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1. (7 marks) Starting with the differentiation property of the Fourier Transform given below and without using the time XT shift property of the Fourier Transform, determine the Fourier Transform of the signal shown. Simplify as much as possible and express your answer in terms of the sinc function as defined. You may need to find a suitable trigonometric identity. t T 2T d²: x (t) F dt² (jw)"X(w) sinc(8) = sin 0 (0) 2. (3 marks) The triangle signal shown can be constructed by 4 XT2 the convolution of two identical rectangle signals as also shown. Use the definition of the Fourier Transform and its convolution property as given to determine the Fourier Transform of the triangle signal. Simplify as much as t possible and express your answer in terms of the sinc -T T function. A x(t) = Xorect (t/T) X, = 8 x -jwt f( t) * g(t) F F(w)G(w) sinc(8)= = sin(6 t -T/2 T/2

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