Recent development of neural vocoders based on the generative adversarial neural network (GAN) has shown obvious advantages of generating raw waveform conditioned on mel-spectrogram with fast inference speed and lightweight networks. Whereas, it is still challenging to train a universal neural vocoder that can synthesize high-fidelity speech from various scenarios with unseen speakers, languages, and speaking styles. In this paper, we propose DSPGAN, a GAN-based universal vocoder for high-fidelity speech synthesis by applying the time-frequency domain supervision from digital signal processing (DSP). To eliminate the mismatch problem caused by the ground-truth spectrograms in the training phase and the predicted spectrograms in the inference phase, we leverage the mel-spectrogram extracted from the waveform generated by a DSP module, rather than the predicted mel-spectrogram from the Text-to-Speech (TTS) acoustic model, as the time-frequency domain supervision to the GAN-based vocoder. We also utilize sine excitation as the time-domain supervision to improve the harmonic modeling and eliminate various artifacts of the GAN-based vocoder. Experiments show that DSPGAN significantly outperforms the compared approaches and it can generate high-fidelity speech for various TTS models trained using diverse data.