Consider the infinite-length, discrete-time sequence $x[n]=0.9^{|n|}$, where $n$ is an integer. The region of convergence of its Z-transform $X(z)$ is given by:

(Note: $z$ is a complex variable)

The Z-transform of a discrete signal $$x[n]$$ is

$$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$.

Which one of the following statements is true?

The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below. Which one of the following is TRUE about the frequency selectivity of these systems?

The z-Transform of a sequence x[n] is given as X(z) = 2z+4−4/z+3/z². If y[n] is the first difference of x[n], then Y(Z) is given by