In the network shown below, maximum power is to be transferred to the load $R_L$.

The value of $R_L$ (in Ω) is ______.

A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5t) is applied to another causal and stable LTI system with impulse response h(0.5t). The resulting output is ____.

For a causal discrete-time LTI system with transfer function

$H(z) = \frac{2z^2 + 3}{\left(z + \frac{1}{3}\right)\left(z - \frac{1}{3}\right)}$

which of the following statements is/are true?

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below

If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is ______.