%%?Chapter?3?-?How?is?sound?processed?in?an?MP3?player?
%?This?is?a?companion?file?to?the?book?“Applied?Signal?Processing“?
%?by?T.Dutoit?and?F.?Marques?Springer?2008.
%?
%?It?is?supposed?to?be?run?cell-by-cell?using?the?cell?mode?of?
%?MATLAB?6?and?later?versions.?Search?for?“what?are?cells“?in?the?
%?product?help?of?MATLAB?to?know?how?to?use?them.
%?
%?This?file?uses?the?SIGNAL_PROCESSING?toolbox?of?MATLAB.
?
%%
%?In?this?script?we?will?see?how?the?limitations?of?the?human?auditory
%?process?have?been?taken?into?account?for?the?design?of?perceptual?audio
%?coders?with?special?emphasis?on?the?principles?underlying?the?MPEG-1
%?layer-I?audio?coding?norm.?We?start?by?examining?a?two-channel?filter?bank
%?using?conventional?filters?（Section?1）?and?QMF?filters?（Section?2）.?We
%?then?extend?our?study?to?a?32-channel?PQMF?filter?bank?（Section?3）?and
%?show?how?it?can?be?efficiently?implemented?using?block-based?lapped
%?transforms?（Section?4）.?We?conclude?by?providing?our?filter?bank?with
%?a?perceptual?quantizer?for?sub-band?signals?（Section?5）.
%
%?Copyright?N.?Moreau?T.?Dutoit?（2007）

clear?all;
set（0‘defaultFigureColor‘‘w‘）;

%%?1.?Two-channel?filter?bank
%?The?MPEG?1?layer?I?coder?is?based?on?quantifying?the?sub-band?signals?of
%?an?analysis-synthesis?filter?bank?（as?we?will?see?later?this?can?also?be
%?interpreted?in?terms?of?block-transform-based?processing）.??
%?The?analysis?filter-bank?at?the?encoder?splits?the?signal?into?（ideally
%?non-overlapping）?frequency?bands.?The?resulting?narrow-band?signals?are
%?then?decimated?and?quantized.?The?decoder?upsamples?each?sub-band?signal
%?and?performs?band-pass-filtering?so?as?to?eliminate?the?aliasing?images
%?due?to?upsampling.????
%?
%?Before?examining?a?complete?M-channel?filter?bank?we?first?discuss?
%?the?2-channel?case?and?the?effect?of?a?decimation?and?interpolation?in
%?each?branch.?
%
%?Let?us?first?generate?a?4-seconds?chirp?signal?（from?0?to?4?kHz）?with?a
%?sampling?rate?of?8?kHz?which?we?will?use?as?a?reference?throughout
%?this?Section.??

Fs=8000;
input_signal=chirp（（0:4*Fs）/Fs044000）;

clf;
soundsc（input_signalFs）;

%%
specgram（input_signal1024Fs256）;

%%
%?Applying?direct?downsampling-upsampling?by?2?results?in?replacing?every
%?other?sample?by?zero.?The?result?is?that?an?artifact?signal?is?added
%?whose?spectrum?is?the?quadrature?mirror?image?of?that?of?the?chirp.?Two
%?sinusoids?can?be?heard?at?any?time.?（Notice?we?multiply?the?signal?by?2
%?when?upsampling?so?that?the?power?of?the?signal?remains?unchanged.）

downsampled=input_signal（1:2:end）;
upsampled（1:2:2*length（downsampled））=2*downsampled;

clf;
specgram（upsampled1024Fs?256）;
soundsc（upsampledFs）;

%%
%?Adding?a?quarter-band?filter?after?upsampling?eliminates?the?image
%?distortion?making?sure?that?only?one?
%?sinusoid?appears?at?any?time.?During?the?first?half?of?the?chirp?that
%?sinusoid?is?the?chirp?itself;?during?the?second?h