Questions & Answers of Z-transform

Weightage of Z-transform

Total 26 Questions have been asked from Z-transform topic of Signals and Systems subject in previous GATE papers. Average marks 1.54.

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

A discreate-time signal  xn=δn-3+2δn-5 has z-transform $X(z).$ If $Y(z)=X(-z)$ is the z-transform of another signal $y[n]$,then

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


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

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.

Two casual discrete-time signals $ x\lbrack n\rbrack $ and $ y\lbrack n\rbrack $ are related as yn=m=0nxm . If the z-transform of yn is 2zz-12 , the value of $ x\lbrack2\rbrack $ is _______.

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

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

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]?

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

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

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)

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

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

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 = ________

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 ________.

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

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

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

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

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?

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

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?

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


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

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