which of the following system is a causal system?(a) y(t)=sin[u(t+3)](b) y(t)=5u(t)+3u(t-1)(c) y(t)=5u(t)+3u(t+1)(d) y(t)=sin[u(t-3)]+sin[u(t+3)]
Question
which of the following system is a causal system?(a) y(t)=sinu(t+3) y(t)=5u(t)+3u(t-1)(c) y(t)=5u(t)+3u(t+1)(d) y(t)=sin[u(t-3)]+sin[u(t+3)]
Solution
A causal system is a system where the output at any time depends only on the values of the input at the present and past times, but not on future inputs.
(a) y(t)=sin[u(t+3)] - This is a non-causal system because the output y(t) depends on the future value of the input u(t+3).
(b) y(t)=5u(t)+3u(t-1) - This is a causal system because the output y(t) depends only on the present input u(t) and past input u(t-1).
(c) y(t)=5u(t)+3u(t+1) - This is a non-causal system because the output y(t) depends on the future value of the input u(t+1).
(d) y(t)=sin[u(t-3)]+sin[u(t+3)] - This is a non-causal system because the output y(t) depends on both past and future values of the input.
So, the only causal system among the given options is (b) y(t)=5u(t)+3u(t-1).
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