Abstract:

This paper introduces a new complex integral transform and applies it to solving first-order complex differential equations with constant coefficients. The transform provides simplified analytical expressions that naturally fit engineering models involving complex signals, channel attenuation, and noise-corrupted communication data. Simulated results show that applying the transform improves signal stability, reduces noise oscillations, and increases the signal-to-noise ratio (SNR). Numerical error analysis further confirms its effectiveness in reconstructing clean signals from noisy environments. These findings demonstrate the transform’s value for smart communication systems, IoT signal modeling, and 5G/6G applications. The approach also supports more secure and resilient digital infrastructures, aligning with modern needs such as reducing cybercrime risks and strengthening trustworthy communication frameworks.