It is challenging to accelerate the training process while ensuring both high-quality generated voices and acceptable inference speed. In this paper, we propose a novel neural vocoder called InstructSing, which can converge much faster compared with other neural vocoders while maintaining good performance by integrating differentiable digital signal processing and adversarial training. It includes one generator and two discriminators. Specifically, the generator incorporates a harmonic-plus-noise (HN) module to produce 8kHz audio as an instructive signal. Subsequently, the HN module is connected with an extended WaveNet by an UNet-based module, which transforms the output of the HN module to a latent variable sequence containing essential periodic and aperiodic information. In addition to the latent sequence, the extended WaveNet also takes the mel-spectrogram as input to generate 48kHz high-fidelity singing voices. In terms of discriminators, we combine a multi-period discriminator, as originally proposed in HiFiGAN, with a multi-resolution multi-band STFT discriminator. Notably, InstructSing achieves comparable voice quality to other neural vocoders but with only one-tenth of the training steps on a 4 NVIDIA V100 GPU machine\footnote{{Demo page: \href{https://wavelandspeech.github.io/instructsing/}{\texttt{https://wavelandspeech.github.io/inst\\ructsing/}}}}. We plan to open-source our code and pretrained model once the paper get accepted.