Nyquist-Shannon sampling theorem on non infinite signals - Electrical Engineering Stack Exchange

can sample , recover signals non infinite "length" using nyquist shannon theorem? example if have signal

$$ x(t)= u(t+5)-u(t-5) $$ , know sampling period t less 10s (t<10). can recover using nyquist theorem? if not , recover it?

edit: have taken fourier transform of signal , : $$x(ω)=2i(\frac{1}{iω}+πδ(ω))sin(5ω)$$ can lead finding period $$\frac{2π}{5} $$ , see if f>= 5/π can recovered. may not possible because used theorem although on finite signal

no need think "finite length". though continuous time signals defined infinite time interval, in practice analyse in finite interval only. x(t) defined in interval [-5 5].

the frequency domain representation of such signal infinite bandwidth sinc function.

hence not possible define particular sample rate per nyquist theorem, reconstruct without losing information. can sample definite sample rate, implicitly band limits signal. sampled signal after reconstruction through dac , lpf, not perfect original 1 band limited. have finite transition time rise , fall.