Consider a continuous-time finite-energy signal f(t) whose Fourier transform vanishes outside the frequency interval [-ω_c,ω_c], where ω_c is in rad/sec.
The signal f(t) is uniformly sampled to obtain y(t)=f(t)p(t). Here, p(t)=Σ_n=-∞^∞δ(t-τ-nT_s), with δ(t) being the Dirac impulse, T_s>0, and τ>0. The sampled signal y(t) is passed through an ideal lowpass filter h(t)=ω_cT_ssin(ω_ct)/(πω_ct) with cutoff frequency ω_c and passband gain T_s.
The output of the filter is given by