卷积算法研究与应用

卷积算法研究与应用(任务书,开题报告,论文12000字)
摘要
随着终端设备的不断提高和普及，人们使用手机、计算机产生了大量的图像和语音，要表示这些大数据量的信息，使用的信号会变得很长，如果直接进行计算，计算量将会较大，速率也低，很不利于实时处理与传输信息。卷积作为信号处理的重要部分，一直在被提升优化，用以解决信号的实时处理与传输难点。
算法发展过程中，最先产生的是线性卷积，以描述线性系统在时域上的，输入和输出之间的关系，然后发展出计算周期序列的周期卷积，最后由周期卷积，发展出可以通过离散傅里叶变换计算的圆周卷积，这三种卷积是卷积算法中最基础的。
在某些实际应用中，可能要求将一个有限长度的序列与一个长度不定或相当长的序列进行线性卷积。若将整个序列存储起来再作大点数的运算，不但运算量太大，而且往往时延也不允许，往往也要求随时接收随时进行处理。在这些情况下，就要将长序列分段，每一段分别与短序列进行卷积，这就是分段卷积。
本文着眼于研究分段卷积的方法及实际应用，了解算法的基本原理，比较实际应用中的优缺点。论文主要工作如下：
1、了解线性卷积、圆周卷积和循环卷积的基本原理，并分析彼此的关系；
2、分析用于处理分段卷积的几种算法，了解优化方法；
3、学习分段卷积在语音信号合成中的应用，本文重点分析和编写了重叠相加法、重叠保留法和线型比例重叠相加法在实际例子中的应用。
4、通过对比算法的计算量和运算效率，可以分析出算法的特点，便于实际中更好的应用。
关键词：卷积；分段卷积；重叠保留法；重叠相加法

 
Abstract
With the development of multimedia communication and computer, a large amount of multimedia information such as image data and voice signal needs to be processed because the amount of data used to represent the information is large, which is reflected in the length of the signal. If the signal processing is carried out directly, The amount will be larger, it is not conducive to the real-time signal processing and transmission. Convolution as an important part of signal processing has been optimized for optimization.
In the traditional algorithm, the first generation is the linear convolution of the relationship between the linear system input and the output in the time domain, and then the periodic convolution of the periodic sequence is calculated. Finally, convolution is carried out by periodic convolution, The convolution of the convolution is the most basic operation in the convolution algorithm.
In some practical applications, it may be desirable to linearly convolize a sequence of finite lengths with a variable length or fairly long sequence. If the entire sequence of storage and then do a large number of operations, not only the amount of computing is too large, and often delay is not allowed, often also require ready to receive at any time to deal with. In these cases, the long sequence is segmented and each segment is convoluted with the short sequence, which is the segmented convolution.
In this paper, we focus on the method and practical application of segmented convolution, understand the basic principle of algorithm, and compare the advantages and disadvantages of practical application. The main work of the paper is as follows:
1.Understand the basic principles of linear convolution, circular convolution and cyclic convolution, and analyze the relationship between each other;
2.Analyze several algorithms for dealing with segmented convolution to understand the optimization method;
3.In this paper, we focus on analyzing and writing the code of overlapping addition method, overlapping reservation method and linear scale superposition method, and the application of segmented convolution in speech signal synthesis.
By comparing the computational complexity and computational efficiency of the algorithm, the characteristics of the algorithm can be analyzed to facilitate the better application in practice.
Key Words：Convolution; Segmented Convolution; Overlay Retention; Overlapping Additive

目录
第1章绪论 1
1.1 研究背景及意义 1
1.2 研究现状 1
1.3 各章节安排 2
第2章卷积运算基本原理 3
2.1 线性卷积运算基本原理 3
2.1.1 卷积运算 3
2.1.2 线性卷积运算 4
2.2 圆周卷积运算基本原理 5
2.2.1 圆周卷积运算 5
2.2.2 圆周卷积与线性卷积的联系 6
2.2.3 基于MFFNT的圆周卷积运算 7
2.2.4 构建主值序列矩阵改进圆周卷积运算 7
2.3 循环卷积运算基本原理 7
2.4 基于FFT的卷积运算 8
2.5 分段卷积运算基本原理 9
2.6 基于MPI同步模型的运算基本原理 10
第3章基于FFT的分段卷积算法 11
3.1重叠相加法 11
3.2重叠保留法 12
3.3 线性比例重叠相加法 13
3.4两种分段卷积算法与直接卷积的比较实验 14
3.4.1 实验安排 14
3.4.2重叠相加法算法流程图及说明 14
3.4.3 重叠相加法与直接卷积比较结果 16
3.4.4 重叠保留法算法流程图及说明 17
3.4.5 重叠保留法与直接卷积比较结果 19
3.5 本章小结 20
第4章三种分段卷积算法在语音信号合成中的应用 21
4.1 重叠相加法在语音信号合成中的应用 21
4.2 重叠保留法进行语音信号合成中的应用 22
4.3 线型比例重叠相加法进行语音信号合成中的应用 22
4.4 本章小结 23
第 5章结论与展望 25
5.1 全文工作总结 25
5.2 未来工作展望 25
参考文献 26
致谢 28