just help me do the exercise part in matlab

1. Estimate impulse response based on correlation Question: Given a "black box system, how to estimate its impulse response/transfer function? Method: Assume the system has impulse response h(n). For input x(n), it gives output y(n) = h(n)*x(n). Consider the cross-correlation Tyx (n) = y(n) * x(-n) = [h(n) + x(n)] + x(-n) = h(n) * rex (n) in which rza(n) is the autocorrelation of the input signal. In the frequency domain, it gives Ryx(W) = HwRxx(W) We will demonstrate that, if the input x(n) is normally distributed random noise, we have approximately by (n) = n(n) This is because the autocorrelation of the random noise is approximately an impulse signal Txx (n) 8(n) and its frequency Rxx(w) * 1. This means we can use random noise as the input for the unknown system, and cross-correlate it with the output of the system, to obtain an approximation of the impulse response of the system. Exercise: For the following systems, compare the estimated impulse response based on correlation with the true impulse response. 1. y() + 0.5y(n-1) = x(n) 2.24+2.4921+2.242-2 2. H(2) 1-0.42-1+0.752-2 1. Estimate impulse response based on correlation Question: Given a "black box system, how to estimate its impulse response/transfer function? Method: Assume the system has impulse response h(n). For input x(n), it gives output y(n) = h(n)*x(n). Consider the cross-correlation Tyx (n) = y(n) * x(-n) = [h(n) + x(n)] + x(-n) = h(n) * rex (n) in which rza(n) is the autocorrelation of the input signal. In the frequency domain, it gives Ryx(W) = HwRxx(W) We will demonstrate that, if the input x(n) is normally distributed random noise, we have approximately by (n) = n(n) This is because the autocorrelation of the random noise is approximately an impulse signal Txx (n) 8(n) and its frequency Rxx(w) * 1. This means we can use random noise as the input for the unknown system, and cross-correlate it with the output of the system, to obtain an approximation of the impulse response of the system. Exercise: For the following systems, compare the estimated impulse response based on correlation with the true impulse response. 1. y() + 0.5y(n-1) = x(n) 2.24+2.4921+2.242-2 2. H(2) 1-0.42-1+0.752-2