Signals and Systems
Z Transform
Practice questions from Z Transform.
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IncorrectLet be a discrete-time signal whose -transform is .
Which of the following statements is/are TRUE?
The discrete-time Fourier transform (DTFT) of always exists
The region of convergence (RoC) of contains neither poles nor zeros
The discrete-time Fourier transform (DTFT) exists if the region of convergence (RoC) contains the unit circle
If , where is the unit impulse and is a scalar, then the region of convergence is the entire -plane
Option (A): The DTFT of exists if is absolutely Summable, ie, if .
This is not true for all signals. For example, False statement.
Option (B): The ROC of a z-transform is defined as the set of points in the z-plane where the z-transform converges. It can contain zero but not poles, as poles would causes divergence.
False statement.
Option (C): The DTFT of exists if the unit circle lies within the of the -transform.
True statement.
Option (D): For , which is a constant.
This converges everywhere in the -plane, making the ROC the entire complex plane.
True Statement.
Hence, options (c) and (d) are correct.
For a causal discrete-time LTI system with transfer function
Which of the following statements is/are true?
Since, the system is given to be causal, ROC must lie outside the outermost pole and hence ROC is
Such ROC will include the unit circle and hence the system is stable.
pole is present in right half part of z-plane non-minimum phase system
