Question: Consider two causal systems: a) y[n] = x[n] - 2x[n-1] + x[n-2] b) y[n] -0.9y[n-1] = x[n] 0.5x[n-1] a) Determine the impulse responses of

Consider two causal systems: a) y[n] = x[n] - 2x[n-1] + x[n-2] b) y[n] -0.9y[n-1] = x[n] 0.5x[n-1] a) Determine the impulse responses of the systems b) Determine the frequency response of the systems from their impulse response. Determine the transfer function of the systems (hint: you can apply z- transform for both sides of the equation, then you have H(z)=Y(z)/X(z). c) d) Calculate the power gains of the filters as a function of w and plot them using Matlab (paste the figures to your solution). e) What are the signal processing features of the systems (Hint: LP/HP/BP or else)?

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