一、小波语音降噪简介

对于噪声频谱遍布于语音信号频谱之中的宽带噪声，如果噪声振幅比大部分的语音信号振幅低，则削去低幅度成分也就削去了宽带噪声。基于这种思路，可以在频域中采取中心限幅的方法，即让带噪语音信号通过一限幅滤波器，高幅度频谱可以通过而低幅成分不允许通过，从而实现噪声抑制。需要注意的是中心削波不可避免地要损害语音质量，通常只在频域中进行，而一般不在时域中实施。
小波降噪的原理类似于中心削波法。小波降噪最初是由Donoho和Johnstone提出的， 其主要理论依据是，小波变换具有很强的去数据相关性，它能够使信号的能量在小波域集中在一些大的小波系数中；而噪声的能量却分布于整个小波域内。因此，经小波分解后，信号的小波系数幅值要大于噪声的系数幅值。因此，幅值比较大的小波系数一般以信号为主，而幅值比较小的系数在很大程度上是噪声。于是，采用阈值的办法可以把信号系数保留，而使大部分噪声系数减小至0。小波降噪的具体处理过程为：将含噪信号在各尺度上进行小波分解，设定一个阈值，幅值低于该阈值的小波系数置为0，高于该阈值的小波系数或者完全保
留， 或者做相应的“收缩”(shrinkage) 处理。最后； 将处理后获得的小波系数用逆小波变换进行重构，得到去噪后的信号。
阈值去噪中，阈值函数体现了对超过和低于阈值的小波系数的不同处理策略，是阈值去噪中关键的一步。设w表示小波系数， T为给定阈值， sgn(*) 为符号函数， 常见的阈值函数主要有：

二、部分源代码

H=figure('color',[0.82,0.82421875,0.832],'position',[250,100,800,500],...'Name','滚动轴承故障诊断系统','NumberTitle','off',...'MenuBar','None');
uicontrol(H,'style','Text','position',[0.2,0.2,0.55,0.05],...'Units','normalized','Horizontal','center',...'String','制作人：**学院','fontsize',16,...'backgroundcolor',[0.82,0.82421875,0.832]);
uicontrol(H,'style','Text','position',[0.2,0.15,0.55,0.05],...'Units','normalized','Horizontal','center',...'String','机械1班  紫极神光','fontsize',16,...'backgroundcolor',[0.82,0.82421875,0.832]);
uicontrol(H,'style','Pushbutton','position',[0.7,0.66,0.2,0.06],...'Units','normalized','Horizontal','center',...bg'String','进入系统','fontsize',15,'call','STYM');
uicontrol(H,'style','Pushbutton','position',[0.7,0.45,0.2,0.06],...'Units','normalized','Horizontal','center',...'String','退出系统','fontsize',15,'call','close(H)');
load mtlb;
a=axes('parent',H,'position',[-0.16 0 1 1.1]);
imshow('11.jpg');
hold on;
axis off;
%mnxh.m文件
uiheight=0.05;
uiweith=0.12;
uilow=0.08;
uileft=0.85;
dif=0.08;uicontrol(f,'style','Text','Position',...[uileft-10*dif uilow+2*dif+13*uiheight uiweith/2 uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','幅值1','tag','fuz1data','backgroundcolor',[0.8,0.9,0.8]);
uicontrol(f,'style','edit','Position',...[uileft-10*dif+uiweith/2 uilow+2*dif+13*uiheight 2*uiweith/3 uiheight],...'Units','normalized','Horizontal','center','tag','fuz1ed','fontsize',10,'String',11);
uicontrol(f,'style','Text','Position',...[uileft-8*dif uilow+2*dif+13*uiheight 2*uiweith/2 uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','频率1','tag','pl1data','backgroundcolor',[0.8,0.9,0.8]);
uicontrol(f,'style','edit','Position',...[uileft-7.6*dif+uiweith/2 uilow+2*dif+13*uiheight 2*uiweith/3 uiheight],...'Units','normalized','Horizontal','center','tag','pl1ed','fontsize',10,'String',12);uicontrol(f,'style','Text','Position',...[uileft-10*dif uilow+2*dif+11*uiheight uiweith/2 uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','幅值3','tag','fuz3data','backgroundcolor',[0.8,0.9,0.8]);
uicontrol(f,'style','edit','Position',...[uileft-10*dif+uiweith/2 uilow+2*dif+11*uiheight 2*uiweith/3 uiheight],...'Units','normalized','Horizontal','center','tag','fuz3ed','fontsize',10,'String',35);
uicontrol(f,'style','Text','Position',...[uileft-8*dif uilow+2*dif+11*uiheight 2*uiweith/2 uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','频率3','tag','pl3data','backgroundcolor',[0.8,0.9,0.8]);
uicontrol(f,'style','edit','Position',...[uileft-7.6*dif+uiweith/2 uilow+2*dif+11*uiheight 2*uiweith/3 uiheight],...'Units','normalized','Horizontal','center','tag','pl3ed','fontsize',10,'String',40);uicontrol(f,'style','Text','Position',...[uileft-5*dif uilow+2*dif+13*uiheight uiweith/2 uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','幅值2','tag','fuz2data','backgroundcolor',[0.8,0.9,0.8]);
uicontrol(f,'style','edit','Position',...[uileft-5*dif+uiweith/2 uilow+2*dif+13*uiheight 2*uiweith/3 uiheight],...'Units','normalized','Horizontal','center','tag','fuz2ed','fontsize',10,'String',15);
uicontrol(f,'style','Text','Position',...[uileft-3*dif uilow+2*dif+13*uiheight 2*uiweith/2 uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','频率2','tag','pl2data','backgroundcolor',[0.8,0.9,0.8]);
uicontrol(f,'style','edit','Position',...[uileft-2.6*dif+uiweith/2 uilow+2*dif+13*uiheight 2*uiweith/3 uiheight],...'Units','normalized','Horizontal','center','tag','pl2ed','fontsize',10,'String',5);uicontrol(f,'style','Pushbutton','position',...[uileft-4.5*dif uilow+2*dif+11*uiheight uiweith uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','无噪音信号','call','wzy');
uicontrol(f,'style','Pushbutton','position',...[uileft-2.3*dif uilow+2*dif+11*uiheight uiweith uiheight],...'Units','normalized','Horizontal','center','fontsize',12,...'String','加噪音信号','call','jzy');

三、运行结果

四、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 沈再阳.精通MATLAB信号处理[M].清华大学出版社，2015.
[2]高宝建,彭进业,王琳,潘建寿.信号与系统——使用MATLAB分析与实现[M].清华大学出版社，2020.
[3]王文光,魏少明,任欣.信号处理与系统分析的MATLAB实现[M].电子工业出版社，2018.