7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function of this causal inverse system (f) Is the inverse system of this system stable? Note: You need to prove your conclusion in a formal way) 7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function of this causal inverse system (f) Is the inverse system of this system stable? Note: You need to prove your conclusion in a formal way)
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Engineering 2022-05-15 21:04:59