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2. In a certain concert hall, echoes of the original signal

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2. In a certain concert hall, echoes of the original signal x(n) are generated due to the reflections at the walls and ceiling. The audio signal experienced by the listener y(n) is a combination of x(n) and its echoes. Let y(n) = x(n) + α x(n-k) where k is the amount of delay in samples and α is its relative strength. Let x(n) = cos (0.2πn) + 0.5 cos (0.6πn), α = 0.1, k = 50. Generate 200 samples of y(n) and plot them. Also obtain the system function.

Do we have to calculate y(1), y(2),.........y(200)?

If, yes; we will have y(1) = cos (0.2pi*1) + 0.5 cos (0.6pi*1)+0.1x(-49)

and x(-49) = cos (0.2pi*-49) + 0.5 cos (0.6pi*-49). Putting this, we can find out y1 and other values y(2),y(3),y4,......y(200). Is this what you want? I can reply in 2 hours after you clarify my doubt.