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QUESTION: 1

Consider a continuous rectangular pulse waveform as shown below:

The Laplace tranform of this above waveform is

Solution:

QUESTION: 2

The Laplace transformation of f(t) is given by F(s).

Given that, the value of f(t) as t →∞

Solution:

QUESTION: 3

The Laplace transform of the signal f(t) = 2e^{-at} sin (bt +θ) is equal to

Solution:

QUESTION: 4

consider a square pulse f(t) as shown in figure below. Let F(s) denote the Laplace transform of f(t)

then the resulting wave form of the inverse Laplace Transform of F^{2}(s) is

Solution:

QUESTION: 5

The Laplace Transform of the signal x(t) = (t^{2} - 2t) u(t - 1)

Solution:

QUESTION: 6

Consider a LTI system with system function The steady-state response of the system is given by (when the excitation is 8 cos2t)

Solution:

QUESTION: 7

The Laplace transform of the signal x(t) whose waveform is shown below is given by

Solution:

QUESTION: 8

The inverse z-transform of a z-domain funcion

Solution:

QUESTION: 9

A discrete-time system is given by the equation

y(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)

The highest degree of ‘z’ in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).

Solution:

QUESTION: 10

Consider the discrete time sequence, and have some ROCs.

- The ROC of X(z) constains the unit circle.
- The ROC of X(z) does not contains the unit circle.
- The discrete sequence x[n], does not have a Fourier transform.
- The discrete sequence x[n] does have a Fourier transform.

Q.

Which is/are correct statement(s)?

Solution:

QUESTION: 11

If the impulse response of discrete-time sequence is h[n] = a^{n} • u[-n - 1], then the system function H(z) equals to, (Assume that α = 1.6)

Solution:

QUESTION: 12

The z-transform X(z) of a discrete-time sequence x[n] is equals to

It is given that the ROC of X(z) does not includes the unit circle, u[n] = 1 for n ≥ 0. The value of x[n] at n = 1 equals to

Solution:

QUESTION: 13

Consider a general signal x(t) which is sampled at sampling rate 1/T to get the discrete-time sequence x(kT) having z-transform X(z). Assume X(s) is the Laplace transform of x(t). For X(s) = X(z), which is the correct relation between s and z?

Solution:

QUESTION: 14

A system is described by the difference equation,

The impulse response of the system is

Solution:

QUESTION: 15

Consider a waveform f(t)as shown in figure below:

The Fourier series of f(t) have

Solution:

QUESTION: 16

The Fourier series expansion of a periodic function f(t) contains only odd harmonics of sine waves. It is clearly say that funciton f(t) is an

Solution:

QUESTION: 17

If X(f) represents the Fourier transform of a signal x(t), which is real and odd symmetric in time, then

Solution:

QUESTION: 18

A signal x(t) has fourier transform X(ω) which is shown in the figure below:

The value present in the signal x(t) at t =0 is

Solution:

QUESTION: 19

A source signal s(t) having a Fourier transform as,

The energy and the power that would be observed through a 1 Ω resistor respectively will be

Solution:

QUESTION: 20

Assuming x(t) is an even function. Then

Fourier transform of x(t) will be:

Solution:

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