Q1:

A linear discrete time system has the characteristic equation z³ – 0.49z = 0. The system

Q2:

A linear discrete time system has the characteristic equation z² + 3z + 2. The system

Q3:

The region of convergence of the z-transform of a unit step function is

Q4:

If the impulse response of a discrete time system is $h\left[n\right]=-2^{n}u\left[-n-1\right]$, then the system function H(z) is equal to

Q5:

If$x\left[n\right]={\left(\frac{1}{3}\right)}^{\left|n\right|}$, then the region of convergence (ROC) of its z-transform in the z-plane will be

Q6:

Two discrete time systems with impulse responses $h_1\left[n\right]=\delta \left[n-2\right]$and $h_2\left[n\right]=\delta \left[n-3\right]$are connected in cascade. The overall impulse response of the cascaded system is

Q7:

A discrete time signal $x\left[n\right]=\delta \left[n-2\right]+2\delta \left[n-6\right]$has z-transform$X\left(z\right)$. If $Y\left(z\right)=X\left(-z\right)$is the z-transform of another signal $y\left[n\right]$, then

Q8:

The steady state value using final value theorem, if $X\left(z\right)=\frac{z}{z-0.5}-\frac{0.5z}{z-1},\left|z\right|>1$

Q9:

A linear  time invariant system is characterized by the system $H\left(z\right)=\frac{1}{1-0.5z^{-1}}+\frac{1}{1-2z^{-1}}$

What is the h(n) if the system is stable

Q10:

What is the z-transform of the finite duration signal

 $X\left(n\right)=\left\{3,5,7,0,2\right\}$

                      $\uparrow$

Q11:

Which of the following series has an ROC as mentioned below?

Q12:

What is the Region of Convergence of the signal$X\left(n\right)=\delta \left(n-k\right),k>0$?

Q13:

The ROC of z-transform of any signal

Q14:

Consider a two sided discrete-time signal (neither left sided, nor right sided). The region of convergence (ROC) of the z-transform of the sequence is

1. All region of z-plane outside a unit circle,

2. All region of z-plane inside a unit circle.

3. Ring in z-plane

Which of the above is/are correct?

Q15:

z-transform deals with discrete time system for their

1. Transient behavior

2. Steady-state behavior

Which of the above behaviors is/are correct?