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End-to-end singing voice synthesis (SVS) model VISinger can achieve better performance than the typical two-stage model with fewer parameters. However, VISinger has several problems: text-to-phase problem, the end-to-end model learns the meaningless mapping of text-to-phase; glitches problem, the harmonic components corresponding to the periodic signal of the voiced segment occurs a sudden change with audible artefacts; low sampling rate, the sampling rate of 24KHz does not meet the application needs of high-fidelity generation with the full-band rate (44.1KHz or higher). In this paper, we propose VISinger 2 to address these issues by integrating the digital signal processing (DSP) methods with VISinger. Specifically, inspired by recent advances in differentiable digital signal processing (DDSP), we incorporate a DSP synthesizer into the decoder to solve the above issues. The DSP synthesizer consists of a harmonic synthesizer and a noise synthesizer to generate periodic and aperiodic signals, respectively, from the latent representation z in VISinger. It supervises the posterior encoder to extract the latent representation without phase information and avoid the prior encoder modelling text-to-phase mapping. To avoid glitch artefacts, the HiFi-GAN is modified to accept the waveforms generated by the DSP synthesizer as a condition to produce the singing voice. Moreover, with the improved waveform decoder, VISinger 2 manages to generate 44.1kHz singing audio with richer expression and better quality. Experiments on OpenCpop corpus show that VISinger 2 outperforms VISinger, CpopSing and RefineSinger in both subjective and objective metrics.