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 ______.

A continuous time signal $x(t) = 2 \cos(8 \pi t + \frac{\pi}{3})$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response

$h(t) = \left( \frac{\sin 2 \pi t}{\pi t} \right) \cos(38 \pi t - \frac{\pi}{2})$

produces an output $x_o(t)$. The expression for $x_o(t)$ is ______.