% 2009-03-05-coding.diary
% Examples of speech coding with LPC

d = wavread('mpgr1_sx419-8k.wav')';
% Linear quantization at 6 bits (64 levels)
max(d)
% ans =
%     0.1481
min(d)
% ans =
%    -0.1549
% So quantize for an absolute maximum of 0.16
dq = myquant(d, 0.16, 64);
% Original sound
sound(d)
% Post quantization
sound(dq)
% Can clearly hear quantization noise during nonsilent periods

% 'added' noise
de = d - dq;
sound(de)
% Sounds like a white noise being gated on and off
% What is the SNR?
% Energy of original signal in dB:
Ed = 10*log10(mean(d.^2))
% Ed =
%   -35.5895
% Energy of difference = added noise
Edq = 10*log10(mean((de).^2))
% Edq =
%   -58.3559
% SNR is the difference
Ed - Edq
% ans =
%    22.7664
% i.e. about 23 dB, rather less than 6db / bit, because not full-scale

% LPC analysis
% Run in "no overlap" mode, so residual exactly reconstructs
% original waveform (but has discontinuities when taken on its own)
[ai,g,ex] = lpcfit(d,12,128,256,0);
% Reconstruction should now be nearly perfect:
r = lpcsynth(ai,g,ex,128,0);
% Energy of difference:
Edr = 10*log10(mean((d-r).^2))
% Edr =
%  -104.1072
% (almost all in a little glitch in the last window)
% So SNR in dB
Ed - Edr
% ans =
%    68.5177
% Very respectable 70 dB SNR - actually almost inf over most of signal

% For residual encoding, we actually want to use the overlapped
% residual:
[ai,g,ex] = lpcfit(d);
r = lpcsynth(ai,g,ex);
% (lengths of d and r don't quite match in this case)
10*log10(mean( (d - r(1:length(d))).^2))
% ans =
%   -46.1717
% i.e. only about 11 dB SNR, but sounds pretty good.
% n.b.: When modifying residual, measure SNR as difference to this 
% 'best case' reconstruction (rather than to the original d)
Er = 10*log10(mean(r.^2)) 
% Er =
%   -35.4634

% Now try quantizing the residual to 6 bits:
min(ex)
% ans =
%   -17.9191
max(ex)
% ans =
%    21.2953
% So quantizing it in the range -18..22 will cause no clipping
eq = myquant(ex, [-18 22], 64);  % 64 = 2^6
rq = lpcsynth(ai,g,eq);
sound(rq)
% Still sounds OK
% How's the noise energy compared to the unquantized resid?
Errq = 10*log10(mean((r-rq).^2))
% Errq =
%   -54.8946
% i.e. the SNR compared to the best reconstruction
Er - Errq
% ans =
%    19.4312
% 20 dB, still OK, but getting significant.
% Actually a worse SNR than quantizing the original (because SNR 
% is dominated by the high-energy regions), but perceptually 
% less noticeable noise.

% Listen to the difference i.e. the 'added noise' in each case
% Don't use autoscalign (soundsc) so we can judge relative level
sound((r-rq)*10)
% Sounds like whispering in the background
sound((d-dq)*10)
% Sounds like added, gated white noise, quite loud