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Let 
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.