Considerarion of practical algorithms for digital signal processing based on varlable rate sampling

在2000-2001年度科研资助项目的基础上，我们开发了一些基于变速率采样的新型数字信号处理算法。在2002-2003年的研究项目中，我们重新考虑了这些算法的实际应用。我们可以用加法和减法来处理这些算法所以我们可以用简单的电路来实现这些算法。本文介绍了本研究的一些结果。具有不同采样率的滤波器之间的连接方法。我们将滤波器之间的连接方法从过采样法改进为一阶插值法。因此，我们可以将频率估计处理的运算量减少到十分之一。基于同步加减处理的频率估计加速。我们提出了一种并行的同步加减法处理，可以将估计时间减少到三分之一左右，并改善了跟踪特性。改进了多阶DFT（MR-DFT）和梳状傅立叶变换对噪声的处理。通过对两个不同相位的MR DFT进行平均运算，提高了MR DFT对噪声的处理能力。对于使用陷波式梳状滤波器的梳状傅里叶变换，我们提出了使用谐振式梳状滤波器的其他新型傅里叶变换（谐振式傅里叶变换），并将谐振式傅里叶变换应用于信号接收器（DTMF接收器）和包括打击声在内的音乐声音转录系统。转录系统为真正的乐器声音和歌唱的声音。对于具有频率变化和噪声的真实音乐声音，我们开发了两个转录系统，分别在并联的陷波或谐振器型梳状滤波器中注意到最小或最大输出。我们还提出了一种使用自适应梳状滤波器的转录系统。这些誊写系统具有良好的音高估计能力。

We developed some algorithms for new digital signal processing based on variable-rate sampling by the research project, grant-in-aid for scientific research of 2000-2001. In the research project of 2002-2003, we reconsidered these algoritluns for the practical use. We can treat these algorithms by mainly additions and subtractions and so we can implement these algorithms by simple circuits. We present some results obtained in this research.1.connection method between filters having different sampling rates.We improved the connection method between filters from the oversampling method to the method using the first-order interpolation. As a result, we could reduce the amount of operations to one tenth for the frequency estimation processing.2.speed-up of frequency estimation based on synchronous addition and subtraction processing.We proposed a parallel synchronous addition and subtraction processing, and we could reduce the estimation time to about one third and improve the tracking characteristic.3.improvement of multi ate DFT(MR-DFT) and comb Fourier transform for noises.We improved the ability of the MR DFT for noises using mean operation of two MR DFT having different phases. For the comb Fourier transform using notch-type comb filters, we proposed other new Fourier transform (resonator Fourier transform) using resonator-type comb filters, and we applied the resonator Fourier transform into a signal receiver (DTMF receiver) and a transcription system for musical sounds including a percussion sound.4.transcription systems for real musical instrument sounds and sung sounds.For real musical sounds having frequency changes and noises, we developed two transcription systems noticing minimum or maximum outputs in the parallel connected notch or resonator type comb filters, respectively. We also proposed a transcription system using adaptive comb filters. These transcription systems can have good ability of the pitch estimation.