GATE Questions & Answers of Transform Theory Electronics and Communication Engg

Transform Theory 4 Question(s)

A causal LTI system has zero initial conditions and impulse response h(t). Its input x(t) and output y(t) are related through the linear constant-coefficient differential equation

d2ytdt2+αdytdt+α2yt=xt.

Let another signal g(t) be defined as

$g\left(t\right)=\alpha^2\int\limits_0^th\left(\tau\right)d\tau+\frac{dh\left(t\right)}{dt}+\alpha h\left(t\right).$

If G(s) is the Laplace transform of g(t), then the number of poles of G(s) is _____.

The trigonometric Fourier series for the waveform f(t) shown below contains

Given ft=L-13s+1s3+4s2 +k-3s.limxft=1 , then the value of K is

Three functions f1(t),f2(t) and f3(t) which are zero outside the interval [0, T], are shown in the figure. Which of the following statements is correct?