i) Consider the following system: y[k]+ay[k-1]+...+any[kn] =bu[k]+bu[k-1]+...+bmu[km] + e[k] What minimum order of persistence of excitation...
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i) Consider the following system: y[k]+a₁y[k-1]+...+any[kn] =b₁u[k]+b₁u[k-1]+...+bmu[km] + e[k] What minimum order of persistence of excitation should the input have to identify the parameters of this system? Explain in detail. ii) Consider the problem of identifying the following system: S: Sy[k]=b₁u[k − 1] + b₂u[k − 2] + ... + b₁u[kn] + e[k] - = Determine for what model order n, do the parameters of the system h,, i 1... n, can be uniquely identified for each of the following input signals. treat the asymptotic case where data is available for k=1... N, N→ ∞ a) u[k] = 1 b) u[k] = (-1)" c) u[n] = 1 + (-1)" i) Consider the following system: y[k]+a₁y[k-1]+...+any[kn] =b₁u[k]+b₁u[k-1]+...+bmu[km] + e[k] What minimum order of persistence of excitation should the input have to identify the parameters of this system? Explain in detail. ii) Consider the problem of identifying the following system: S: Sy[k]=b₁u[k − 1] + b₂u[k − 2] + ... + b₁u[kn] + e[k] - = Determine for what model order n, do the parameters of the system h,, i 1... n, can be uniquely identified for each of the following input signals. treat the asymptotic case where data is available for k=1... N, N→ ∞ a) u[k] = 1 b) u[k] = (-1)" c) u[n] = 1 + (-1)"
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