Problem 1: Determine if the following statements are True or False and briefly describe the reasons for your answers. (a) The Laplace transform of an LTI system's zero-input response is always equal to the system's transfer function, H(s). 12 s(s+3)(s+2)' concluded that the final value (that is, when t approaches infinity) of this signal must be 2. (b) The Laplace transform of a signal is ; . Then, according to the Final Value Theorem, it can be (c) The Nyquist sampling rate for signal (t) = sinc²(50xt) + sinc(80rt) is equal to 200z rad/s.

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Problem 1:
Determine if the following statements are True or False and briefly describe the reasons
for your answers.
(a) The Laplace transform of an LTI system's zero-input response is always equal to the system's transfer
function, H(s).
(b) The Laplace transform of a signal is ;
12
s(s+3)(s+2)'
. Then, according to the Final Value Theorem, it can be
concluded that the final value (that is, when t approaches infinity) of this signal must be 2.
(c) The Nyquist sampling rate for signal (t) = sinc²(50xt) + sinc(80nt) is equal to 200z rad/s.
Transcribed Image Text:Problem 1: Determine if the following statements are True or False and briefly describe the reasons for your answers. (a) The Laplace transform of an LTI system's zero-input response is always equal to the system's transfer function, H(s). (b) The Laplace transform of a signal is ; 12 s(s+3)(s+2)' . Then, according to the Final Value Theorem, it can be concluded that the final value (that is, when t approaches infinity) of this signal must be 2. (c) The Nyquist sampling rate for signal (t) = sinc²(50xt) + sinc(80nt) is equal to 200z rad/s.
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