The even impulse pair is the Fourier transform of cos(π k), I I(x) congruent 1/2 δ(x + 1/2) + 1/2 δ(x - 1/2). It satisfies I I(x)*f(x) = 1/2 f(x + 1/2) + 1/2 f(x - 1/2), where * denotes convolution, and integral_(-∞)^∞ I I(x) d x = 1. The odd impulse pair is the Fourier transform of i sin(π s), I I(x) congruent 1/2 δ(x + 1/2) - 1/2 δ(x - 1/2).
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