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SAMPLING AND RECONSTRUCTION WITH INTERSAMPLE ERROR A fundamental requirement of sampled-data systems is the sampling of continuoustime signals to obtain a representative set of numbers that can be used by a digital computer. The primary goal of this chapter is to provide an understanding of this process. The first section explores theoretical aspects of sampling and the formal considerations of signal recovery, including ideal Wiener filtering in signal interpolation. Aliasing of signal and noise are considered next in a detailed development involving a heterodyne basis of evaluation. . | Multisensor Instrumentation 6a Design. By Patrick H. Garrett Copyright 2002 by John Wiley Sons Inc. ISBNs 0-471-20506-0 Print 0-471-22155-4 Electronic 6 SAMPLING AND RECONSTRUCTION WITH INTERSAMPLE ERROR 6-0 INTRODUCTION A fundamental requirement of sampled-data systems is the sampling of continuoustime signals to obtain a representative set of numbers that can be used by a digital computer. The primary goal of this chapter is to provide an understanding of this process. The first section explores theoretical aspects of sampling and the formal considerations of signal recovery including ideal Wiener filtering in signal interpolation. Aliasing of signal and noise are considered next in a detailed development involving a heterodyne basis of evaluation. This development coordinates signal bandwidth sample rate and band-limiting prior to sampling to achieve minimum aliasing error under conditions of significant aliasable content. The third section addresses intersample error in sampled systems and provides a sample-rate-to-signal-bandwidth ratio fsJBW expressing the step-interpolator representation of sampled data in terms of equivalent binary accuracy. The final section derives a mean-squared error criterion for evaluating the performance of practical signal recovery techniques. This provides an interpolated output signal accuracy in terms of the corresponding minimum required sample rate and suggests a data conversion system design procedure that is based on considering system output performance requirements first. 6-1 SAMPLED DATA THEORY Observation of typical sensor signals generally reveals band-limited continuous functions with a diminished amplitude outside of a specific frequency band except for interference or noise which may extend over a wide bandwidth. This is attributable to the natural roll-off or inertia associated with actual processes or systems providing the sensor excitation. Sampled-data systems provide discrete signals of 121 122 SAMPLING AND .
