5. Consider the 'top-hat' function which is zero everywhere except between -1 and 1 where it...

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5. Consider the 'top-hat' function which is zero everywhere except between -1 and 1 where it takes value 1. Show, using only elementary integration, that the convolution of this function with itself gives a 'triangular function', f(x): = 0 x x > 2 Find the Fourier transform of the 'triangular function' f(x) using the result for the Fourier transform of a convolution. 5. Consider the 'top-hat' function which is zero everywhere except between -1 and 1 where it takes value 1. Show, using only elementary integration, that the convolution of this function with itself gives a 'triangular function', f(x): = 0 x x > 2 Find the Fourier transform of the 'triangular function' f(x) using the result for the Fourier transform of a convolution.