Abstract
The integrated square error is calculated between a band-limited signal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s(t)</tex> and a linearly interpolated signal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{L}(t)</tex> obtained from the sampled data of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s(t)</tex> . Band-limited signals, nonperiodic or periodic, are considered. It is shown that the integrated square error together with the energy of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{L}(t)</tex> 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.
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