Integrated square error for linear interpolation of band-limited signals

The integrated square error is calculated between a band-limited signal
s(t)
and a linearly interpolated signal
s_{L}(t)
obtained from the sampled data of
s(t)
. Band-limited signals, nonperiodic or periodic, are considered. It is shown that the integrated square error together with the energy of
s_{L}(t)
is found from a closed-form evaluation using the power spectrum of the original band-limited signal. Two examples are included to illustrate the ease of application. The integrated-square-error criterion has been used extensively in the design of filters and control systems. Minimization and calculation of the integrated square error can be found in [1]-[6], etc.