## 1 Introduction
The autoregressive (AR) model has proved useful for processing stationary random process, for example, for spectral analysis even with short time segments of information. In fact, respiratory sounds can be represented as a response of a system formed by lung parenchyma and chest wall to a white noise input which models the respiratory sounds source; hence, the system may be modeled as an all-pole filter. Several AR-based models have been presented in the literature. In [48], AR-based features were used to feed two classifiers, a k-nearest neighbour (k-NN) classifier and a quadratic classifier, in order to discriminate between pathological and healthy patients. In [49], the authors combined sixth-order AR coefficients, wavelet coefficients, and crackle parameters as input for a k-NN and single layer perceptron. In a multichannel scenario (i.e., using several microphones), multivariate AR version called vector AR (VAR) has been used in [50] as input for SVM and Gaussian mixture model (GMM) classifiers. Moreover, in [51], the authors proposed a crackle detection system using a threshold over the coefficients of a time-varying AR (TVAR) model showing superior results than using waveform analysis. There are studies that have evaluated the detection of abnormal lung sounds from a physical perspective. In [52], it was asserted that determining the origin of abnormal sounds can provide valuable insights, potentially narrowing down the range of possible pathological causes and pinpointing the specific affected lung region. This information can prove invaluable in the context of diagnosis and treatment planning. To address this matter, [53] introduced an algorithm capable of effectively imaging sound sources, a capability demonstrated through computer simulations and experiments involving life-sized gelatin models of the human thorax. Their findings suggest that meaningful spatial information can be extracted from recordings employing as few as 16 microphones. Recently, in [54], a discussion of these types of studies covering auscultatory methods was presented. Alternatively, in this paper we aim to detect and localize the temporal occurrence of adventitious sounds on an input single-channel respiratory signal. In fact, the information about the temporal location will serve to focus a doctor's attention on the regions of the signal where crackles are present. In this paper, we investigate the effect of the autoregressive (AR)-based frequency features that characterizes the spectral envelope of a breathing signal. In particular, we propose the utilization of complex valued poles derived from the AR model as inputs for a support vector machine (SVM) classifier using the radial basis function (RBF) kernel. The proposed approach has been compared with other state-of-the-art approaches including the iterative envelope mean-fractal dimension (IEM-FD) and the time-varying autoregressive (TVAR) methods. Finally, the proposed AR-based features are combined with a state-of-the-art convolutional neural network (CNN) architecture for crackle detection [55]. The outcomes of this comparison revealed notable enhancements in the performance metrics associated with the proposed methodology for characterizing and detecting crackles events. In fact, when dealing with limited data quantities, SVM presents a preferable choice whereas deep learning models typically entail a substantial number of tunable weights (free variables) that necessitate calibration with data. Actually, when the quantity of these weights exceeds or approximates the number of available training examples, deep models tend to essentially \"memorize\" the data, which can lead to overfitting. On the contrary, when a suitable kernel function is applied, SVM provides a robust, efficient, easily interpretable solution and is less prone to overfitting in classification problems. The paper is organized as follows. Section 2 reviews the dataset used in this work and details the proposed method.