## 1 Introduction  
Ultrasonic testing (UT) is the most widespread non-destructive testing (NDT) technique for the assessment of the structural integrity of highly attenuating and scattering materials, such as carbon fiber reinforced polymers (CFRP), both during manufacturing and in service [1, 2]. However, the multi-layered structure of the material poses a challenge for the sensitivity and resolution of the testing system, especially when the sample is thick and/or it has complex geometry [3]. The signal-to-noise ratio (SNR) achievable for the echo signal of a defect or the backwall is strongly limited by the multiple reflections due to theply interfaces, a fact that limits the minimum detectable defect size. Hence, the minimum detectable defect size guaranteed by the testing system is not as small as required. To overcome this problem, the sensitivity of a UT system can be improved by exploiting hardware or software approaches and/ or tools [4, 5]. Among them, one of the most effective solutions is using phased array (PA) techniques that allow the shape and position of the sound field in the sample under test (SUT) to be manipulated electronically [6, 7, 8]. In pulse-echo mode, transmitting and receiving elements coincide, while in pitch-catch configuration, transmitting and receiving elements are distinct, usually grouped in two separated probes as in the present case of a pulse-compression-based system [9]. Using a PA transducer, the UT beam can be steered or focused on multiple angles/positions in the SUT by simply applying proper time delay patterns to the transmitting elements. Thus, all the elements are fired together, and a unique resulting beam is produced with the desired shape or orientation from the coherent superposition of the singular ultrasonic fields [7]. The response of the sample to this excitation is acquired separately for each receiving element. A proper delay pattern is applied on the digitalized output signals that are then summed to produce the total output signal for the specific angle/focusing law. By collecting measurement signals for a set of angles or focusing positions, not only the SNR of the single 1D measurement can be enhanced, but 2D or 3D images of the SUT can be retrieved [10; 11]. For instance, a real-time sector scan image of the sample can be reconstructed by exploiting the full aperture of a linear array transducer and by steering the beam in the desired range of angles. Thanks to the developments of digital signal generation, acquisition, and processing systems in the last few decades, sector scan images can be produced in real-time with quite high rates, as in medical UT [12]. However, ultrasonic images with even better spatial resolution and SNR can be obtained by post-processing techniques such as full matrix capture (FMC), where each transmitting element is fired alone, and the responses of all the receiving elements are collected and stored. Starting from these data, the total focusing method (TFM) is used to generate 2D or 3D images [13; 14]: for the pixels of the image, a specific delay is calculated and applied to all the possible pairs of transmitting and receiving elements and then the signals from all the pairs are summed to calculate the pixel intensity. TFM images provide a better sensitivity than steering or dynamically focusing images for the detection of small defects [15; 16]. In addition, time reversal and multiple signal classification (MUSIC) algorithms were proposed for their ability to resolve closely spaced scatterers [17]. In addition to PA techniques, many other efforts have been made to define signal processing protocols capable of increasing the sensitivity and resolution of the various UT inspection methods. An example of such techniques is pulse compression (PuC). The core of the procedure is to exploit time and frequency domain signal modulation techniques [18]. The technique is well established in the NDT community and has been proven to improve SNR in a wide span of applications.