快速滤波器组在语音信号处理中的应用

论文总字数：27667字

摘 要

频率估计是一个有大规模应用范围的基本信号处理过程，例如通信、医疗、视频及音频。信号的频率估计算法可以分为基于时域和基于频域两大类算法。基于频域的频率估计算法由于其在估计性能上的明显优势，受到研究者广泛的关注。此类估计算法大都以离散傅里叶变换（Discrete Fourier Transform，DFT）为核心设计，而在数字系统中实现DFT的快速傅里叶变换（Fast Fourier Transform，FFT）的频率响应特性远不如一种特殊形式的多相滤波器组——快速滤波器组（Fast Filter Bank，FFB）。

本文首先研究了近年来提出的比较经典的两种频率估计算法，包括修正协方差算法（Modified Covariance， MC）和基于ODD-DFT变换域的频率估计算法。给出两种算法的推导过程和仿真结果，对两种算法的性能做出了比较和评估。

然后，研究了快速滤波器组的基础理论，分析了其相对快速傅里叶变换所具有的性能优势。在详细探讨了快速滤波器组各级子滤波器的关系以及快速滤波器组的设计方法后，给出了快速滤波器组的原型滤波器的低复杂度优化设计方法和具体实现步骤。

最后，通过推导，提出适合宽线性信号的离散傅里叶变换（DFT）频率估计算法。并运用复数最小二乘算法——CLS-DFT算法，使得估计性能得到改进。然后将快速滤波器组（FFB）代替离散傅里叶变换（DFT），进行频率估计。使用CLS-FFB算法以进一步提高其频率估计性能，并推导出该算法对宽线性信号的频率估计表达式。通过仿真对其在估计精度上的提高做出证明。

关键词：频谱感知，频率估计，快速滤波器组，宽线性信号，复数最小二乘法。

Abstract

Frequency estimation is a fundamental signal-processing problem which has wide applications in many fields, such as communications, medical, video and audio. The algorithms frequency estimation can be divided into two types, i.e., time domain based algorithms and frequency domain based algorithms. Due to the high accuracy in estimation performance, frequency estimation algorithms based on the latter algorithm has attracted much attention. These frequency estimation algorithms are mostly based on discrete Fourier transform (DFT), which is realized by use of fast Fourier transform in digital systems. However, the characteristic of frequency response performance is much poorer than a special polyphase bank called fast filter bank (FFB).

Firstly, two typical frequency estimation algorithms proposed in recent years are shown in this paper, including modified covariance method (MC) and ODD-DFT frequency estimation algorithm, which is based on frequency domain. Their derivation processes are given respectively and simulations results are given and compared.

Secondly, the basic theory of fast filter bank is introduced, and its advantages compared with fast Fourier transform are presented. After detailed discussion on the relationship between the fast filter bank and its sub filter, and the method to design a fast filter bank, the method to optimize the design of prototype filter of the fast filter bank is introduced.

Finally, the frequency estimation algorithm based on DFT, which is suitable for widely linear signal, is proposed. The complex-valued least squares (CLS) is used to improve the performance of frequency estimation. By replacing DFT with FFB and the use of CLS, the performance of frequency estimation is improved. Frequency estimation algorithm based on CLS-FFB for widely linear signal is probed. The results of simulations show that CLS-FFB algorithms have higher estimation accuracy than CLS-DFT algorithms.

Keywords: Spectrum sensing, Frequency estimation, Fast filter bank, Widely linear signal, Complex-valued least squares

目 录

摘要 I

Abstract II

目 录 III

第一章 绪论 1

1.1 研究背景 1

1.2 世界研究现状 2

1.2.1 快速滤波器组世界研究现状 2

1.2.2 频率估计世界研究现状 3

1.3 论文的主要工作及其结构安排 4

第二章 经典频率估计算法研究 6

2.1 基于ODD-DFT变换域的频率估计算法 6

2.2 修正协方差算法 10

2.3本章小结 12

第三章 快速滤波器组的研究及实现 13

3.1 低复杂度快速滤波器组的设计与应用 13

3.2 快速滤波器组（FFB） 14

3.2.1 快速滤波器组（FFB）及其树形结构 14

3.2.2 FFB原型滤波器低复杂度优化设计 15

3.3 本章小结 17

第四章 基于DFT和FFB的频率估计算法 18

4.1 宽线性信号的概念 18

4.2 基于DFT的宽线性信号频率估计 18

4.3 基于FFB的宽线性信号频率估计 21

4.4 本章小结 23

第五章 结束语 25

第六章 致谢 26

参考文献 27

绪论

研究背景

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