These days, a wide variety of wireless systems are used and new wireless systems appear one after another on the market. In this regard, we proposed a unified wireless system that we call flexible wireless system. Comprising flexible access points and a flexible signal processing unit, it collectively receives a wideband spectrum that includes multiple signals from various wireless systems. In cases of simultaneous multiple signal reception, however, reception performance degrades due to the interference among multiple signals. To address this problem, we propose a new signal separation and reconstruction method for spectrally overlapped signals. The method analyzes spectral information obtained by the short time Fourier transform to extract amplitude and phase values at each center frequency of overlapped signals. Using these values enables signals from received radio wave data to be separated and reconstructed for simultaneous multi-system reception. Computer simulation results obtained in evaluating the method's performance confirmed its effectiveness.