音频频谱分析仪设计与实现

实验八 音频频谱分析仪设计与实现
一、实验原理
MATLAB 是一个数据分析和处理功能十分强大的工程实用软件，其数据采集工具箱为实现数据的输入和输出提供了十分方便的函数和指令。

本实验基于声卡与MATLAB 实现音频信号频谱分析仪。

1、频率(周期)检测
对周期信号来说，可以用时域波形分析来确定信号的周期，也就是计算相邻两个信号波峰的时间差或过零点的时间差。

采用过零点（ti ）的时间差T （周期）。

频率即为f=1/T ，由于能够求得多个T 值，故采用他们的平均值作为周期的估计值。

2、峰值检测
在一个周期内，求出信号最大值m ax y 与最小值min y 的差得一半记为A ，同样得到多个A 值，但第一个A 值对应的m ax y 和min y 不是在一个周期内搜索得到的，故以除第一个以外的A 值的平均作为幅值的估计值。

3、相位检测
采用过零法，即通过判断与同频零相位信号过零点时刻，计算其时间差，然后换成相应的相位差。

）
π（T /ti -12=ϕ，同样以ϕ的平均值作为相位的估计值。

4、数字信号统计量估计
（1）峰值P 的估计
在样本数据x 中找出最大值与最小值，其差为双峰值，双峰值的一半即为峰值。

（2）均值估计
∑=Ｎｉ＝０
ｉｙN 1)y (E ，N 为样本容量。

（3）均方值估计
∑=Ｎｉ＝０ｉｙ22N 1
)y (E
（4）方差估计
∑=Ｎｉ＝０
ｉｙ2))(E -(N 1)y (D y 5、频谱分析原理
时域分析只能反映信号的幅值随时间的变化情况，除但频率分量的简单波形外，很难明确提示信号的频率组成和各频率分量大小，而频谱分析能很好的解决此问题。

（1）DFT 与FFT
对于给定的时域信号y ，可以通过Fourier 变换得到频域信息Y 。

Y 可按下式计算
式中，N 为样本容量，Δt = 1/Fs 为采样间隔。

采样信号的频谱是一个连续的频谱，不可能计算出所有的点的值，故采用离散Fourier 变换(DFT)，即
式中，Δf = Fs/N。

但上式的计算效率很低，因为有大量的指数(等价于三角函数)运算，故实际中多采用快速Fourier变换(FFT)。

其原理即是将重复的三角函数算计的中间结果保存起来，以减少重复三角函数计算带来的时间浪费。

由于三角函数计算的重复量相当大，故FFT 能极大地提高运算效率。

（2）频率、周期的估计
对于Y(kΔf)，如果当kΔf = ~
f时，Y(kΔf)取最大值，则
~
f为频率的估计值，由于采样
间隔的误差，~
f也存在误差，其误差最大为Δf / 2。

周期T=1/f。

从原理上可以看出，如果在标准信号中混有噪声，用上述方法仍能够精确地估计出原标准信号的频率和周期。

（3）频谱图
为了直观地表示信号的频率特性，工程上常常将Fourier变换的结果用图形的方式表示，即频谱图。

以频率f为横坐标，|Y(f)|为纵坐标，可以得到幅值谱；
以频率f为横坐标，arg Y(f)为纵坐标，可以得到相位谱；
以频率f为横坐标，Re Y(f)为纵坐标，可以得到实频谱；
以频率f为横坐标，Im Y(f)为纵坐标，可以得到虚频谱。

根据采样定理，只有频率不超过Fs/2的信号才能被正确采集，即Fourier变换的结果中频率大于Fs/2的部分是不正确的部分，故不在频谱图中显示。

即横坐标f ∈[0, Fs/2]
6、模块划分
模块化就是把程序划分成独立命名且可独立访问的模块，每个模块完成一个子功能，把这些模块集成起来构成一个整体，可以完成制定的功能，满足用户需求。

二、实验内容
设计一个音频频谱分析仪，功能包括：
（1）音频信号输入，从声卡输入、从W A V文件输入、从标准信号发生器输入；
（2）信号波形分析，包括幅值、频率、周期、相位的估计，以及统计量峰值、均值。

均方值和方差的计算。

（3）信号频谱分析，频率、周期的估计，图形显示幅值谱、相位谱、时频谱、虚频谱和功率谱的曲线。

三．实验结果
1.声卡输入
（1）正弦波（2）方波（3）三角波
（4）锯齿波（5）白噪声程序
function varargout = fanwenhan(varargin)
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @fanwenhan_OpeningFcn, ...
'gui_OutputFcn', @fanwenhan_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
function fanwenhan_OpeningFcn(hObject, eventdata, handles, varargin) handles.inputtype=0;
xlabel(handles.plot1,'freqency(Hz)');
xlabel(handles.plot2,'freqency(Hz)');
xlabel(handles.plot3,'freqency(Hz)');
xlabel(handles.plot4,'freqency(Hz)');
xlabel(handles.plot5,'freqency(Hz)');
ylabel(handles.plot1,'amplitude');
ylabel(handles.plot2,'phase(rad)');
ylabel(handles.plot3,'real');
ylabel(handles.plot4,'Imaginary');
ylabel(handles.plot5,'power');
handles.output = hObject;
function varargout = fanwenhan_OutputFcn(hObject, eventdata, handles) varargout{1} = handles.output;
function figure1_CreateFcn(hObject, eventdata, handles)
function timeanalyse_Callback(hObject, eventdata, handles)
Fs=str2double(get(findobj('Tag','samplerate'),'String'));
N=str2double(get(findobj('Tag','samplenum'),'String'));
if handles.inputtype==0
msgbox('No wave exist! Please choose a input type!');
return;
end
n=1;
ymax=max([handles.y(1) handles.y(2)]);
ymin=min([handles.y(1) handles.y(2)]);
from=str2double(get(handles.pointfrom,'String'));
to=str2double(get(handles.pointto,'String'));
if from<1 | to-from<5;
msgbox('Error range!');
return;
end
for i=from+2:to-1;
if handles.y(i-1)<0 & handles.y(i-2)<0 & handles.y(i)>=0 & handles.y(i+1)>0
if handles.y(i)==0
ti(n)=i;
else
ti(n)=i-handles.y(i)/(handles.y(i)-handles.y(i-1));
end
amp(n)=(ymax-ymin)/2;
ymax=0;
ymin=0;
n=n+1;
else
if ymax<handles.y(i)
ymax=handles.y(i);
end
if ymin>handles.y(i)
ymin=handles.y(i);
end
end
end
n=n-1;
for i=1:n-1
T(i)=ti(i+1)-ti(i);
end
freq=Fs/mean(T);
set(handles.outt,'String',1/freq);
set(handles.outfreq,'String',num2str(freq));
set(handles.outamp,'String',num2str(mean(amp(2:n-1))));
phase=2*pi*(1-(ti(1:n-1)-1)./T+floor((ti(1:n-1)-1)./T));
set(handles.outphase,'String',num2str(mean(phase)));
set(handles.outpeak,'String',(max(handles.y(from:to))-min(handles.y(f rom:to)))/2);
set(handles.outmean,'String',mean(handles.y(from:to)));
set(handles.outmeansquare,'String',mean(handles.y(from:to).^2));
set(handles.outs,'String',std(handles.y(from:to))^2);
function WAVfile_Callback(hObject, eventdata, handles)
h=findobj('Tag','filename');
set(h,'enable','on');
h=findobj('Tag','freq');
set(h,'enable','off');
h=findobj('Tag','amp');
set(h,'enable','off');
h=findobj('Tag','phase');
set(h,'enable','off');
set(findobj('Tag','recordtime'),'enable','off');
set(handles.channel,'enable','on');
set(handles.fileopen,'enable','on');
set(handles.gensig,'enable','off');
set(handles.wavetype,'enable','off');
set(handles.add,'enable','off');
set(handles.startrecord,'enable','off');
function soundcard_Callback(hObject, eventdata, handles) set(findobj('Tag','recordtime'),'enable','on');
h=findobj('Tag','filename');
set(h,'enable','off');
h=findobj('Tag','freq');
set(h,'enable','off');
h=findobj('Tag','amp');
set(h,'enable','off');
h=findobj('Tag','phase');
set(h,'enable','off');
set(handles.channel,'enable','off');
set(handles.fileopen,'enable','off');
set(handles.gensig,'enable','off');
set(handles.wavetype,'enable','off');
set(handles.add,'enable','off');
set(handles.startrecord,'enable','on');
function generator_Callback(hObject, eventdata, handles) h=findobj('Tag','filename');
set(h,'enable','off');
h=findobj('Tag','freq');
set(h,'enable','on');
h=findobj('Tag','amp');
set(h,'enable','on');
h=findobj('Tag','phase');
set(h,'enable','on');
set(findobj('Tag','recordtime'),'enable','off');
set(handles.channel,'enable','off');
set(handles.fileopen,'enable','off');
set(handles.gensig,'enable','on');
set(handles.wavetype,'enable','on');
set(handles.add,'enable','on');
set(handles.startrecord,'enable','off');
function filename_Callback(hObject, eventdata, handles)
function filename_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function freq_Callback(hObject, eventdata, handles)
function freq_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function amp_Callback(hObject, eventdata, handles)
function amp_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function phase_Callback(hObject, eventdata, handles)
function phase_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function samplerate_Callback(hObject, eventdata, handles)
function samplerate_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function samplenum_Callback(hObject, eventdata, handles)
function samplenum_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function ampfreq_CreateFcn(hObject, eventdata, handles)
function recordtime_Callback(hObject, eventdata, handles)
function recordtime_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function startrecord_Callback(hObject, eventdata, handles)
Fs=str2double(get(findobj('Tag','samplerate'),'String'));
handles.y=wavrecord(str2double(get(findobj('Tag','recordtime'),'Strin g'))*Fs, Fs,'int16');
handles.inputtype=1;
guidata(hObject,handles);
plot(handles.time,handles.y);
title('WAVE');
ysize=size(handles.y)
set(handles.samplenum,'String',num2str(ysize(1)));
function fileopen_Callback(hObject, eventdata, handles)
temp = wavread(get(findobj('Tag','filename'),'String'));
channel=str2double(get(handles.channel,'String'));
handles.y=temp(:,channel);
handles.inputtype=2;
guidata(hObject,handles);
plot(handles.time,handles.y);
title('WAVE');
ysize=size(handles.y)
set(handles.samplenum,'String',num2str(ysize(1)));
function gensig_Callback(hObject, eventdata, handles)
Fs=str2double(get(findobj('Tag','samplerate'),'String'));
N=str2double(get(findobj('Tag','samplenum'),'String'));
x=linspace(0,N/Fs,N);
soundtype=get(handles.wavetype,'Value');
frequency=str2double(get(handles.freq,'String'));
amp=str2double(get(handles.amp,'String'));
phase=str2double(get(handles.phase,'String'));
switch soundtype
case 1
y=amp*sin(2*pi*x*frequency+phase);
case 2
y=amp*sign(sin(2*pi*x*frequency+phase));
case 3
y=amp*sawtooth(2*pi*x*frequency+phase,0.5);
case 4
y=amp*sawtooth(2*pi*x*frequency+phase);
case 5
y=amp*(2*rand(size(x))-1);
otherwise
errordlg('Illegal wave type','Choose errer');
end
if get(handles.add,'Value')==0.0
handles.y=y;
handles.y=handles.y+y;
end
handles.inputtype=3;
guidata(hObject,handles);
plot(handles.time,handles.y);
title('WAVE');
axis([0 N -str2double(get(handles.amp,'String'))
str2double(get(handles.amp,'String'))]);
function outfreq_Callback(hObject, eventdata, handles)
function outfreq_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function outamp_Callback(hObject, eventdata, handles)
function outamp_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function outphase_Callback(hObject, eventdata, handles)
function outphase_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
function outpeak_Callback(hObject, eventdata, handles)
function outpeak_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function outmean_Callback(hObject, eventdata, handles)
function outmean_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function outmeansquare_Callback(hObject, eventdata, handles)
function outmeansquare_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function outs_Callback(hObject, eventdata, handles)
function outs_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function foutfreq_Callback(hObject, eventdata, handles)
function foutfreq_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function foutamp_Callback(hObject, eventdata, handles)
function foutamp_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function foutphase_Callback(hObject, eventdata, handles)
function foutphase_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function edit18_Callback(hObject, eventdata, handles)
function edit18_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function edit19_Callback(hObject, eventdata, handles)
function edit19_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function edit20_Callback(hObject, eventdata, handles)
function edit20_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function edit21_Callback(hObject, eventdata, handles)
function edit21_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
function freqanalyse_Callback(hObject, eventdata, handles)
Fs=str2double(get(findobj('Tag','samplerate'),'String'));
N=str2double(get(findobj('Tag','samplenum'),'String'));
if handles.inputtype==0
msgbox('No wave exist! Please choose a input type!');
return;
end
from=str2double(get(handles.pointfrom,'String'));
to=str2double(get(handles.pointto,'String'));
sample=handles.y(from:to);
f=linspace(0,Fs/2,(to-from+1)/2);
Y=fft(sample,to-from+1);
[C,I]=max(abs(Y));
set(handles.foutt,'String',1/f(I));
set(handles.foutfreq,'String',f(I));
Y=Y(1:(to-from+1)/2);
plot(handles.plot1,f,2*sqrt(Y.*conj(Y)));
plot(handles.plot2,f,angle(Y));
plot(handles.plot3,f,real(Y));
plot(handles.plot4,f,imag(Y));
plot(handles.plot5,f,abs(Y).^2);
xlabel(handles.plot1,'freqency(Hz)');
xlabel(handles.plot2,'freqency(Hz)');
xlabel(handles.plot3,'freqency(Hz)');
xlabel(handles.plot4,'freqency(Hz)');
xlabel(handles.plot5,'freqency(Hz)');
ylabel(handles.plot1,'amplitude');
ylabel(handles.plot2,'phase(rad)');
ylabel(handles.plot3,'real');
ylabel(handles.plot4,'Imaginary');
ylabel(handles.plot5,'power');
function pointfrom_Callback(hObject, eventdata, handles)
function pointfrom_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function pointto_Callback(hObject, eventdata, handles)
function pointto_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function play_Callback(hObject, eventdata, handles)
Fs=str2double(get(findobj('Tag','samplerate'),'String'));
wavplay(handles.y,Fs);
function scale_Callback(hObject, eventdata, handles)
val=get(hObject,'value');
val=10^(val*5+1);
x=get(handles.xmove,'Value')*str2double(get(handles.samplenum,'String '));
axis(handles.time,[x val+x min(handles.y) max(handles.y)]);
function scale_CreateFcn(hObject, eventdata, handles)
usewhitebg = 1;
if usewhitebg
set(hObject,'BackgroundColor',[.9 .9 .9]);
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function scale2_Callback(hObject, eventdata, handles)
val=get(hObject,'value');
val=10^(val*5+1);
xlim(handles.plot1,[0 val]);
xlim(handles.plot2,[0 val]);
xlim(handles.plot3,[0 val]);
xlim(handles.plot4,[0 val]);
function scale2_CreateFcn(hObject, eventdata, handles)
usewhitebg = 1;
if usewhitebg
set(hObject,'BackgroundColor',[.9 .9 .9]);
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function channel_Callback(hObject, eventdata, handles)
function channel_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function wavetype_Callback(hObject, eventdata, handles)
function wavetype_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function add_Callback(hObject, eventdata, handles)
function add_DeleteFcn(hObject, eventdata, handles)
function xmove_Callback(hObject, eventdata, handles)
val=get(handles.scale,'value');
val=10^(val*5+1);
x=get(hObject,'Value')*str2double(get(handles.samplenum,'String')); axis(handles.time,[x val+x min(handles.y) max(handles.y)]);
function xmove_CreateFcn(hObject, eventdata, handles)
usewhitebg = 1;
if usewhitebg
set(hObject,'BackgroundColor',[.9 .9 .9]);
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function analyseall_Callback(hObject, eventdata, handles)
if get(hObject,'Value')==0.0
set(handles.pointfrom,'Enable','on');
set(handles.pointto,'Enable','on');
else
set(handles.pointfrom,'String','1','Enable','off');
set(handles.pointto,'String',get(handles.samplenum,'String'),'Enable' ,'off');
end
function outt_Callback(hObject, eventdata, handles)
function outt_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function foutt_Callback(hObject, eventdata, handles)
function foutt_CreateFcn(hObject, eventdata, handles)
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor' ));
end
function gensig_CreateFcn(hObject, eventdata, handles)
function add_CreateFcn(hObject, eventdata, handles)
function startrecord_CreateFcn(hObject, eventdata, handles)
function freqanalyse_CreateFcn(hObject, eventdata, handles)
结果分析
通过不断的尝试及计算，得到上述实验结果，可以看到设置不同的采样频率和采样点数将分析出不同的结果，其无论在时域分析或频域分析上都有影响，如对频率、相位的判断等。

但本音频频谱分析仪还是很好的显示了我们需要得到的数据。