Determine if each of the following systems are invertible. If it is, construct t

Question

Determine if each of the following systems are invertible. If it is, construct the inverse system. If it is not, find two input signals to the system that have the same output

a) y(t) = x(t-4)

b) y(t) = cos[x(t)]

Explanation / Answer

a) system is , y(t) = x(t-4) => y(t+4) = x((t+4) - 4) => y(t+4) = x(t) since for a particular output y(t), there is only a single input that produces it, The system is invertible. Inverse System : y(t) = x(t+4) b) clearly if we take x(t) = 0 or x(t) = 2*pi, the output will be y(t) = 1 in both cases. Since, same output is produced by two different input signals, The system is not invertible Two signals: x(t) = 0 and x(t) = 2*pi

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