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Based on person-job fit and self-determination theory, this paper examined the effects of (in)congruence between autonomy expectation and perceived autonomy on proactive behaviour, and the moderating role of humble leadership in this relationship among Chinese public employees.

Data were collected from a two-wave survey, and the research model was tested using polynomial regression and response surface methodology.

Results suggested that employees' proactive behaviour will be highest when autonomy congruence was achieved, while autonomy incongruence led to different levels of proactive behaviour based on the specific situations. Furthermore, the moderating effect of humble leadership was proved such that it accentuated the positive influence of autonomy congruence on proactive behaviour.

Managers should be fully aware of the benefits and importance of person-job fit and strive to reduce autonomy incongruence. Meanwhile, humble leadership should be considered in the context of granting autonomy to boost proactivity.

This paper re-emphasises the importance of autonomy by utilising a congruence perspective to understand the effects of autonomy on proactive behaviour. Meanwhile, it incorporates an important boundary condition, humble leadership, on the effects of autonomy congruence and thus offers a more nuanced understanding. Further, this paper not only highlights the significance of underexplored concepts among public employees, but also extends autonomy (in)congruence study to a new context and culture.

The purpose of this paper is to analyze the mechanism and filter efficacy of accumulation generation operator (AGO)/inverse accumulation generation operator (IAGO) in the frequency domain.

The AGO/IAGO in time domain will be transferred to the frequency domain by the Fourier transform. Based on the consistency of the mathematical expressions of the AGO/IAGO in the gray system and the digital filter in digital signal processing, the equivalent filter model of the AGO/IAGO is established. The unique methods in digital signal processing systems “spectrum analysis” of AGO/IAGO are carried out in the frequency domain.

Through the theoretical study and practical example, benefit of spectrum analysis is explained, and the mechanism and filter efficacy of AGO/IAGO are quantitatively analyzed. The study indicated that the AGO is particularly suitable to act on the system's behavior time series in which the long period parts is the main factor. The acted sequence has good effect of noise immunity.

The AGO/IAGO has a wonderful effect on the processing of some statistical data, e.g. most of the statistical data related to economic growth, crop production, climate and atmospheric changes are mainly affected by long period factors (i.e. low-frequency data), and most of the disturbances are short-period factors (high-frequency data). After processing by the 1-AGO, its high frequency content is suppressed, and its low frequency content is amplified. In terms of information theory, this two-way effect improves the signal-to-noise ratio greatly and reduces the proportion of noise/interference in the new sequence. Based on 1-AGO acting, the information mining and extrapolation prediction will have a good effect.

The authors find that 1-AGO has a wonderful effect on the processing of data sequence. When the 1-AGO acts on a data sequence X, its low-pass filtering effect will benefit the information fluctuations removing and high-frequency noise/interference reduction, so the data shows a clear exponential change trends. However, it is not suitable for excessive use because its equivalent filter has poles at the non-periodic content. But, because of pol effect at zero frequency, the 1-AGO will greatly amplify the low-frequency information parts and suppress the high-frequency parts in the information at the same time.