## 1 Introduction
Even with modern advancements focused on deep learning [12] and x-vectors [13], the cepstrum transformation and consequent usage of MFCCs or MFCC-related features still remained crucial in pre-processing for speech recognition. With these premises, acoustic variabilities such as background noise, acoustic environments, microphone differences, and intra-speaker variabilities still appear as crucial and the behavior of MFCCs has to be evaluated in that regard. Other features must be considered as alternatives or useful additions, as they are in many other voice analysis applications such as Speech Emotion Recognition or disease detection [14; 15; 16; 17]. Data augmentation involves the generation of additional synthetic data from pre-existing data in order to enlarge the training set and make the algorithms more robust to variations. Thus, audio-domain data augmentation involves techniques that model real-world criticalities such as background noise or reverberation, and the interaction between the effects of such techniques and the features used for SR (namely MFCCs) is a point of interest of the whole field and this paper in particular. Although other techniques exist, such as pitch shifting or audio stretching, they are unnatural artifacts that do not model real-world mechanics and may lead to unrealistic sets and non-generalized performances. A comprehensive timeline of speaker recognition is presented in Figure 1, where the importance of MFCCs as input features for SR throughout the years is evident, regardless of the models. Figure 1: Timeline of speaker recognition regarding models (above) and input features. ZCR = zero-crossing rate; PLP = Perceptual Linear Predictive; RNN = Recurrent Neural Network; DNN = Deep Neural Network (generic). MFCCs are notably sensitive to background noise, as demonstrated by [PERSON] and [PERSON], among others [18], and this leads many solutions to minimize the effect of lower-energy components. An alternative feature family was proposed by [PERSON] in the form of RASTA-PLP (relative spectral--perceptual linear predictive) coefficients [19]. These are an evolution of the PLP method [3] based on the principle that background noise or additional variabilities, such as those induced by different microphones, have a definite and generally non-changing spectral footprint. Conversely, the unavoidable variations in speech and voice lead to a faster-evolving spectrum. With these premises, RASTA coefficients aim to remove slowly varying frequency components with a pipeline like that outlined here:  
1. Compute the power spectrum of the signal;
2. Warp the frequency (\(x\)-axis) according to the Bark scale;
3. Filter the Bark spectrum in the frequency domain with a RASTA-type filter (see [19]) that removes slowly varying frequency components;
4. Inverse transform (IDFT);
5. Rescale according to an equal loudness curve and raise to the power of 0.33 according to the power law of hearing [20];
6. Compute an all-pole model and extract its coefficients as RASTA-PLP features. The robustness of SR systems to noise and reverb is a common issue that has not had enough discussion in the literature, although the two phenomena are almost unavoidable in real-world acoustic analyses. The general approach in the literature usually involves facing noise and reverb posteriorly by attempting noise removal and/or \"speech enhancement\" techniques, which often include deep learning (DL) models. It is, however, well known that such techniques have unpredictable effects on the spectrum of the signal, which may hinder the generalization power of the SR models. With these premises, the focus of this study is to quantify the effectiveness of the commonly used acoustic features when noise and reverb are present in the data fed to pre-trained SR models. The usage of noise-robust features such as RASTA features, when properly paired to the gold-standard MFCCs, may mitigate the decay in performance of SR models and make them robust for noise or reverb without a loss of generalization.