## 1 Introduction
Both of these approaches achieve significantly higher accuracy and smoother F0 trajectory on noisy and clean speech. Therefore, we propose here an improvement to the continuous F0 algorithm in terms of temporal resolution and accuracy by using adaptive the Kalman-filter, time-warping, and instantaneous-frequency approaches. We show its effectiveness with regard to the background noise using some comprehensive evaluation methods already existing in the literature. Such a statistical framework is guided by the vocoder (which is also called speech analysis/synthesis system) to reproduce human speech. A vocoder is the most important component of various speech synthesis applications such as TTS synthesis [16], voice conversion [17], or singing synthesizers [18]. Although there are several different types of vocoders that use analysis/synthesis, they follow the same main strategy. The analysis stage is used to convert the speech waveform into a set of parameters, whereas in the synthesis stage, the entire parameter set is used to reconstruct the original speech signal. [PERSON] et al. [19] presented an experimental comparison of the wide range of important vocoder types that had previously been invented. In general terms, we can group state-of-the art vocoder-based TTS into three categories. (a) Source-filter models: STRAIGHT [20] and mixed excitation [21]; (b) sinusoidal models: Harmonic plus Noise Model [22] and Ahocoder [23]; (c) end-to-end complex models: WaveNet-based waveform generation [24] and Tacotron [25]. Each model has the advantage of working reasonably well for a particular speaker, which makes them attractive to researchers. Althoughthey offer speech quality comparable to natural human speech, each of them has several drawbacks that we should take into consideration. STRAIGHT synthesis is very slow to use in real-time applications, since it depends on high-order fast Fourier transform for high-resolution spectral synthesis [26]. Sinusoidal vocoders like HNM, on the other hand, usually have more parameters (each frame has to be represented by a set of frequencies, amplitude, and phase) than in the source-filter models, in which more memory would be required to code and store the speech segments. Similarly, neural models (e.g., WaveNet [[https://deepmind.com/blog/wavenet-generative-model-raw-audio/](https://deepmind.com/blog/wavenet-generative-model-raw-audio/)]([https://deepmind.com/blog/wavenet-generative-model-raw-audio/](https://deepmind.com/blog/wavenet-generative-model-raw-audio/))[27]) require a large quantity of voice data for each speaker, high-frequency, the autoregressive nature of the model, and a great deal computation power for training the neural networks, making them difficult to use in practice [28; 29]. Therefore, we believe that vocoder-based statistical parametric speech synthesis (SPSS) still offers a flexible and tractable solution to TTS that could be improved in terms of quality. We attempt in this study to develop a vocoder-based high-quality TTS synthesis system, while still maintaining the computational efficiency of the approach. In our recent work in SPSS, we proposed a computationally feasible residual-based vocoder [13] using a continuous F0 model [9] and maximum voiced frequency (MVF) [30]. In this method, the voiced excitation consisting of pitch synchronous residual frames is low-pass filtered while the unvoiced part is high-pass filtered according to the MVF contour as a cutoff frequency. This approach was especially successful for modeling speech sounds with mixed excitation. In [31], we further controlled the time structure of the high-frequency noise component by estimating a suitable true envelope. Similar to other vocoders (e.g., a lack of noise in STRAIGHT [32]), the noise component in the continuous vocoder is still not accurately modeled, and limits the overall perceived quality. To mitigate the problem above, a valid and reliable method for calculating levels of noise in human speech would be required to give appropriate information for SPSS.