An LTI system has the impulse response h(t) = sin(20 pi t+ 10) u (t - 1). a. Is

Question

An LTI system has the impulse response h(t) = sin(20 pi t+ 10) u (t - 1). a. Is this system causal? Explain your answer. b. Is this system BIBO stable? Justify your answer. If it is unstable, also specify a bounded input that produces an unbounded output. An LTI system has the impulse response h(t) = exp(-t) u (t - 1). a. Is this system causal? Explain your answer. b. Is this system BIBO stable? Justify your answer. If it is unstable, also specify a bounded input that produces an unbounded output. An LTI system has the impulse response h(t) = u(t) - u(t - 0.1). Specify all positive frequencies at which the transfer function exactly equal to zero. Two signals, a(t) and b(t), are convolved to produce a new signal c(t). Signal a(t) starts at time t = 1 and ends at time t = 5: b(t) starts at t = -1 and ends at t = 1, when must c(t) start and stop?

Explanation / Answer

Answe1:- a) The system is causal because the output depends on the prrsent and past values of input due to presence of u(t - 1) term.

b) The system has it's value between -1 and 1 for all value of t. Hence the given system is BIBO stable. If a system reaches a value +/- infinity for any input value then system is not BIBO stable.

Answer3:- The given signal is a pulse having pulse width, T=0.1s. Hence the positive frequency where it's spectrum will have a value zero are:- 10Hz, 20Hz, 30Hz, … . Note that the pulse has transform as a sinc signal.

Answer4:- The signal c(t) will have 5+3-1 terms i.e 7 terms in the convolution result. If we perform a(t)*b(t) it means keeping a(t) as it is and folding and moving b(t), this will give c(t) to start from t=1 and end at t=8, because before t=1, signal a(t) is not defined.

If we perform b(t)*a(t) then from t=-1 to t=6.

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