PYQs Based test 7: Signals & Systems

The energy of the signal $x(t)=\frac{\sin \left(4\pi \mathrm{t}\right)}{4\pi \mathrm{t}}$ is______

Let h(t) denote the impulse response of causal system with transfer function

$H\left(s\right)=\frac{1}{s+1}$

Consider the following three statements

S₁: The system is stable

S₂: $\frac{h\left(t+1\right)}{h\left(t\right)}$ is independent of time

S₃: A non – causal system with same transfer function is stable for the above system

Let $x\left[n\right]={\left(-\frac{1}{9}\right)}^{n}u\left[n\right]-{\left(-\frac{1}{3}\right)}^{n}u\left[-n-1\right]$. The Region of convergence (ROC) of the z-transform

Consider the signal x(t) = e${}^{-|t|}$. Let X(jω) = $\underset{-\infty }{\overset{\infty }{\int }}x\left(t\right)e^{-j\omega t}dt$ be the Fourier transform of x(t). The value of X(j0) is

For the periodic signal x(t) shown below with period T = 8s, the power in the 10${}^{th}$ harmonic is