For functions f (t) &amp; g(t), this operation is defined as   +∞ f (τ) Ã— g(t − τ)
A theorem stating that the support of this operation applied to two functions with some required properties is equal to the sum of the support of each function is due to Edward Titchmarsh. In order to 3 ditch this operation for matrix multiplication, a Toeplitz matrix is constructed. An efficient algorithm for performing this operation is the overlapp-add method. A common way to perform this operation by hand on two discrete time signals, f and g, is to construct an array with f as the first row and g 6 as the second row, then form new rows by multiplying the first row by the first, second, etc. elements of the second row, shifting over one column and down a row every time the index is increased for the second row, and finally summing down the created columns. The (*) Fourier transform of this operation 9 between functions f and g is equal to the multiplication of the Fourier transform of f and the Fourier transform of g, which is important because this operation applied to the input of an LTI system and the system's impulseresponse yields the output. For functions f (t) &amp; g(t), this operation is defined as   +∞ f (τ) Ã— g(t − τ) dτ. For      12 10 points, identify this mathematical operation represented by a star.
A theorem stating that the support of this operation applied to two functions with some required properties is equal to the sum of the support of each function is due to Edward Titchmarsh.
convolution 