The error performance of a digital FM system is studied in the presence of additive Gaussian noise. This system is a conventional one employing a voltage-controlled oscillator as the modulator and a limiter-discriminator followed by a low-passfilter as the demodulator.The notion of "clicks" introduced by Rice, and used by Mazo and Salz, is adopted and the performance of the above system is theoretically studied when the intersymbol interference caused by band limitation cannot be neglected. Special consideration has been given to binary frequency-shift keying (FSK) systems. For such systems, the probability of error is given in a closed form. T I. INTRODUCTION-HISTORICAL REVIEW H E I'M receivers have been studied by several investigators [1]-[SI.The primary studies were concerned with the signal-to-noise (S/N) performance of analog signals. The criterion of S/N transfer is not satisfactory, however, in digital data transmission. A better measure of performance then is the probability of making false decisions at the receiver (called-the probability of error and denoted by P,) . In nonlinear systems, this probability cannot, in general, be directly related to the S/N ratio. I n addition, it was observed that when the noise input to the FM receiver exceeds a certain value, the S/N value measured at the output is much poorer than the one predicted by the linearized analysis. Rice [a] related this phenomenon to the expected number of clicks per second at the output.Bennett and Salz [SI analyzed binary FM systems taking into consideration the distortion effects due t o band limitations, but neglected the influence of the postdetection filter. This filter, though, strongly influences the proper selection of signals for best performance.More recently, Mazo and Salz [Z] using the notion of "clicks' [l] developed a theory for predicting the performance of digital FA4 systems with the post-detection filter included. No consideration was given, however, to the distortions produced by band limiting the FM wave. Such distortions were included in the paper by Tjhung and Wittke [SI. Their influence on the performance of the

In computer music fields, such as algorithmic composition and live coding, the aural exploration of parameter combinations is the process through which systems’ capabilities are learned and the material for different musical tasks is selected and classified. Despite its importance, few models of this process have been proposed. Here, a rule extraction algorithm is presented. It works with data obtained during a user auditory exploration of parameters, in which specific perceptual categories are searched. The extracted rules express complex, but general relationships, among parameter values and categories. Its formation is controlled by functions that govern the data grouping. These are given by the user through heuristic considerations. The rules are used to build two more general models: a set of “extended or Inference Rules” and a fuzzy classifier which allow the user to infer unheard combinations of parameters consistent with the preselected categories from the extended rules and between the limits of the explored parameter space, respectively. To evaluate the models, user tests were performed. The constructed models allow to reduce complexity in operating the systems, by providing a set of “presets” for different categories, and extend compositional capacities through the inferred combinations, alongside a structured representation of the information.Peer ReviewedPostprint (author's final draft

This manuscript explores fuzzy rule learning for sound synthesizer programming within the performative practice known as live coding. In this practice, sound synthesis algorithms are programmed in real time by means of source code. To facilitate this, one possibility is to automatically create variations out of a few synthesizer presets. However, the need for real-time feedback makes existent synthesizer programmers unfeasible to use. In addition, sometimes presets are created mid-performance and as such no benchmarks exist. Inductive rule learning has shown to be effective for creating real-time variations in such a scenario. However, logical IF-THEN rules do not cover the whole feature space. Here, we present an algorithm that extends IF-THEN rules to hyperrectangles, which are used as the cores of membership functions to create a map of the input space. To generalize the rules, the contradictions are solved by a maximum volume heuristics. The user controls the novelty-consistency balance with respect to the input data using the algorithm parameters. The algorithm was evaluated in live performances and by cross-validation using extrinsic-benchmarks and a dataset collected during user tests. The model’s accuracy achieves state-of-the-art results. This, together with the positive criticism received from live coders that tested our methodology, suggests that this is a promising approach.

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Abstract-Algorithmic composition is the process of creating musical material by means of formal methods. As a consequence of its design, algorithmic composition systems are (explicitly or implicitly) described in terms of parameters. Thus, parameter space exploration plays a key role in learning the system's capabilities. However, this task has surprisingly received little attention. Two main problems appear when working on exploring parameter spaces. First, depending on the system, the dimension of the output space maybe very large. And second, the produced changes on the human perception of the outputs, as a response to changes on the parameters, could be highly non-linear. The present work describes a methodology for the human perceptual (or aesthetic) exploration of generative systems' parameter spaces. As the systems' outputs are intended to produce an aesthetic experience on humans, audition plays a central role in the process. The methodology starts from a set of parameter combinations which are perceptually evaluated by the user. The sampling process of such combinations depends on the system under study and possible on heuristic considerations. The evaluated set is processed by a compaction algorithm able to generate linguistic rules describing the distinct perceptions (classes) of the user evaluation. The semantic level of the extracted rules allows for interpretability, while showing great potential in describing high and low-level musical entities. Previous work and the experiments that lead to the current methodology and algorithm are described in detail. As the resulting rules represent discrete points in the parameter space, further possible extensions for interpolation between points are also discussed. Finally, some practical implementations are presented together with paths of current and further research.