How would i down-sample a .wav file then reconstruct it using nyquist? - in MATLAB

Question

This is all done in MATLAB 2010

My objective is to show the results of: undersampling, nyquist rate/ oversampling

First i need to downsample the .wav file to get an incomplete/ or impartial data stream that i can then reconstuct.

Heres the flow chart of what im going to be doing So the flow is analog signal -> sampling analog filter -> ADC -> resample down -> resample up -> DAC -> reconstruction analog filter

what needs to be achieved:

F= Frequency

F(Hz=1/s) E.x. 100Hz = 1000 (Cyc/sec) F(s)= 1/(2f)

Example problem: 1000 hz = Highest frequency 1/2(1000hz) = 1/2000 = 5x10(-3) sec/cyc or a sampling rate of 5ms

This is my first signal processing project using matlab.

what i have so far.

% 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)

Can anyone tell me how to make it better, and how to do the sampling at verious frequencies?

heres the .wav file http://www.4shared.com/audio/11xvNmkd/piano.html

EDIT:

%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);

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

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

what do you mean, from my previous questions ive asked about nyquist sampling using a msp430 micro controller, this has nothing to do with that. — Andrew
It means you click the green checkmark on an answer for one of your previous questions, as done in this question. It awards the author extra points and allows future users & searchers to see which answer was most helpful. — tyblu
Most helpful for my question about the msp430 board yea. . . — Andrew

mtrw mtrw · Accepted Answer · 2010-12-28T07:59:22

The easiest thing to do is change sample rates by an integer factor. Downsampling consists of running the data through a low-pass filter followed by discarding samples, while upsampling consists of inserting samples then running the data through a low pass filter (also known as a reconstruction filter or interpolating filter). Aliasing occurs when the filtering steps are skipped or poorly done. So, to show the effect of aliasing, I suggest you simply discard or insert samples as required, then create a new WAV file at the new sample rate. To discard samples, you can do:

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);

To create samples you can do:

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);

You can just play back the written WAV files to hear the effects.

As an aside, you asked for improvements to your code - I prefer to initialize the t vector as t = (0:(length(left)-1))/fs;.

How would i down-sample a .wav file then reconstruct it using nyquist? - in MATLAB

2 Answers