## 1 Introduction  
Acoustic signal processing is a distinctive application in numerous sectors in life, like industry and communications. In electric motor diagnosis, acoustic noise investigation is a robust alternative to complement the information given by other methods [1; 2; 3; 4]. A common issue in these machines is the occasional occurrence of rotor damage, such as broken bars. These faults may indeed lead to disastrous disappointments and constrained motor blackouts that can infer critical misfortunes for the businesses using them. In particular, it is especially important in the case of high-voltage motors that are used in exceptionally large machines. Figure 1 depicts a picture of the rotor of a motor with broken bars.  
The acoustic noise analysis permits rotor damage to be detected and adjacent broken rotor bars to be classified, as proven in previous works [5]. With regards to the detection of non-adjacent bar breakages, it has not been reliably solved by other techniques like vibration or current analysis techniques that have even provided false-negative diagnostics when detecting this fault [6].  
Noise-based diagnosis algorithms based on fast Fourier transform (FFT) and other spectral methods that rely on subspace vectors were considered in [5; 6; 7; 8; 9; 10; 11; 12]. However, the FFT has a drawback: it is not immune to noise since the spectrum of a noisy signal also includes the noise spectrum. To overcome this constraint, a few researchers have utilized high-resolution spectral algorithms, with the impediment of not knowing a priori the number of subspaces designated to the noise [7; 8].  
Recently, a filter based on the windowed Fourier transforms (WFT) [13] has also been considered, a strategy that lies in a choice of amplitudes: multiexpanded in the spectrum [14], or an algorithm based on calculations on spectral vector subspaces such as MUSIC and ESPRIT [15]. Furthermore, wavelet-based strategies [11; 16; 17; 18; 19; 20; 21; 22] or empirical mode decomposition (EMD) [23] have also been considered.  
The application of higher-order cumulants or bispectrum, or its one-dimensional component, has been employed for fault diagnosis in [24; 25; 26; 27]. However, the use of all the data within the bispectrum lies in two-dimensional Fourier transforms that may increase computational cost.  
Other methods different from the examination of sound signals allow the number of broken bars to be distinguished and the deficiencies in a motor to be analyzed, such as artificial intelligence algorithms [12; 28; 29; 30], thermal images processing [6], and chaos theory methods [31].  
Nevertheless, none of them have demonstrated being substantially sufficient for the case of non-adjacent broken bar diagnosis. Subsequently, we propose a method based on calculations that imply second-order statistics, convolution, and spectral subtractions for the failure detection of bar breakages, using the noise of an induction motor. These calculations are used not only as it were to identify adjacent bar breakages, but also to examine the plausibility of identifying non-adjacent broken bars and hence improve the outcomes of classical methods.  
As commented, one of the cornerstones of the condition monitoring area is the detection of non-adjacent broken bars. Diagnosis tools like the conventional motor current signature analysis (MCSA) may lead to false-positive detection of non-adjacent breakages [32]. Recent efforts have been addressed to detect rotor bar failures, regardless of if the bars were consecutive or not [33; 34]. Here, we propose a new acoustic approach that enables us to detect failures. The method also works for the detection of non-adjacent broken bars.  
In Section 2, we present the foundations of the analyzed fault and of the tools considered in our work. In Section 3, we show that the convolution of a signal motor with its autocovariance permits diminishing the noise. We present the proposed design and the results in Section 4, and the conclusions in Section 5.