4) Noting that the Dirichlet kernel is an even function, show that the partial sum of...

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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 SN(x)= π 1 f(x+y) + f(x - y) S 2 0 == TT where Dy is the Dirichlet kernel. discontinuity at x = a, then DN (y)dy, Conclude that if f is a smooth function with a jump f(a+) + f(a) 2 SN (a) → 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 SN(x)= π 1 f(x+y) + f(x - y) S 2 0 == TT where Dy is the Dirichlet kernel. discontinuity at x = a, then DN (y)dy, Conclude that if f is a smooth function with a jump f(a+) + f(a) 2 SN (a) →

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A Answer 1 The Dirichlet kernel is an even function defined as Dxy 12 cos2nxL where L is the period ... View the full answer