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The traditional vocoders have the advantages of high synthesis efficiency, strong interpretability, and speech editability, while the neural vocoders have the advantage of high synthesis quality. To combine the advantages of two vocoders, inspired by the traditional deterministic plus stochastic model, this paper proposes a novel neural vocoder named NeuralDPS which can retain high speech quality and acquire high synthesis efficiency and noise controllability. Firstly, this framework contains four modules: a deterministic source module, a stochastic source module, a neural V/UV decision module and a neural filter module. The input required by the vocoder is just the spectral parameter, which avoids the error caused by estimating additional parameters, such as F0. Secondly, to solve the problem that different frequency bands may have different proportions of deterministic components and stochastic components, a multiband excitation strategy is used to generate a more accurate excitation signal and reduce the neural filter's burden. Thirdly, a method to control noise components of speech is proposed. In this way, the signal-to-noise ratio (SNR) of speech can be adjusted easily. Objective and subjective experimental results show that our proposed NeuralDPS vocoder can obtain similar performance with the WaveNet and it generates waveforms at least 280 times faster than the WaveNet vocoder. It is also 28% faster than WaveGAN's synthesis efficiency on a single CPU core. We have also verified through experiments that this method can effectively control the noise components in the predicted speech and adjust the SNR of speech. Examples of generated speech can be found at https://hairuo55.github.io/NeuralDPS.