In this paper, we presented a novel spectral estimation method, the dyadic aggregated autoregressive model (DASAR), that characterizes the spectrum dynamics of a modulated signal. DASAR enhances automatic modulation classification (AMC) on environments where new or unknown modulation techniques are introduced, and only size-restricted data is accessible to train classification algorithms. A key component for obtaining efficient machine learning-based classification is the development of valuable knowledge-descriptive features. DASAR constructs a multi-level spectral representation by subdividing a signal into successive dyadic segments where each partition is modeled as an aggregation of singlefrequency autoregressive processes. Thus, the model ensures a robust representation at the segment level, while the multi-level decomposition can capture time-varying spectra. As a feature extraction model, DASAR can provide useful learning features related to signals with complex spectra. The effectiveness of our model was tested on a dataset comprised of 11 different modulation techniques and realistic transmission medium characteristics. Using only 200 128-point samples per modulation scheme (1% of the available signal samples) and a proper selection of a classification algorithm, DASAR reaches accuracy up to 70.96% compared with a maximum accuracy of 43.62% using the state-of-art methods tested under the same conditions. INDEX TERMS Automatic modulation classification, signal processing, spectrum modeling, autoregressive model, machine learning. I. INTRODUCTION A reliable communication system enforces that a transmitted message will only be understood if the transmitter and receiver have complete information about the communication parameters, including the type and characteristics of the desired modulation (i.e., the techniques to adapt the message to the transmission medium conditions). However, it is feasible to infer some properties about the communication channel's configuration if we intercept the modulated message passing through the channel. This inference is the central goal in automatic modulation classification (AMC) [1]. AMC was developed for military applications such as electronic warfare, surveillance, and threat analysis [2]. Nevertheless, its relevance made it fundamental for other widespread civilian purposes, including software-defined radio (SDR) and spectrum management. SDR is the base of selforganized communication infrastructures that rely on AMC to recognize the modulation in real-time and to adapt or optimize resources during the ongoing transmission process. The rapid progress and spread of high-speed wireless communication networks (especially 5G and WiFi 802.11ax), and the consequent spectrum saturation, impulse the role of AMC in spectrum management allowing the regulatory entities to detect misused spectrum ranges by non-authorized communication channels. AMC algorithms can be classified into likelihood-based (LB-AMC) and feature-based (FB-AMC) methods [1], [2],

Background Various interacting and interdependent components comprise complex interventions. These components create difficulty in assessing the true impact of interventions designed to improve patient-centered outcomes. Interrupted time series (ITS) designs borrow from case-crossover designs and serve as quasi-experimental methodology able to retrospectively assess the impact of an intervention while accounting for temporal correlation. While ITS designs are aptly situated for studying the impacts of large-scale public health policies, existing ITS software implement rigid ITS methodology that often assume the pre- and post-intervention phases are fully differentiated (by a known change-point or set of time points) and do not allow for changes in both the mean functions and correlation structure. Results This article describes the Robust Interrupted Time Series (RITS) toolbox, a stand-alone user-friendly application researchers can use to implement flexible ITS models that estimate the lagged effect of an intervention on an outcome, level and trend changes, and post-intervention changes in the correlation structure, for single and multiple ITS. The RITS toolbox incorporates a formal test for the existence of a change in the outcome and estimates a change-point over a set of possible change-points defined by the researcher. In settings with multiple ITS, RITS provides a global over-all units change-point and allows for unit-specific changes in the mean functions and correlation structures. Conclusions The RITS toolbox is the first piece of software that allows researchers to use flexible ITS models that test for the existence of a change-point, estimate the change-point (if estimation is desired), and allow for changes in both the mean functions and correlation structures at the change point. RITS does not require any knowledge of a statistical (or otherwise) programming language, is freely available to the community, and may be downloaded and used on a local machine to ensure data protection.

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