Digital signal processing using variable sampling and its applications

这项研究是为了开发一种新的数字信号处理方法，它可以注意信号的时间，即何时采样、多长时间延迟、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，主要使用加法和减法。基于自适应采样率的频率估计算法(1)频率估计算法通过同步加减法从累加值的周期中进行同步加减，可以估计输入频率，并根据估计的频率设置新的采样率。(2)基于自适应陷波的频率估计算法我们改变自适应陷波的延迟时间，以减小自适应陷波的幅度，或者根据自适应陷波输出中过零点的周期来估计输入频率。基于多速率采样的离散傅立叶变换算法(1)多速率离散傅立叶变换算法(MR-DFT)在这种MR-DFT中，通过加法和减法对每个信号分量的极值进行采样和累加。(2)梳状傅里叶变换(CFT)该算法适用于任意信号频率组成的信号，当信号分量数为N3时，其乘法次数为O(N)与联立方程方法中O(N^3)的乘法次数之和。转录系统(1)使用同步加减法的转录系统(2)基于级联梳状滤波器的转录系统，以及自适应梳状滤波器(3)基于并行梳状滤波器的转录系统使用奇异值分解(SVD)的梳状滤波器输出，或者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