Questions & Answers of Z-transform

Question No. 18

Consider the sequence xn=anun+bnun, where un denotes the unit-step sequence and 0<a<b<1. The region of convergence (ROC) of the z-transform of xn is

Question No. 218

A discreate-time signal  xn=δn-3+δn-5 has z-transform X(z). If Y(z)=X(-z) is the z-transform of another signal y[n],then

Question No. 241

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal xn=2.0n,-<n<+ , then the ROC of its z-transform is represented by


Question No. 54

For the discrete time system shown in the figure, the poles of the system transfer function are Located at

Question No. 55

The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1, we can conclude.

Question No. 128

Two casual discrete-time signals x[n] and y[n] are related as yn=m=0nxm . If the z-transform of yn is 2zz-12 , the value of x[2] is _______.

Question No. 215

The value of $\sum\limits_{n=0}^\infty n\left(\frac12\right)^n$ is _____.

Question No. 228

Consider a four-point moving average filter defined by the equation yn=i=03αixn-i . The condition on the filter coefficients that results in a null at zero frequency is

Question No. 252

Suppose x[n] is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z=±2j . Which one of the following statements is TRUE for the signal x[n]?

Question No. 13

C is a closed path in the z-plane given by |z|=3. The value of the integral $\oint_C\left(\frac{z^2-z+4j}{z+2j}\right)dz$

Question No. 53

Let  xn=-19nun--13nu-n-1 The Region of Convergence (ROC) of the z-transform of x[n]

Question No. 128

Let x[n]=x[-n]. Let X(z) be the z-transform of x[n]. If 0.5+j 0.25 is a zero of ,X(z) which one of the following must also be a zero of X(z)

Question No. 154

The input-output relationship of a causal stable LTI system is given as

yn=αyn-1+β xn

If the impulse response h[n] of this system satisfies the condition n=0hn=2, the relationship between α and β is

Question No. 228

For an all-pass system Hz=z-1-b1-az-1, where He-jω=1 for all ω
if Rea0,Ima0,then b equals

Question No. 253

Let H1z=1-pz-1-1,H2z=1-qz-1-1,Hz=H1z+rH2z. The quantities p,q,r are real numbers. Consider p=12,q=-14,r<1. If the zero of Hz lies on the unit circle, then r = ________

Question No. 255

The z-transform of the sequence x[n] is given by Xz=11-2z-12  , with the region of convergence z>2. Then, x2 is ________.

Question No. 18

If xn=1/3n-1/2nun, then the region of convergence (ROC) of its Z-transform in the Z-plane will be

Question No. 29

Two systems H1 (z) and H2 (z) are connected in cascade as shown below. The over all output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H2 (z) is

Question No. 14

Consider the z-transform X(z) = 5z2 + 4z-1 + 3; 0<|z| < ∞ . The inverse z transform x[n] is

Question No. 15

Two discrete time systems with impulse responses h1[n] = δ [n -1] and h2[n] = δ [n – 2] are connected in cascade. The overall impulse response of the cascaded system is

Question No. 42

The transfer function of a discrete time LTI system is given by


Consider the following statements:

S1: The system is stable and causal for ROC:z>12

S2: The system is stable but not causal for ROC:z<14

S3: The system is neither stable nor causal for ROC:14<z<12

Which one of the following statements is valid?

Question No. 7

The ROC of Z-transform of the discrete time sequence xn=13nun-12nu-n-1 is

Question No. 40

A system with transfer function H(z) has impulse response h(·) defined as h(2) = 1, h(3) = -1 and h(k) = 0 otherwise. Consider the following statements
      S1 : H(z) is a low pass filter
      S2 : H(z) is a FIR filter
Which of the following is correct?

Question No. 78

In the following network, the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.

The samples x(n) (n = 0, 1, 2, ...) are given by

Question No. 79


In the following network, the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.

The expression and the region of convergence of the z-transform of the sampled signal are

Question No. 51

The z-transform X[z] of a sequence x[n] is given by Xz=0.51-2z-1. It is given that the region of convergence of X[z] includes the unit circle. The value of x[0] is