我如何对 .wav 文件进行下采样，然后使用奈奎斯特重建它？ - 在 MATLAB 中

Question

这一切都是在 MATLAB 2010 中完成的。

我的目标是显示以下结果：欠采样、奈奎斯特率/过采样

首先，我需要对 .wav 文件进行下采样以获得不完整/或公正的数据流，然后我可以重新构建该数据流。

这是我要做的事情的流程图所以流程是模拟信号 - >采样模拟滤波器-> ADC->向下重新采样 ->重新采样 -> DAC->重构模拟滤波器

需要实现什么：

F=频率

F(Hz=1/s) Ex 100Hz = 1000（周期/秒） F(s)= 1/(2f)

示例问题：1000 Hz = 最高 频率 1/2(1000hz) = 1/2000 = 5x10(-3) 秒/周期或采样率 5毫秒

这是我使用 matlab 的第一个信号处理项目。

到目前为止我所拥有的。

% Fs = frequency sampled (44100hz or the sampling frequency of a cd)

[test,fs]=wavread('test.wav'); % loads the .wav file
left=test(:,1);

% Plot of the .wav signal time vs. strength

time=(1/44100)*length(left);
t=linspace(0,time,length(left));
plot(t,left)
xlabel('time (sec)');
ylabel('relative signal strength')

**%this is were i would need to sample it at the different frequecys (both above and below and at) nyquist frequency.*I think.***

soundsc(left,fs) % shows the resaultant audio file , which is the same as original ( only at or above nyquist frequency however) 

谁能告诉我如何让它变得更好，以及如何以不同的频率进行采样？

这是 .wav 文件 http://www.4shared.com/audio/11xvNmkd/piano。 html

编辑：

%Play decimated file ( soundsc(y,fs) ) 
%Play Original file ( soundsc(play,fs ) )
%Play reconstucted File ( soundsc(final,fs) )

[piano,fs]=wavread('piano.wav'); % loads piano
play=piano(:,1); % Renames the file as "play"

t = linspace(0,time,length(play));          % Time vector
x = play;
y = decimate(x,25);

stem(x(1:30)), axis([0 30 -2 2])   % Original signal
title('Original Signal')
figure
stem(y(1:30))                        % Decimated signal
title('Decimated Signal')

%changes the sampling rate

fs1 = fs/2;
fs2 = fs/3;
fs3 = fs/4;
fs4 = fs*2;
fs5 = fs*3;
fs6 = fs*4;

wavwrite(y,fs/25,'PianoDecimation');


%------------------------------------------------------------------

%Downsampled version of piano is now upsampled to the original
[PianoDecimation,fs]=wavread('PianoDecimation.wav'); % loads piano
play2=PianoDecimation(:,1); % Renames the file as "play

%upsampling
UpSampleRatio = 2;  % 2*fs = nyquist rate sampling
play2Up=zeros(length(PianoDecimation)*UpSampleRatio, 1);
play2Up(1:UpSampleRatio:end) = play2; % fill in every N'th sample

%low pass filter

ResampFilt = firpm(44, [0 0.39625 0.60938 1], [1 1 0 0]);


fsUp = (fs*UpSampleRatio)*1;
wavwrite(play2Up,fsUp,'PianoUpsampled');

%Plot2
%data vs time plot
time=(1/44100)*length(play2);
t=linspace(0,time,length(play2));
stem(t,play2)
title('Upsampled graph of piano')
xlabel('time(sec)');
ylabel('relative signal strength')



[PianoUpsampled,fs]=wavread('PianoUpsampled.wav'); % loads piano
final=PianoUpsampled(:,1); % Renames the file as "play"


%-------------------------------------------------------------
%resampleing
[piano,fs]=wavread('piano.wav'); % loads piano
x=piano(:,1); % Renames the file as "play"
m = resample(x,3,2);

原文： http://www.4shared.com/audio/11xvNmkd/piano.html

新的： http://www.4shared.com/audio/nTRBNSld/PianoUs.html

Answer 1

最简单的方法是将采样率更改为整数倍。 下采样包括通过低通滤波器运行数据，然后丢弃样本，而上采样包括插入样本，然后通过低通滤波器运行数据（也称为重建滤波器或插值滤波器）。当过滤步骤被跳过或做得不好时，就会出现混叠。因此，为了显示锯齿的效果，我建议您只需根据需要丢弃或插入样本，然后以新的采样率创建一个新的 WAV 文件。要丢弃样本，您可以执行以下操作：

DownSampleRatio = 2;
%# Normally apply a low pass filter here
leftDown = left(1:DownSampleRatio:end); %# extract every N'th sample
fsDown = fs/DownSampleRatio;
wavwrite(leftDown, fsDown, filename);

要创建样本，您可以执行以下操作：

UpSampleRatio = 2;
leftUp = zeros(length(left)*UpSampleRatio, 1);
leftUp(1:UpSampleRatio:end) = left; %# fill in every N'th sample
%# Normally apply a low pass filter here
fsUp = fs*UpSampleRatio;
wavwrite(leftUp, fsUp, filename);

您只需播放写入的 WAV 文件即可听到效果。

顺便说一句，您要求改进代码 - 我更喜欢将 t 向量初始化为 t = (0:(length(left)-1))/fs; 。

Answer 2

您需要的 DSP 技术称为抽取。