What is the relationship between the Laplace Transform and the Fourier Transform?

The Fourier Transform is a special case of the Laplace Transform, evaluated along the imaginary axis.

Which of the following methods is not used for obtaining the Inverse Laplace Transform of X(s)? A) Partial Fractions B) Series Method C) Complex Inversion Formula D) Integral Transform

D) Integral Transform

True or False: The Region of Convergence (ROC) for a z-transform is independent of the magnitude of z.

False. The ROC for a z-transform depends on the magnitude of z.

Riddle: I can be represented as a ratio of two polynomials in s or z, yet I unveil the dynamics of a system. What am I?

A rational system function.

If the Laplace Transform of x(t) is X(s), then the Inverse Laplace Transform of X(s) is given by ______.

X(t)

What is the necessary condition for the stability of a continuous rational system?

All poles must lie in the left half-plane (Re(s) < />

Which of the following statements about the z-transform is true? A) It can only be applied to finite energy signals. B) It can be applied to a broader class of signals than the DTFT. C) The DTFT is more general than the z-transform. D) The z-transform does not converge for any signal.

B) It can be applied to a broader class of signals than the DTFT.

Fill in the blank: The Inverse Z-Transform is used to obtain the sequence x[n] when ______ is known.

X[z]

True or False: A causal LTI system must have an impulse response that is non-zero for all time.

False. A causal LTI system has an impulse response that is zero for all time t < />

What is the implication of having the imaginary axis included in the ROC of a stable LTI system?

The system is stable if the imaginary axis lies within the ROC.