6. Nyquist's Problem
By the sampling theorem, any bandlimited signal can be expressed as
$$x(t) = \sum_{n=-\infty}^{\infty} a_n g(t - nT),$$
where $$a_n = x(nT)$$ and $$g(t) = sinc(\frac{t}{T})$$. Suppose the PAM communication system sends $$x(t)$$
over a bandlimited channel with bandwidth 10 kHz, i.e., its frequency response is
$$C(f) = \begin{cases} 1, & |f| < 10,000 \\ 0, & |f| > 10,000. \end{cases}$$