1. Consider a stable and causal system with impulse response h(t) and system function H(S). Suppose H(S) is rational, contains a pole at S = - 2, and does not have a zero at the origin. The location of all other poles and zero is unknown for each of the following statements. Let us determine whether statement is true or false. f[h(t) e-3t] convergesh(t) has finite durationH(s) = H(- s) Choose correct option.
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- By: guest on 02 Jun 2017 12.54 amStatement 1 is false, since f{h(t)e3t} corresponds to the value of the Laplace transform of h(t) at s = 3. If this converges, it implies that s = - 3 is in the ROC. A casual and stable system must always have its ROC to the right of all its poles. However, s = - 3 is not to the right of the pole at s = - 2. Statement 2 is false, because it is equivalent to stating that H(0) = 0. This contradicts the fact that H(s) does not have a zero at the origin. Statement 3 is false. If h(t) is of finite duration, then if its Laplace transform has any points in its ROC, ROC must be the entire s-plane. However, this is not consistent with H(s) having a pole at s = - 2. Statement 4 is false. If it were true, then H(s) has a pole at s = - 2, it must also have a pole at s = 2. This is inconsistent with the fact that all the poles of a causal and stable system must be in the left half of the s-plane.
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