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

$\frac{{d}^{2}y\left(t\right)}{d{t}^{2}}+\alpha \frac{dy\left(t\right)}{dt}+{\alpha }^{2}y\left(t\right)=x\left(t\right).$

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