3. (a) Let () be the rectangular pulse Il-oa()e-a, a 0 otherwise. Show that la sinc ka where sinc...
3. (a) Let () be the rectangular pulse Il-oa()e-a, a 0 otherwise. Show that la sinc ka where sincx(note: in Engineering the alternate definition sincis often used). Use the symmetry of Fourier transform process to deduce that the Fourier transform of sinc i:s (b) Show that the' n-translates of sincTI are orthonormal 1 m n sinc π(x-m) sinc π(1-n) dr= 16 m メn. Hint: Use the shifting and scaling properties together with the Plancherel formula.
3. (a) Let () be the rectangular pulse Il-oa()e-a, a 0 otherwise. Show that la sinc ka where sincx(note: in Engineering the alternate definition sincis often used). Use the symmetry of Fourier transform process to deduce that the Fourier transform of sinc i:s (b) Show that the' n-translates of sincTI are orthonormal 1 m n sinc π(x-m) sinc π(1-n) dr= 16 m メn. Hint: Use the shifting and scaling properties together with the Plancherel formula.