Singing, 4

SOLUTION OF THE EXERCISE https://www.w3.org/1998/Math/MathML" display="inline"> N ∘ 3 : Entering below, from top to bottom : the operator sing-sing (t) the antisinging operator https://www.w3.org/1998/Math/MathML" display="inline"> x ( t ) : a , b , c , d , e , etc … shown below but reversed as it is known, that for convolution, its representation must be drawn in reverse on a movable piece of paper. the result of the product of this convolution which must be reduced to 1 for t and be zero for the others. A set of three time-domain signal diagrams illustrating impulse scaling, time reversal, and convolution-based signal construction. https://www.w3.org/1999/xlink" xlink:href="#long-desc30"/> https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003761020/e10523ab-dbe3-4c4f-8f3e-863ae3683950/content/pg217_1.tif "/> Place the first value of the operator https://www.w3.org/1998/Math/MathML" display="inline"> x ( t ) under the value 1 of the operator sing-sing. It must be : https://www.w3.org/1998/Math/MathML" display="inline"> a . 1 = 1 where https://www.w3.org/1998/Math/MathML" display="inline"> a = 1 . Move one notch to the right with the operator https://www.w3.org/1998/Math/MathML" display="inline"> x ( t ) , it will give : https://www.w3.org/1998/Math/MathML" display="block"> b ⋅ 1 - 2 a k 1 k 2 = 0 ; where b = 2 k 1 k 2 Move another step, it will give: https://www.w3.org/1998/Math/MathML" display="inline"> c ⋅ 1 - 2 b k 1 k 2 + 3 a k 1 k 2 2 = 0 https://www.w3.org/1998/Math/MathML" display="block"> where c = k 1 k 2 2 Move another step, it will give: https://www.w3.org/1998/Math/MathML" display="inline"> d ⋅ 1 - 2 c k 1 k 2 + 3 b k 1 k 2 2 - 4 k 1 k 2 3 ⋅ a = 0 https://www.w3.org/1998/Math/MathML" display="block"> where d = 0 Moving successive steps, 1,2,3, it will be found that https://www.w3.org/1998/Math/MathML" display="inline"> e , f , g … = 0 .