I was unable to solve a convolution question.Question is attached herewith.
I don't know how to initiate for solving the problem and what is the final expression that prove the convolution of a top-hat function with itself is the triangle function.
I was unable to solve a convolution question.Question is attached herewith.
I don't know how to initiate for solving the problem and what is the final expression that prove the convolution of a top-hat function with itself is the triangle function.
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fix one top hat function - say centered at the origin - and move another from minus infinity to plus infinity. plot the area of overlap of the two top hats as a function of the displacement of the center of the second one from the origin. you can see why it must be of finite support and triangular in shape.