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