Truncated sampling expansions

Bounds on the output of a linear system are developed and used to reexamine the nature of the truncation error eNin the sampling expansion of a band-limited signalf(t). It is shown that iff(t)has finite energy, then the maximum of|e_{N}|is bounded by the mean-square value of the errorH(\omega)in the approximation ofe^{i\tau\omega}by a truncated Fourier series. Iff(t)has finite power, then the mean-square value of eNis bounded by the maximum of|H(\omega)|.