**1. Introduction**

Gait disorders are usually associated with an ageing population as well as stroke survivors with hemiplegia, thus leading to both a reduced quality of life and an increased mortality rate. The detection of gait events or gait characteristics is essential to numerous applications including the development of control mechanisms in drop foot correction devices [1–5], human activity recognition for healthcare [6,7], motor recovery assessments for effective rehabilitation strategies [1,8], especially for patients with lower limb motor dysfunction following a severe stroke. Heel strike (HS) and toe off (TO) are regarded as two core gait events in a normal gait cycle, which provide information on the swing, stance, and stride gait parameters. Hence, it is essential to develop an effective algorithm for the accurate detection of HS and TO gait events.

With the rapid development of wearable electronic devices, inertial sensors such as accelerometers are fast becoming widely used in gait analysis due to their portable, low-power consumption, and

low-cost characteristics. In this regard, various algorithms aiming at gait event detection based on acceleration signals have been proposed in the recent years. In previous studies [4,9–11], a number of proposed algorithms have attempted to detect gait events based on a peak detection approach that integrates a filtering technique to the acceleration signal based on a set of predefined thresholds in the time domain. However, prior knowledge of the optimal thresholds is relatively difficult to adapt to different subjects in a real-world environment. Also, some attempts have been made to utilize machine learning algorithms for gait event detection via classification models especially with labelled datasets [12]. Note that such machine learning based approaches are limited because their operational procedures are driven by black-box models. Thus, it is difficult for developers and clinicians to truly understand the mechanism of gait event detection that often hinders proper interpretation for practical applications [9,13,14]. By exploiting the limitations of the above described threshold-based approaches and machine learning based methods [1,8], continuous wavelet transform (CWT) based methods have been considered as an alternative solution. By simultaneously providing a signal's information in the time and frequency domains through a series of decomposition and reconstruction operation, the wavelet transform method has been utilized as an effective tool in various fields, such as signal de-noising [15], speech/signal processing and evaluation [16–18], and health threatening illness diagnosis [19]. In the aspect of gait research, CWT based methods have been proven to offer a time-frequency representation with the capability to capture and analyze varying frequencies of acceleration signals, be adaptive to irregular acceleration patterns even in the presence of frequency variations, as well as to attenuate inherent noise and baseline drift [20]. Considering these advantages, wavelet transforms are being increasingly used and have been reported to have good results particularly for gait event detection [13,20–28].

Table 1 summarizes the recently proposed CWT-based methods for detecting gait events, in which different mother wavelets were used in those previous studies. Note that the selection of an appropriate mother wavelet has been stated as a central and open question in the application of wavelet transforms for gait signal analysis [29]. Thus, finding an appropriate mother wavelet for gait events detection could be a crucial step, which would benefit coefficient reconstruction and feature extraction from the signal in time and frequency domains. Meanwhile, in other research domains such as signal de-noising, several mother wavelet selection criteria have been investigated based on some qualitative or quantitative approaches [15,17,30–33]. Apart from the fact that the quantitative method has been strongly advocated, mother wavelet selection based on accuracy driven criteria has attracted a lot of research attention in the recent years due to its simplicity and reliability [30]. However, how to determine the appropriate mother wavelet in gait event detection was rarely reported in the previous studies, so the criteria for the mother wavelet selection is still lacking. Additionally, while most of the previous studies concentrated on the gait analysis of healthy subjects and Parkinson's disease (PD) patients, as showed in Table 1, few studies have been conducted to detect the gait events for hemiplegic patients who often suffer from gait disorders.

Towards determining an appropriate mother wavelet on gait event detection for both healthy subjects and hemiplegic patients, this study firstly constructed a general CWT algorithm. Secondly, we investigated the performance of 32 commonly applied mother wavelets in the recognition of two important gait events (HS and TO) using the acceleration signals obtained from 16 participants (including healthy subjects and hemiplegic patients) during level ground walking. By comparing the performance of different mother wavelets based on both accuracy (time-error, F1-score) and quantitative criteria (cross-correlation coefficient, energy-to-Shannon entropy ratio), the appropriate mother wavelet would be obtained. In this paper, the remaining part is organized as follows. Section 2 describes the improved general CWT algorithm and the criteria for selecting the appropriate mother wavelet. Section 3 presents the experimental results for gait event detection amongst the different mother wavelets and the different wavelet selection criteria in both healthy subjects and hemiplegic patients. Section 4 presents the discussion, and finally Section 5 concludes the work.


**Table 1.** A brief summary of some previous studies for gait event detection based on wavelet transforms.
