## 1 Introduction
In their most recent work [15], it was reported that using the optimum filter parameters and polarity thresholding method for recombination, the SNR of defects with sizes as small as 2% cross-sectional area (CSA) could be improved significantly. Nonetheless, the technique depends on various parameters which can depend on the pipes' characteristics. Another recently developed method is the spectral subtraction, investigated by [PERSON] et al. [16]. In this method, the noise signature is calculated using a small section of the retrieved signal where no real pipe feature exists. Afterwards, this signal is subtracted from the total signal using a sliding window where a significant reduction of coherent noise level could be achieved. Nonetheless, achieving noise signature in the practical inspection of pipelines is difficult as the location of defects and even pipe features might be unknown. Guided-waves are dispersive and multimodal [17]. Depending on the excitation frequency, multiple wave modes can be generated at the point of excitation. Guided-wave modes are categorised based on their displacement patterns (mode shapes) within the structure. Three main families of waves exist in pipes, which are longitudinal, torsional and flexural. Longitudinal and torsional waves are axisymmetric waves, while flexural waves are nonaxisymmetric. The popular nomenclature used for them are in the format of \(X\) (\(n\),\(m\)), where \(X\) can be replaced by the letters \(L\) for longitudinal, \(T\) for torsional and \(F\) for flexural waves; \(n\) shows the harmonic variations of displacement and stress around the circumference and \(m\) represents the order of existence of the wave mode [18]. In general inspection,the practice is to generate a single pure axisymmetric wave which tends to ease the interpretation of results. However, variations in the transducers' transfer function and their placement will cause the flexural waves to be received; furthermore, wave mode conversion also causes flexural waves to be received [5; 17; 18; 19]. Dispersion causes the energy of a signal to spread out in space and time as it propagates [6]. Figure 1a shows an example of a dispersion curve calculated from 8-inch schedule 40 steel pipe using RAPID software [21]. [PERSON] et al. introduced a method to use dispersion curves in order to both simulate [22] and remove [6] the effect of dispersion. Using the developed formula, an example of a dispersive wave is shown in Figure 1b, which is based on the dispersion curves of F (4,2). Unlike T (0,1), which is nondispersive across its whole frequency range [23], flexural waves are dispersive. Therefore, for ease of inspection, the torsional wave which is both axisymmetric and nondispersive is used. The common concept in all the aforementioned signal processing methods is the usage of dispersion and multimodality of guided-waves in order to increase the SNR. Afterwards, the signals are inspected in time-domain to report on the location of anomalies. It has already been demonstrated in the literature that the spectral domain can be processed to remove the noise. Looking at the problem with another perspective, instead of noise removal, the spectral domain can also be used to detect the signal of interests (defect) automatically. The excitation sequence is not dispersive and axisymmetric; hence, no significant changes in the frequency response of the received signal should be inspected. Therefore, a sliding window is used where the power spectrum of each iteration is compared with the one achieved from the excitation sequence. The primary motivation is to enable automated inspection of pipelines without the need for any inspectors. However, at this stage, the developed algorithm can be used as a tool, along with the conventional detection methods, to provide more certainty in interoperation of the results and reduce the number of outliers called due to the coherent noise. It is expected that experience of this algorithm will help develop automated inspection of pipelines.