/*?Copyright?（C）?2003-2008?Jean-Marc?Valin

???File:?mdf.c
???Echo?canceller?based?on?the?MDF?algorithm?（see?below）

???Redistribution?and?use?in?source?and?binary?forms?with?or?without
???modification?are?permitted?provided?that?the?following?conditions?are
???met:

???1.?Redistributions?of?source?code?must?retain?the?above?copyright?notice
???this?list?of?conditions?and?the?following?disclaimer.

???2.?Redistributions?in?binary?form?must?reproduce?the?above?copyright
???notice?this?list?of?conditions?and?the?following?disclaimer?in?the
???documentation?and/or?other?materials?provided?with?the?distribution.

???3.?The?name?of?the?author?may?not?be?used?to?endorse?or?promote?products
???derived?from?this?software?without?specific?prior?written?permission.

???THIS?SOFTWARE?IS?PROVIDED?BY?THE?AUTHOR?‘‘AS?IS‘‘?AND?ANY?EXPRESS?OR
???IMPLIED?WARRANTIES?INCLUDING?BUT?NOT?LIMITED?TO?THE?IMPLIED?WARRANTIES
???OF?MERCHANTABILITY?AND?FITNESS?FOR?A?PARTICULAR?PURPOSE?ARE
???DISCLAIMED.?IN?NO?EVENT?SHALL?THE?AUTHOR?BE?LIABLE?FOR?ANY?DIRECT
???INDIRECT?INCIDENTAL?SPECIAL?EXEMPLARY?OR?CONSEQUENTIAL?DAMAGES
???（INCLUDING?BUT?NOT?LIMITED?TO?PROCUREMENT?OF?SUBSTITUTE?GOODS?OR
???SERVICES;?LOSS?OF?USE?DATA?OR?PROFITS;?OR?BUSINESS?INTERRUPTION）
???HOWEVER?CAUSED?AND?ON?ANY?THEORY?OF?LIABILITY?WHETHER?IN?CONTRACT
???STRICT?LIABILITY?OR?TORT?（INCLUDING?NEGLIGENCE?OR?OTHERWISE）?ARISING?IN
???ANY?WAY?OUT?OF?THE?USE?OF?THIS?SOFTWARE?EVEN?IF?ADVISED?OF?THE
???POSSIBILITY?OF?SUCH?DAMAGE.
*/

/*
???The?echo?canceller?is?based?on?the?MDF?algorithm?described?in:

???J.?S.?Soo?K.?K.?Pang?Multidelay?block?frequency?adaptive?filter?
???IEEE?Trans.?Acoust.?Speech?Signal?Process.?Vol.?ASSP-38?No.?2?
???February?1990.
???
???We?use?the?Alternatively?Updated?MDF?（AUMDF）?variant.?Robustness?to?
???double-talk?is?achieved?using?a?variable?learning?rate?as?described?in:
???
???Valin?J.-M.?On?Adjusting?the?Learning?Rate?in?Frequency?Domain?Echo?
???Cancellation?With?Double-Talk.?IEEE?Transactions?on?Audio
???Speech?and?Language?Processing?Vol.?15?No.?3?pp.?1030-1034?2007.
???http://people.xiph.org/~jm/papers/valin_taslp2006.pdf
???
???There?is?no?explicit?double-talk?detection?but?a?continuous?variation
???in?the?learning?rate?based?on?residual?echo?double-talk?and?background
???noise.
???
???About?the?fixed-point?version:
???All?the?signals?are?represented?with?16-bit?words.?The?filter?weights?
???are?represented?with?32-bit?words?but?only?the?top?16?bits?are?used
???in?most?cases.?The?lower?16?bits?are?completely?unreliable?（due?to?the
???fact?that?the?update?is?done?only?on?the?top?bits）?but?help?in?the
???adaptation?--?probably?by?removing?a?“threshold?effect“?due?to
???quantization?（rounding?going?to?zero）?when?the?gradient?is?small.
???
???Another?kludge?that?seems?to?work?good:?when?performing?the?weight
???update?we?only?move?half?the?way?toward?the?“goal“?this?seems?to
???reduce?the?effect?of?quantization?noise?in?the?update?phase.?This
??