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This pape r present s a method of solving for Fourier coe ffi c ien ts where the dependent variable ca n be e xpressed as a piece wise continuou s fun c tion , whe n various conditions of continuity and s moothing are ass umed. An e xample is inc luded 10 show th e e ffec t of s moothing in the region of a di scontinuity for a sys tem co mposed of Iwo ma le rial s tha t e xhibit a d iscontinuilY a t Ihe ir interface a nd surro unded by a third materia l whic h does nOI have a di sco ntinuit y. An advanlage to be ga ine d from s nlOothin g is a n inc rease in the conve rge nce of a finit e Fourier se ri es re prese nt a tion of a piecewi se co ntinu ous fun c tion in the region of the di scontinuities.

Determination and smoothing of Fourier coefficients representing piecewise continuous functions