High-quality brain signal data recorded by Stereoelectroencephalography (SEEG) electrodes provide clinicians with clear guidance for presurgical assessments for epilepsy surgeries. SEEG, however, is limited to selected patients with epilepsy due to its invasive procedure. In this work, a brain signal synthesis framework is presented to synthesize SEEG signals from non-invasive EEG signals. First, a strategy to determine the matching relation between EEG and SEEG channels is presented by considering both signal correlation and spatial distance. Second, the EEG-to-SEEG generative adversarial network (E2SGAN) is proposed to precisely synthesize SEEG data from the simultaneous EEG data. Although the widely adopted magnitude spectra has proved to be informative in EEG tasks, it leaves much to be desired in the setting of signal synthesis. To this end, instantaneous frequency spectra is introduced to further represent the alignment of the signal. Correlative spectral attention (CSA) is proposed to enhance the discriminator of E2SGAN by capturing the correlation between each pair of EEG and SEEG frequencies. The weighted patch prediction (WPP) technique is devised to ensure robust temporal results. Comparison experiments on real-patient data demonstrate that E2SGAN outperforms baseline methods in both temporal and frequency domains. The perturbation experiment reveals that the synthesized results have the potential to capture abnormal discharges in epileptic patients before seizures.