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?

The causal signal with z-transform   is (u[n] is the unit step signal)

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?

Consider a discrete time signal given by

The region of convergence of its Z – transform would be

Let  be the Z – transform of a causal signal x[n], Then, the values of x[2] and x[3] are

If , then the region of convergence (ROC) of its Z-transform in the Z-plane will be

The z-transform of a signal x[n] is given by.  It is applied to a system, with a transfer function.  Let the output be y(n). Which of the following is true?

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  

Given  with , the residue of  at for  will be

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.

y[n] denotes the output and x[n] denotes the input of a discrete-time system given by the difference equation y[n] – 0.8y[n – 1] = x[n] + 1.25x[n + 1].  Its right-sided impulse response is

If u(t) is the unit step and  δ(t) is the unit impulse function, the inverse z-transform of for k ≥ 0 is: