###### Abstract  
Given the constraints on the invariant distribution in chaotic systems, flexibly setting the probability distribution of chaotic signals poses a significant challenge. To tackle this issue, this paper proposes a strategy that transforms the task into solving and modifying the probability density function of the chaotic intrinsic signal. Initially, kernel density estimation algorithms are employed to address the issue of obtaining smooth probability density functions for high-dimensional chaotic signals. Any chaotic signal can serve as the intrinsic signal source, with its probability density function and distribution function being solvable using this algorithm. Subsequently, a graph-based transformation algorithm is introduced for the flexible adjustment of chaotic signal probability distribution. This algorithm can convert the intrinsic signal into a chaotic signal with the desired distribution type based on the characteristics of the target distribution, providing an analytical expression for the transformation relationship. Finally, the effectiveness of this strategy is validated by generating uniform distribution chaotic signals using a Chua chaotic signal as the intrinsic source. The outstanding performance of this signal in suppressing common-mode conducted electromagnetic interference in high-frequency converters is highlighted. The experimental results demonstrate this strategy's ability to flexibly configure probability distribution types of chaotic signals. Additionally, chaotic signals with a uniform distribution can achieve uniform power spectrum shaping, with a suppression effect on maximum common-mode conducted electromagnetic interference reaching 16.56 dB. chaotic signal; probability distribution; uniform distribution; information encryption; image encryption; electromagnetic compatibility +
Footnote †: journal: Medical  
uniform distributions in their invariant distributions [26]. Nonetheless, the range of chaotic systems with uniformly distributed invariant distributions is quite limited, especially in higher-dimensional chaotic systems with greater dynamical complexity, where their invariant distributions tend to be non-uniform. Consequently, the array of chaotic signals with uniform distributions obtainable through this approach is quite restricted. To diversify the range of chaotic signals exhibiting uniform distributions, some researchers have advocated for employing composite systems [27; 28]. The research outlined in [27] reveals that one-dimensional composite mappings can generate chaotic signals with uniform distributions, exemplified by the logistic-tent system, logistic-sine system, and tent-sine system. Likewise, [28] indicates that utilizing a three-dimensional logistic-sine cascading mapping can produce even more uniformly distributed chaotic signals. Nevertheless, these composite systems still require the inclusion of chaotic systems with limit distributions that demonstrate uniformity. Hence, the assortment of chaotic signals with uniform distributions derived from this approach remains relatively constrained. To broaden the spectrum of uniformly distributed chaotic signals, some researchers have proposed an alternative approach involving the manipulation of non-uniformly distributed chaotic systems to obtain such signals [29; 30; 31]. Reference [29] successfully obtained a type of uniformly distributed chaotic signal by accumulating folded chaotic signals. However, the oscillation frequency of the resulting chaotic signal is closely tied to the sampling frequency and the size of the folding domain, necessitating iterative adjustments of these parameters to achieve a more desirable uniform distribution. Conversely, reference [30] employed a method of output distortion and conjugate mapping to synthesize uniformly distributed chaotic signals using multiple chaotic systems. Yet, this method is operationally complex, and implementing inverse mapping without obtaining the analytical distribution function is challenging.