基于稀疏傅里叶变换的信号压缩算法研究

基于稀疏傅里叶变换的信号压缩算法研究(任务书,开题报告,外文翻译,论文14000字)
摘要
本文借助MATLAB软件对基于稀疏傅里叶变换的信号压缩进行了仿真，包括窗函数的构造，对稀疏的信号进行压缩与重构，验证压缩算法的正确性。
论文主要研究基于稀疏傅里叶变换的信号压缩的关键技术，包括频谱重排，平坦窗设计，重构算法。过程包括：利用信号频域上的大值点，进行分箱子处理，保证每个箱子中只有一个或者零个大值点。为了验证算法的正确性，需要证明压缩后的信号可以完整还原出原信号，利用定位循环找出箱子中大值点的位置，在通过估值循环算出时域上的信号。
研究结果表明：当信号具有稀疏性，基于稀疏傅里叶变换的信号压缩算法是可行的，压缩的过程中可以忽略冗余的数据，保留有用的信号。如果信号的稀疏性不够明显，则不能很好的重构原信号。经研究得出，该算法的运算效率大于快速傅里叶变换，稀疏信号的压缩领域还有很大的发展空间。
本文的特色：文中不仅全面论证了该算法比普通算法运算效率更高，还对该算法的实际应用进行了可行性的研究。分析了算法的不足与待突破的关键技术，并对压缩技术的未来进行了展望。
关键词：稀疏傅里叶变换；信号压缩；信号重构

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Abstract
In this paper, the software compression based on sparse Fourier transform is simulated by MATLAB software, including the construction of window function, compressing and reconstructing the sparse signal, and verifying the correctness of the compression algorithm.
This paper mainly studies the key technologies of signal compression based on sparse Fourier transform, including spectrum rearrangement, flat window design and reconstruction algorithm. The process includes the use of the signal point on the frequency field, the sub-box processing to ensure that each box only one or zero point. In order to verify the correctness of the algorithm, it is necessary to prove that the compressed signal can completely restore the original signal, use the positioning cycle to find the position of the large point in the box, and calculate the signal in the time domain through the estimation cycle.
The results show that when the signal is sparseness, the signal compression algorithm based on sparse Fourier transform is feasible. In the process of compression, redundant data can be neglected and the useful signal can be retained. If the sparsity of the signal is not obvious enough, the original signal can not be reconstructed very well. It is concluded that the algorithm is more efficient than fast Fourier transform, and there is still a lot of room for spatially signal compression.

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The characteristics of this paper are not only a comprehensive demonstration of the algorithm than the average algorithm is more efficient, but also the practical application of the algorithm feasibility study. Analyzes the shortcomings of the algorithm and the key technology to be broken, and prospects the future of compression technology.
Key words: sparse Fourier transform, signal compression, signal reconstruction
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目录
第1章绪论    1
1.1研究的目的及意义    1
1.2国内外研究现状    2
1.3研究内容    4
第2章稀疏傅里叶变换的理论研究    5
2.1快速傅里叶变换    5
2.2稀疏傅里叶变换理论    5
2.3稀疏傅里叶变换的可行性研究    8
第3章信号压缩理论的研究    10
3.1范数约束准则    10
3.2频谱重排    10
3.3平滑窗函数滤波器    11

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3.4频域降采样    13
3.5重构算法    13
第4章信号的压缩算法与仿真    15
4.1算法仿真    15
4.2仿真结果与分析    16
第5章总结    21
参考文献    22
附录    23
致谢    30 [版权所有：http://DOC163.com]