Consider the infinite-length, discrete-time sequence , where  is an integer. The region of convergence of its Z-transform  is given by: (Note:  is a complex variable)

If the -transform of a finite-duration discrete-time signal  is , then the  transform of the signal  is

The Z-transform of a discrete signal  is

Which one of the following statements is true?

Consider a signal , where u[n] = 0 if n < 0, and u[n] = 1 if n ≥ 0. The z-transform x[n – k], k > 0 is  with region of convergence being

The pole-zero plots of three discrete-times 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?

H(z) is a transfer function of a real system.  When a signal is the input to such a system, the output is zero. Further the Region of Convergence (ROC) of is the entire Z-plane (except z = 0).  It can then be inferred that H(z) can have a minimum of  

Consider the discrete-time system shown in the figure where the impulse response of G(z) is g(0) = 0, g(1) = g(2) = 1, g(3) = g(4) = ……. = 0

This system is stable for range of values of K

,  are Z-transforms of two signals x[n], y[n] respectively.  A linear time invariant system has the impulse response h[n] defined by these two signals as , where * denotes discrete time convolution. Then the output of the system for the input  

A signal is processed by a causal filter with transfer function G(s). For a distortion free output signal waveform, G(s) must

 is a low-pass digital filter with a phase characteristics same as that of the above question if

The discrete time signal , where ↔ denotes a transform-pair relationship, is orthogonal to the signal.

A discrete real all pass system has a pole at : it, therefore