load handel

whos

% y sound signal vector
% Fs sample frequency

x = [0:length(y)-1];
x = x/Fs;  %Fs is 8192

% so if Fs is 8192 what is the step size of x? 1/Fs, so x is incremented by .000122 at each step
x(1:10)

plot(x,y);
xlabel('time in seconds');
ylabel('amplitude of signal (displacement)');

sound(y)

% can easily pull out pieces of the signal by indexing into the vector
plot(x(1:4000),y(1:4000));
xlabel('time in seconds');
ylabel('amplitude of signal (displacement)');

sound(y(1:4000));


% let's take a look at quantization
ll = 1601; ul=2200;
clf
plot(x(ll:ul),y(ll:ul));
xlabel('time in seconds');
ylabel('amplitude of signal (displacement)');

sound(y(ll:ul));


% uniform quantization
hold on
plot(repmat([x(ll) x(ul)]',[1,17]),repmat([-1:(1/2^3):1],[2 1]),'g-')

% quantization levels 
[-1:(1/2^3):1]

% quantize using 4 bits - 2^4 levels = 16 levels of quantization
y4bit = round(y*(1+1/2^3)/(1/2^3)); 
y4bit = y4bit*(1/2^3);

% zoom in on a section
plot(x(ll:ul),y4bit(ll:ul),'r-');

% average quantization error
mean(abs(y4bit-y))

% sound at 4 bits of quantization
sound(y4bit);

% now let's try 8 bits of quantization
y8bit = round(y*(1+1/2^7)/(1/2^7)); 
y8bit = y8bit*(1/2^7);

% zoom in on a section - quantization error has gotten much smaller
clf
plot(x(ll:ul),y(ll:ul));
xlabel('time in seconds');
ylabel('amplitude of signal (displacement)');
hold on
plot(x(ll:ul),y8bit(ll:ul),'r-');


% average quantization error
mean(abs(y8bit-y))

sound(y8bit);

% now 16 bit 
y16bit = round(y*(1+1/2^15)/(1/2^15)); 
y16bit = y16bit*(1/2^15);

sound(y16bit);

clf
hist(y,50);


% let's look at quantization 

% remember uniform quantization looks like this
ll = 1601; ul=2200;
clf
plot(x(ll:ul),y(ll:ul));
xlabel('time in seconds');
ylabel('amplitude of signal (displacement)');

% uniform quantization
hold on
plot(repmat([x(ll) x(ul)]',[1,17]),repmat([-1:(1/2^3):1],[2 1]),'g-')


% non-uniform quantization might look something like this
clf
plot(x(ll:ul),y(ll:ul));
xlabel('time in seconds');
ylabel('amplitude of signal (displacement)');

% non-uniform quantization -- quantize at a finer level near 0 and coarser near +/-1
ys = sort(y);
breaks = ys([round(1:length(ys)/16:length(ys)) length(ys)]);
hold on
plot(repmat([x(ll) x(ul)]',[1,17]),repmat(breaks(:)',[2 1]),'g-')


% quantization error visualization
d = abs(repmat(y,[1,length(breaks)])-repmat(breaks(:)',[size(y,1),1]));
[ min_d, min_d_pos ]=min(d,[],2);
y4bit_non_linear = breaks(min_d_pos);
% here we see that at the places where you quantize at a finer level, error is smaller
% while at the coarser level errors are larger (but at high amplitudes you expect not 
% to be able to here these errors as much as at low amplitudes - hence the use of 
% non-uniform quantization).
plot(x(ll:ul),y4bit_non_linear(ll:ul),'r-');

% zoom in on a section

% sound with 4 uniform bits of quantization
sound(y4bit(1:24000))

% is more noisy than sound with 4 non-uniform bits of quantization
sound(y4bit_non_linear(1:24000))

% and quantization error is also smaller for non-linear than linear

% uniform quantization error
mean(abs(y4bit-y))

% non-uniform quantization error
mean(abs(y4bit_non_linear-y))