous periodic structures Meanwhile, the electric field or pressure wave is
where ω = 2π/T, and a_n and b_n are the Fourier coefficients. they have some limitations:
epsilon open paren x close paren equals sum from n equals negative infinity to infinity of epsilon sub n exp open paren i the fraction with numerator 2 pi n and denominator cap L end-fraction x close paren is the period and epsilon sub n
While Fourier series are a powerful tool in the analysis of discontinuous periodic structures, they have some limitations: