## 1 Introduction  
The importance of assessing the actual integrity and quality of deep foundations has long been recognized since the last decades. Difficult soils and hydrogeological conditions (occurrence of weak and specific soils in the sections, the aggressiveness and dynamic effects of subsoil waters, etc.) can cause pile defects and impair its constructed pile geometry and material quality, which reduces pile strength and capacity. Methods to control the quality of construction procedures for deep foundations, such as drilled shafts and driven piles, have been provided by the use of nondestructive evaluation (NDE) techniques (e.g., [1, 2]). Low-strain testings, such as the impact echo test method, have been extensively used to evaluate pile integrity, uniformity, and continuity, by checking for possible defects, imperfections, and anomalies in physical dimensions and consistency of the pile material. In addition, the application of low-strain testing methods has been used to evaluate the conditions in end-bearing, such as soft pile toe, due to improper base cleaning, or rock-socketed status of the pile toe [3; 4]. In general, the interpretation of sonic integrity test results needs considerable experience and knowledge in testing, subsoil condition, and construction method. Various guidelines are presented in the literature regarding the interpretation of low-strain integrity test results for the identification of geometric defects or spatial imperfections, such as estimating the cross-sectional area of necking (reduction) or bulge (enlargement) of the pile shaft section, their location, and extent [5; 6]. In most cases, the typical method for signal processing and analysis of results in impact echo tests of piles for the evaluation of their integrity is by linear/nonlinear amplification of the original signal scale response to superimpose any reflected peaks and enhance weak echoes. The basic method of scale amplification of the original signal alone may sometimes fail to identify local and hidden discontinuities, irregularities, and small defects for complex signals, whose interpretation is sometimes obscured by noise. A numerical signal process tool that can substantially improve and strengthen the signal characteristics can be provided by wavelet analysis through the wavelet transform (WT) method. The application of the wavelet transform for low-strain integrity testing has been found to be a promising signal processing tool [7]. [PERSON] et al. [8] presented finite element generated responses of an imaginary pile with a 20% impedance increase at the middle, in which they indicated that the change in impedance was difficult to identify in the time domain, whereas the defect could be observed clearly in the wavelet transform. The wavelet packet transform (WPT) is an extension of the WT, which provides a complete level-by-level decomposition of the signal [9]. WPT has become a popular signal processing method, which has been applied in various fields, such as in the medical industry [10], wind industry [11; 12], electric power industry [12], condition monitoring and fault diagnosis of mechanical systems and structures [13; 14; 15; 16; 17; 18], fatigue damage analysis of composites [19], and many more. The WPT is a signal analysis tool that has the feature of time-frequency resolution. It can be applied to time-varying signals, where the Fourier transform does not produce useful results, and the wavelet transform does not produce sufficient results [20]. The WPT can be considered as an extension to the discrete wavelet transform (DWT), which performs better in the reconstruction process than the discrete one. However, guidelines and recommendations on the interpretation of decomposed signals from low-strain pile integrity tests lack in the literature.