Specific emitter identification (SEI) technology is significant in device administration scenarios, such as self-organized networking and spectrum management, owing to its high security. For nonlinear and non-stationary electromagnetic signals, SEI often employs variational modal decomposition (VMD) to decompose the signal in order to effectively characterize the distinct device fingerprint. However, the trade-off of VMD between the robustness to noise and the ability to preserve signal information has not been investigated in the current literature. Moreover, the existing VMD algorithm does not utilize the stability of the intrinsic distortion of emitters within a certain temporal span, consequently constraining its practical applicability in SEI. In this paper, we propose a joint variational modal decomposition (JVMD) algorithm, which is an improved version of VMD by simultaneously implementing modal decomposition on multi-frame signals. The consistency of multi-frame signals in terms of the central frequencies and the inherent modal functions (IMFs) is exploited, which effectively highlights the distinctive characteristics among emitters and reduces noise. Additionally, the complexity of JVMD is analyzed, which is proven to be more computational-friendly than VMD. Simulations of both modal decomposition and SEI that involve real-world datasets are presented to illustrate that when compared with VMD, the JVMD algorithm improves the accuracy of device classification and the robustness towards noise.