Question: 4) Noting that the Dirichlet kernel is an even function, show that the partial sum of the Fourier series of a 27-periodic and integrable function

4) Noting that the Dirichlet kernel is an even function, show that the partial sum of the Fourier series of a 27-periodic and integrable function f is given by TT SN (2C) : flacty) +f(x - y), DN (y) dy. TT 2 0 where Do is the Dirichlet kernel. Conclude that if f is a smooth function with a jump discontinuity at x = a, then SN(a) - flat) + f(a) 2

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