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In this paper we discuss the possible use of chaotic signals for testing Analog-to-Digital Converters (ADCs), with particular reference to the well-known Code Density Test (CDT, also called Histogram Test). In detail, we discuss the implementation of a chaos-based discrete-time noise generator circuit, providing the theoretical analysis of its statistical characterization. The implementation of the chaos-based device is discussed with reference to a generic hardware architecture, taking into account the nonidealities introduced by the presence of noise and the variability of the circuit parameters. Based on this device, we propose a method for generating noisy samples that are distributed, over a target subinterval of the circuit output range, according to a probability density function (pdf) that can be made arbitrarily close to the ideal uniform pdf, in exchange for an acceptable reduction of the uniform-distributed samples generation rate. Theoretical results, also supported by two experiments, confirm the reliability of the proposed solution, showing that chaotic systems can represent an alternative with respect to traditional methods for the generation of signals to be used in the Code Density Test of ADCs.

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There is an odd contradiction about much of the empirical (experimental) literature: The data is analysed using statistical tools which presuppose that there is some noise or randomness in the data, but the source and possible nature of the noise are rarely explicitly discussed. This paper argues that the noise should be brought out into the open, and its nature and implications openly discussed. Whether the statistical analysis involves testing or estimation, the analysis inevitably is built upon some assumed stochastic structure to the noise. Different assumptions justify different analyses, which means that the appropriate type of analysis depends crucially on the stochastic nature of the noise. This paper explores such issues and argues that ignoring the noise can be dangerous.