Let s(t) be the standard beacon signal that is being communicated. Below you can find its...

 

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Let s(t) be the standard beacon signal that is being communicated. Below you can find its Fourier Series representation s(t) = 2.5 + 2 sin(t) + 3 cos(t) + 0.5 cos(2t) + 0.3 sin (2t). The periodic interference is given by n(t) = 0.5 cos (120 t) and the measurement signal with noise is given as follows: y(t) = s(t) + n(t) Let g(t) be the filter function and let ỹ(t) be the function that results from applying g(t) to y(t). Using the Fourier transform of the convolution theorem, propose the design of a filtering function g(t) which removes from y(t) the effect of the periodic noise n(t) assuming that we only know that its fundamental period is equal to 2pi/120. Make sure to write the analytical expression of g(t) and its Fourier transform. Also, please write the mathematical expression that relates ỹ(t) as a function of g(t)and y(t) Let s(t) be the standard beacon signal that is being communicated. Below you can find its Fourier Series representation s(t) = 2.5 + 2 sin(t) + 3 cos(t) + 0.5 cos(2t) + 0.3 sin (2t). The periodic interference is given by n(t) = 0.5 cos (120 t) and the measurement signal with noise is given as follows: y(t) = s(t) + n(t) Let g(t) be the filter function and let ỹ(t) be the function that results from applying g(t) to y(t). Using the Fourier transform of the convolution theorem, propose the design of a filtering function g(t) which removes from y(t) the effect of the periodic noise n(t) assuming that we only know that its fundamental period is equal to 2pi/120. Make sure to write the analytical expression of g(t) and its Fourier transform. Also, please write the mathematical expression that relates ỹ(t) as a function of g(t)and y(t)