(1 point) In this problem you will apply the inverse fast Fourier transform to =...

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(1 point) In this problem you will apply the inverse fast Fourier transform to č = (-1, 1+i, − 2 − 3i, −1+3i, 3, −1−3i, −2+ 3i, 1 - i) - (A) Split è into its even and odd components: Ceven -1 Codd = 1+i = = -2 = 2 9 = 2 -2-3i F¹{e} F¹ {e} = 6 F₁¹{e} = -10 -1+3i (B) Compute the inverse Fourier transforms of the even and odd components: -2 F-¹{even} F-¹ {Codd } = (²² = 0 + 2 1 0 - 2 + w -2+2i +w² -4i +³ 6+61 (C) Combine the inverse Fourier transforms of the even and odd components to get the transform of c Fo¹{e}= Fi¹{e}: = 6 F₂¹{e} = F3¹{e} = -10 F₁¹ {e} = -2 F3¹{e} = 0 - w -2+2i -2+2i 3 -1-3i w²4i 6i+6 | ش 1 = || -2+3i 1-i || = 6 -4i -2 = 10 -2*0.41421 40.91168 -2 4+2*0.41421 = 2 -10 6+6i = -2+2i (1 point) In this problem you will apply the inverse fast Fourier transform to č = (-1, 1+i, − 2 − 3i, −1+3i, 3, −1−3i, −2+ 3i, 1 - i) - (A) Split è into its even and odd components: Ceven -1 Codd = 1+i = = -2 = 2 9 = 2 -2-3i F¹{e} F¹ {e} = 6 F₁¹{e} = -10 -1+3i (B) Compute the inverse Fourier transforms of the even and odd components: -2 F-¹{even} F-¹ {Codd } = (²² = 0 + 2 1 0 - 2 + w -2+2i +w² -4i +³ 6+61 (C) Combine the inverse Fourier transforms of the even and odd components to get the transform of c Fo¹{e}= Fi¹{e}: = 6 F₂¹{e} = F3¹{e} = -10 F₁¹ {e} = -2 F3¹{e} = 0 - w -2+2i -2+2i 3 -1-3i w²4i 6i+6 | ش 1 = || -2+3i 1-i || = 6 -4i -2 = 10 -2*0.41421 40.91168 -2 4+2*0.41421 = 2 -10 6+6i = -2+2i

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