How would I drop a sample .wav file and then restore it using nyquist? - in MATLAB

Question

All this is done in MATLAB 2010

My goal is to show results: undersampling, nyquist rate / oversampling

First I need to reduce the size of the .wav file to get an incomplete / or unbiased data stream that can then be restored.

There is a flow chart of what they should do. Thus, the stream is an analog signal → analog sampling filter → ADC → reselection → reselection → DAC → analog recovery filter

what should be achieved:

F = Frequency

F (Hz = 1 / s) Ex 100 Hz = 1000 (Cyc / sec) F (s) = 1 / (2f)

Example problem: 1000 hz = highest frequency 1/2 (1000 Hz) = 1/2000 = 5x10 (-3) s / cycle or 5ms sample rate

This is my first signal processing project using matlab.

what i still have.

% 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 someone tell me how to do this better, and how to sample at credential frequencies?

heres.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

Answer 1

The simplest is to change the sampling rate to an integer coefficient. Downsampling consists of triggering data through a low-pass filter and then dropping samples, while upsampling consists of inserting samples and then triggering data through a low-pass filter (also known as a reconstruction filter or an interpolation filter). Offset occurs when filtering steps are skipped or performed incorrectly. So, to show the smoothing effect, I suggest that you simply drop or insert samples as needed, and then create a new WAV file with a new sampling rate. To drop the 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 simply play back recorded WAV files to listen to effects.

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

Answer 2

The required DSP technique is called decimation .