## 1 Introduction  
Pipelines are the main means of transferring oil and gas. They are usually installed in hostile locations and must be inspected to avoid failures that would be harmful to the environment. Ultrasonic guided-wave (UGW) enables long-range inspection of pipelines from one single test point. For example, the UGW technique in pulse-echo mode can enable inspections of up to 50 m (in normal testing conditions); hence, it is cost efficient in the inspection of large structures. The received signals are inspected in time-domain where inspectors spot anomalies in the data based on their local signal-to-noise ratio (SNR). In any region where the envelope of the signal has higher energy than the regional noise level, an anomaly is reported which can indicate a defect or a feature of the pipe [1; 2; 3]. UGWs are multimodal: for each excitation frequency, multiple wave modes are transmitted and received. In the inspection, the goal is to achieve a pure axisymmetric wave, but due to the imperfect testing conditions [4; 5], nonaxisymmetric waves will also be received. This is the main source of the coherent noise in the inspection. To allow ease of inspection, many researchers have applied digital signal processing methods that use the differences in these wave modes to either detect the axisymmetric wave or filter the nonaxisymmetric waves to increase the SNR of the received anomalies. One of the widely used techniques in the signal processing of guided-waves is the work of [PERSON] et al. [6], which uses previously calculated dispersion curves in order to compensate for the effect of dispersion for the wave mode of interest in a certain propagation distance. In 2013, [PERSON] et al. [7] used the basis of the dispersion compensation technique and introduced a novel method to design waveforms in order to precompensate for a certain propagation distance. Pulse compression is another approach that has been previously investigated in the literature. Instead of exciting a narrowband sine wave sequence, pulse compression uses a known coded sequence and processes the received signal by applying match-filtering in order to detect the known sequence. One of the initial attempts of testing pulse compression in the guided-wave was done by [PERSON] et al. [8; 9], where chirp sequences were excited using air-coupled piezoelectric transducer in order to generate Lamb waves in aluminum plates. Higher SNR and peak values for the signals of interests were achieved in the experiments; however, the effect of dispersion was not considered, and therefore a decrease in signal amplitude was expected. In 2010, they published another paper using the same system where the phase modulation based on Golay codes were used where the enhancement of 21 dB in SNR using a 16-bit Golay code was achieved compared to the conventional pulse transmission. [PERSON] et al. [10; 11], introduced an iterative dispersion compensation for removing the dispersion effect of guided-wave propagation. Most recently, [PERSON] et al. [12] developed a two-dimensional compressed pulse analysis in order to enhance the achieved SNR of each wave mode. In the pulse compression approaches, the results are always a trade-off between the spatial resolution and SNR, as having a result with higher propagation energy and \(\delta\)-like correlation means that the signal duration must be increased. Furthermore, the transfer function of the excitation system can affect the accuracy of the coded waveforms. These two factors indicate that the initial waveform design and the accuracy of inspection using this method depend on the testing conditions. On the other hand, other approaches have also been reported in the literature where narrowband sine waves were used as excitation sequence. [PERSON] et al. investigated split-spectrum processing [13; 14; 15], where the time-domain signal is decomposed into multiple signals in different frequency bands, and then recombined in time-domain in order to remove the coherent noise.