GATE Questions & Answers of Laplace Transform and z-Transform

What is the Weightage of Laplace Transform and z-Transform in GATE Exam?

Total 20 Questions have been asked from Laplace Transform and z-Transform topic of Signals and Systems subject in previous GATE papers. Average marks 1.65.

The Laplace Transform of ft=e2tsin5tut is

Let $S=\sum_{n=0}^\infty\limits n\alpha^n\;\mathrm{where}\;\left|\mathrm\alpha\right|<1$. The value of α in the range 0<α<1 such that S=2α is _______.

Consider a causal LTI system characterized by differential equation dytdt+16yt=3xt. The response of the system to the input xt=3e-t3ut, where u(t) denotes the unit step function, is

The solution of the differential equation, for t>0,y''t+2y't+yt=0 with initial conditions y0=0 and y'0=1 is(ut denotes the unit step function),

Consider a linear time-invariant system with transfer function


If the input is cost and the steady state output is Acost+α, then the value of A is _________.

Consider a discrete time signal given by 


The region of convergence of its Z-transform would be

The Laplace transform of $f\left(t\right)=2\sqrt{t/\pi}$  is  $s^{-3/2}$.  The Laplace transform of $g\left(t\right)=\sqrt{1/\pi t}$  is

The z-Transform of a sequence $x\left[n\right]$ is given as $ X\left(z\right)=2z+4-4/z+3/z^2 $. If $y\left[n\right]$ is the first difference of $x\left[n\right]$ , then $Y\left(z\right)$ is given by

Let XZ=11-z-3 be the Z-transform of a causal signal xn. Then, the values of x2 and x3 are

The transfer function V2(s)V1(s) of the circuit shown below is

The impulse response of a continuous time system is given by h(t) =δ(t -1) +δ(t - 3) . The value of the step response at t = 2 is

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

Let the Laplace transform of a function f(t) which exists for t>0 be F1s and the Laplace transform of its delayed version f(t-τ) be F2s. Let F1*s be the complex conjugate of F1s with the Laplace variable set as s=σ+jω. If Gs=F2s.F1*sF1s2, then the inverse Laplace transform of Gs is

Given f(t) and g(t) as shown below:

g(t) can be expressed as

Given f(t) and g(t) as shown below:

The Laplace transform of g(t) is

The z-transform of a signal x[n] is given by 4z-3 + 3z-1 + 2 - 6z2 + 2z3. It is applied to a system, with a transfer function H(z) = 3z-1 - 2. 2. 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 x[n]=(1+j)n is the input to such a system, the output is zero. Further, the Region Of convergence (ROC) of

1-12z-1H(z) is the entire Z-plane (except z=0). It can then be inferred that H(z) can have a minimum of

Given Xz=zz-a2 with Z>a, the residue of X(z)zn-1 at z=a for n0 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

X(z) = 1 - 3z-1, Y(z) = 1 + 2z-2 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 h[n] = x[n-1]*y[n] where * denotes discrete time convolution. Then the output of the system for the input δ[n-1]