PYQs Based Test - 04 : Signals & Systems

The waveform of a periodic signal $\mathrm{x}\left(\mathrm{t}\right)$ is shown in the figure.



A signal g(t) is defined by $\mathrm{g}\left(\mathrm{t}\right)=\mathrm{x}\left(\frac{\mathrm{t}-1}{2}\right)$. The average power of $\mathrm{g}\left(\mathrm{t}\right)$ is __________.

Consider the signal x(t) = cos(6πt) + sin(8πt), where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t) = x(2t + 5) is

Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If $P\left(z\right)=H\left(z\right)H\left(\frac{1}{z}\right)$ has a zero at $z=\frac{1}{2}+\frac{1}{2}j$, and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?

Let the signal f(t) = 0 outside the interval [T₁, T₂], where T₁ and T₂ are finite. Furthermore, $\left|\mathrm{f}\left(\mathrm{t}\right)\right|<\infty$. The region of convergence (ROC) of the signal’s bilateral Laplace transform F(s) is

The value of $\sum _{n=0}^{\infty }n{\left(\frac{1}{2}\right)}^n$ is _________.