Digital signal processing using variable sampling and its applications

本研究开发了一种新的数字信号处理方法，即注意信号的时间，即采样时？延误多久？，何时输出？因此，我们可以开发以下新的数字信号处理算法及其应用，主要是使用加减法。采用自适应采样率的频率估计(1)同步加减法的频率估计算法通过同步加减法累加值的周期估计输入频率，并根据估计的频率设置新的采样率。(2)基于自适应陷波滤波器的频率估计算法我们通过改变自适应陷波滤波器的延迟时间来减小其幅值，或者根据自适应陷波滤波器输出过零点的周期来估计输入频率。(1)多速率离散傅立叶变换算法（MR-DFT）在这种MR-DFT中，对每个信号分量的极值进行采样，并使用加法和减法进行累积。这个算法是通过一个傅立叶系数的一次乘法计算出来的。(2)梳状傅里叶变换（CFT）该算法适用于由任意信号频率组成的信号，当信号分量的个数为N.3时，用O(N)与联立方程法中的O（N^3）相乘的次数进行计算。转录系统(1)采用同步加减法的转录系统(2)基于级联梳状滤波器和自适应梳状滤波器的转录系统(3)基于并行梳状滤波器的转录系统，利用梳状滤波器输出的奇异值分解（SVD），或相邻梳状滤波器输出之间的相似性

This research has been carried out to develop a new digital signal processing noticing signal time, I.e., when sampling?, how much delay?, and when output? As a result, we could develop the following new digital signal processing algorithms and its applications using additions and subtractions mainly.1. Frequency estimation using adaptive sampling rate(1) Frequency estimation algorithm using synchronous addition and subtraction From the period of the accumulated value by the synchronous addition and subtraction, we can estimate the input frequency and set a new sampling rate based on the estimated frequency.(2) Frequency estimation algorithm using adaptive notch filters We change the delay time of the adaptive notch filter so as to decrease the amplitude of the adaptive notch filter or based on the period of the zero-crossing points in the output of the adaptive notch filter and estimate the input frequency.2. Discrete Fourier transform algorithm using multirate sampling(1) Multirate discrete Fourier transform algorithm(MR-DFT) In this MR-DFT, the extreme values of each signal component are sampled and accumulated using additions and subtractions. This algorithm is calculated by one multiplication for one Fourier coefficient.(2) Comb Fourier transform (CFT) This algorithm can be applied to the signals composed of arbitrary signal frequencies and calculated by the number of the multiplications of O( N ) comparing with O( N^3 ) in the simultaneous equation method when the number of signal components is N.3. Transcription system(1) Transcription system using synchronous addition and subtraction(2) Transcription system based on cascaded comb filters, and adaptive comb filters(3) Transcription system based on the parallel comb filters using singular value decomposition (SVD) of the comb filter outputs, or similarity between the adjacent comb filter outputs