The continuous time signal $x(t)$ is real, periodic with period $T$ and satisfies the Dirichlet conditions.

The Fourier series representation of $x(t)=\sum_{n=-\infty}^{\infty} a_n e^{j\left(\frac{2 \pi n t}{T}\right)}$ and $x(t)$ satisfies the following:

$$ x\left(t-\frac{T}{2}\right)=-x(t) $$

For any integer $m$, which of the following options is correct?

Consider a real signal $x(t),-\infty

Let $E[x(t)]=\int_{-\infty}^{\infty}[x(t)]^2 d t$.

Which of the following options correctly represents the ratio, $E[x(t)] / E[3 x(-3 t+)]$ ?

Consider a real baseband signal $x(t)=e^{-2 t}$, for $t$ (in seconds) $\geq 0$. If $99 \%$ of energy of $x(t)$ lies within $B \mathrm{~Hz}$, then which of the following options is TRUE for the value of $B$ ?

Consider the discrete time system $(S)$ with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_1[n]$ and $h_2[n]$ are linear and time invariant.

Which of the following statements is necessarily TRUE?