thuật toán trích Đặc trưng mfcc

8/11/2019 Thut Ton Trch c Trng MFCC

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1.1 Thut ton trch c trng MFCC thng thng

S khi thut ton trch c trng MFCC thng thng c ch ra

trongHnh 1.1-1.N c t tn nh vy do lm cong vnh tn sphi tuyn theo

thang tn sMel. Trc ht, ting ni c ly mu bi mt bchuyn i A/D.

Mc d tai ngi c thnghe c m thanh vi tn st20Hz ti 20KHz, nhng

ting ni thng thng ch khong tn s di 5KHz, v vi cht lng m

thanh thoi th s c bng thng gii hn l 4KHz. Vi l do ny, chng ti s

dng bng thng 4KHz trong ti ny v tn sly mu y l 8KHz.

Pre-emphasisFrame

BlockingWindowing |FFT|

Mel

Frequency

Filter bank

Cepstrum

Logged

energyDelta

Speechsamples

MFCC

Hnh 1.1-1 S khi thut ton trch c trng MFCC thng thng.

1.1.1

Pre-emphasis

Ting ni sau khi c sha sc tin nhn (pre-emphasized) vi b

lc p ng xung hu hn (finite impulse responseFIR) bc mt v pha ca n

tuyn tnh v thc thi n gin. Dotrong ting ni, cc thnh tthp hn thng

cha ng nhiu nng lng hn, v vy n c xem xt hn khi m hnh ha so

vi cc thnh tcao hn. Do , mt b lc pre-emphasis c dng khuch

i tn hiu cc tn scao hn. Hm truyn ca b lc c cho bi phng

trnh(Error! No text of specified style in document..1),trong tham satiu

biu t 0.9 n 1. Trong min thi gian, mi quan h gia ng ra vi ng vo

c ch ra trong phng trnh (Error! No text of specified style in

document..2),visil im thica tn hiu ting ni khi cha qua blc v is

l l im thica tn hiu ting ni sau khi c pre-emphasis.


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(Error! Notext of

specified

style indocument..1)

(Error! Notext of

specified

style in

document..2)

Khi a = 0.97, l gi trc dng trong hthng nhn dng ting ni bng

phn mm, p ng tn sca blc c chra trongHnh 1.1-2,= (na

tn sly mu) bin tngln 35dB so vi = 0.

Hnh 1.1-2 p ng tn sca blc Pre-emphasis

1.1.2

Frame Blocking

Bi v tn hiu ting ni l tn hiu bin i chm theo thi gian, trong mt

h thng nhn dng ting ni th ting ni c phn on thnh nhng khong


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(Error! Notext ofspecified


Hnh 1.1-4 Ca sHamming 160 im.


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Frame

Frame

Frame

...

160 mu

X

Hnh 1.1-5 Windowing trong phn tch ting ni.

Hnh 1.1-5 minh ha lm thno mt ca sHamming c p dng ln

tn hiu ting ni trong phn tch ting ni. Ting ni sau khi c chia thnh

nhng frame c chiu di 160 mu vi 50% chng lp, 160 im ca sHamming

c nhn vi mi frame theo tng mu. Cc frame ng ra ca sc lin tc ti

im u v im cui ca mi frame. Bc ny c thc din gii bi phng

trnh(Error! No text of specified style in document..4),trong lfn l frame

c pre-emphasis thn, ham(l)thay cho ca sHamming lwfn l frame thn

sau khi qua ca sHamming.


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(Error! Notext of

specified


1.1.4

FFT

Bin i Fourier nhanh (FFT) c dng tnh ton phca tn hiu ting

ni. chnh l sthc thi php bin i Fourier ri rc (DFT) t hiu sut cao

vi iu kin rng buc l phc nh gi ti nhng tn sri rc, nhng tn

sny c nhn vi Nfs (cc tn strc giao vi nhau), trong sf l tn s

ly mu, N l chiu di ca DFT. Thut ton FFT chyu cu khi lng tnh ton

tlvi NlogN,trong khi DFT yu cu khi lng tnh ton tlvi 2N .

phn gii tn sca DFT bgii hn bi 2 yu t: chiu di ca tn hiu

v chiu di ca DFT [14]. Nu tn hiu c to ra bi vic cng hai tn hiu sin

m tn sca hai tn hiu ny rt gn vi nhau, khi phn bit hai tn sny

chng ta phi quan st tn hiu vi phn on di. i vi chiu di ca DFT,

ph tn s c to ra bi N im DFT bao gm N/2 im vi cch u nhau

phn b gia 0 n phn na tn s ly mu. V vy tch ri hai tn s c

khong cch gn nhau th khong cch gia cc im phi nhhn khong cch

gia hai nh. Khi cc frame c ca sha vi chiu di l 160 im, chiu di

DFT c thit lp l 256 im t c phn gii tn stt vi khi lng

tnh ton c th chp nhn c khi thc thi thc t. Sau khi bin i FFT 256im, chc bin (cn bc 2) ca 128 im u tin c dng cho bc tnh

ton tip theo bi tnh cht i xng ca php bin i FFT.


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1.1.5 Mel Frequency Bank

Mt bng b lc s c dng m hnh cc tng ban u ca phn

chuyn i trong h thng thnh gic con ngi vi 2 l do sau. Thnht, v tr

ca vic dch chuyn cc i dc theo mng rung trong tai ngi kch thch tht lvi logarithm ca tn s m thanh. Thhai, cc tn sca m thanh phc

hp bn trong mt bng tn xc nh ca mt vi tn sdanh nh khng thc

nhn ra mt cch ring lc.

H thng thnh gic ca con ngi khng tuyn tnh vi tn s m thanh

nhn c, mt thang o Mel c dng nh x tn s m thanh nhn c

sang thang o tuyn tnh. Thang tn s ny c nh ngha bi phng trnh

(Error! No text of specified style in document..5) v c minh ha Hnh

1.1-6.N xp xnh thang tuyn tnh trong khong t0 n 1000Hz, xp xnh

thang logarithm bn ngoi tn s1000Hz.


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( ) (Error! Notext ofspecified


Hnh 1.1-6 Thang tn sMel

Bng thng b l

c thang o Mel thng thng trong nh

n d

ng ti

ng ni

bao gm mt s b lc bandpass hnh tam gic c phn bbn trong bng

thng tn hiu. Chng c cch u nhau trn thang Mel v bng thng ca

chng c thit ksao cho im 3dB nm khong gia hai blc kcn nhau.

Hnh 1.1-7(a) v Hnh 1.1-7(b) cho thy cc b lc ny trn thang Mel v trn

thang tn sthng thng tng ng.


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Hnh 1.1-7 Mt bng blc Mel, theo thang Mel (a) v theo thang tn sthng thng(b)

S b lc l mt trong nhng thng s m nh hng n chnh xc

nhn dng ca hthng.

H s cng sut th k ca frame thn c tnh ton bi phng trnh

(Error! No text of specified style in document..6),trong njS l im phthj

ca frame thn, v FCkjchhsthjca blc thk.

(Error! No

text ofspecified

style in

document..6)

yKl sblc.


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1.1.6 Cepstral Analysis

Tn hiu ting nisc thc m tnh l kt quca php tch chp tn

hiu kch thch vi p ng xung ca b thanh m, n c thc chia thnh 2

phn thng qua cc phng trnh di y, vigl tn hiu kch thch v vl png xung ca b m thanh [15].

(Error! Notext of

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style in

document..7)

(Error! Notext of

specified

style in

document..8)

(Error! No

text of

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style in

document..9)

Phng trnh(Error! No text of specified style in document..7) chra mi

quan h gia g v v trong min thi gian, phng trnh (Error! No text of

specified style in document..8) chra mi quan htrong min tn s. Sau khi ly

logarithm 2 v, chng ta c phng trnh(Error! No text of specified style in

document..9),vi tn hiu kch thch v p ng xung ca b thanh m c tch

ri nhau. p ng ca b thanh m quyt nh ng bao ca ph, trong khi

phca tn hiu kch thch biu din cc thnh phn ph ca ting ni. i vi


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nhn dng ting ni, ng bao ca phhu ch hn cc thnh phn ph, v vy

chng ta c thsdng php bin i Fourier ngc tm ng bao ca ph.

Cepstrum c nh ngha l php bin i Fourier ngc ca cc h s

cng sut sau khi ly logarithm. N c thc n gin ha nh l php bin i

DCT.

[

] (Error! No

text of

specified style

in

document..10)

trong pl bc (tht) ca cc hscepstral. Thng thng, i vi mi frame

0C khng dng trong phn tch bi v n khng ng tin cy. Cc hscepstrum

c bc thp phn nh thng tin b thanh m ca tn hiu ting ni. Trong php

phn tch phcho vic nhn dng ting ni, thng thng chsdng t8 n 16

hscepstrum c bc thp, trong a scc ng dng dng 12 hscepstrum.

1.1.7

Energy Calculation

Cng sut ca mi frame cng l thnh phn trong c trng MFCC. N

c tnh ton nh l logarithm ca cng sut tn hiu, c ngha l i vi frame

thn, mi frame c 160 mu 160...,,2,1, lsnl ,


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(Error! No

text of

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indocument..11)

Nng lng ny c tnh ton c lp trc khi pre-emphasis v

windowing trong cc hthng nhn dng ting ni bng phn mm.

1.1.8

Delta Coefficient

Cht lng ca h thng nhn dng ting ni c thc ci thin nhiu

hn bng cch thm vo tnh o hm theo thi gian c c nhng thng sdng c bn. Trong x l tn hiu s, o hm cp 1 theo thi gian c thc

xp xbi

(Error! Notext ofspecified style

in

document..12)


in

document..13)

Phng trnh (Error! No text of specified style in document..12) cn

c gi l sai phn li, cn phng trnh (Error! No text of specified style in

document..13) cn c gi l sai phn tin. V vy, cc hsdelta c thc

tnh ton bng cch sdng cng thc hi quy bn di, trong dnl vect hs


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delta ca frame thn. tnh hsdelta dn, dng cc vect hsdng tCn2

n Cn+2, vi Cnl vect bao gm log nng lng v 12 hscepstral ca frame

thn


in

document..14)

1.1.9

Kt lun

Sau qu trnh m ttrn, mt frame 160 mu c chuyn i thnh

mt vector bao gm 26 phn t, trong gm 1 h s nng lng, 12 h s

cepstral v cc o hm bc nht theo thi gian ca chng. nframe c thto ra n

4vector c trng bi v mt hsdelta cn cc thng tin tnh ttframen . Cc vector c trng ny c sdng trong qu trnh hun luyn vnhn dng.


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1.2 Thut ton trch c trng MFCC hiu chnh cho thc hin

phn cng

Thut ton trch c trngMFCC yu cu mt lng ln cc php ton v

hu ht cng sut tnh ton tiu thtrong qu trnh bin i Fourier. Trong chng

ny, chng ti gii thiu mt thut ton trch c trng MFCC c hiu chnh.

Khi sdng phng php ngh, khi lng tnh ton c gim i mt na. Skhi ca thut ton mi c minh ha Hnh 1.2-1.Cc skhc bit chnh

gia thut ton thng thng v thut ton ci tin c nhn mnh bi cc khi

t nt.

Pre-emphasis Sub-Frame Windowing |FFT|

Mel

Frequency

Filter bank

Cepstrum

Logged

energyDelta

Speech

samples

MFCC

Overlap

Hnh 1.2-1 S khi thut ton trch c trng MFCC hiu chnh.


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1.2.1 Pre-emphasis

Blc pre-emphasis cng tng tnh blc c dng trong thut ton

thng thng c trnh by trn. Trong phn mm nhn dng ting ni hsa

c thit lp bng 0.97, nhng thun tin cho thc thi phn cng, chng ti sdng 3231a . THnh 1.2-2 chng ta c ththy rng chc mt sai khc nh

vp ng tn sca 2 b lc, iu ny c chra bi cc kt quth nghim

c trnh by phn sau.

Thun li ca vic dng hsblc 3231a c gii thch bi phng

trnh (Error! No text of specified style in document..15). Trong h thng tnh

ton snhphn th 1321 is c tnh bng cch dch phi 1is i 5 bit. Bng cch

sdng tnh cht ny, php nhn chn gin l php ton dch v tr, v vy c

thi gian tnh ton ln din tch chip c gim bt.


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11

1

1

321

32

31

32

31,

iii

ii

iii

sss

ss

aasss

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Hnh 1.2-2 p ng tn sca blc pre-emphasis

1.2.2 Sub-Frame Blocking

Trong bc ny gii thiu mt thut ng mi tn l sub-frame. Mtframe thng thng bao gm mt vi sub-frame m khng c chng lp gia cc

sub-frame k cn nhau, chng lp gia cc frame thng thng c thxem nh

vic dng li ca cng sub-frame. Nh tho lun trong phn1.1.2,ting ni sau

khi c pre-emphasis c chia ra thnh nhng frame c chiu di 20ms vi

50% chng lp, chng ti xut chia tn hiu ting ni thnh nhng sub-frame c

chiu di 10ms, v vy 2 sub-frame k tip nhau to thnh mt frame thng

thng. Vi tn sly mu l 8KHz, chiu di ca mi sub-frame by gichcn

80 im ( 8001.08000 ).

THnh 1.2-3,chng ta c ththy rng c3 sub-frame to thnh 2 frame,

v vy nsub-frame sbao gm n-1 frame.


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Frame fn

Frame fn+1

Frame fn+2

Sub-frame

sfn ...

...

160 mu

80mu

(a)

(b)Sub-framesfn+1

Sub-frame

sfn+2

Sub-frame

sfn+3

Hnh 1.2-3 Sub-Frame v Frame

1.2.3 Windowing

Khi tn hiu ting ni c chia thnh nhng sub-frame c chiu di 80

im, trong gii thut mi ny, mt ca sHamming 80 im c p dng cho

mi sub-frame gim i hiu ng bin ca mi phn on. Nh c cp n

trong phn1.1.3,bp sng chnh v cc bp sng phca hm ca snh hng

n vic phn tch phca cc tn hiu ting ni. Khi kch thc ca sgim i

mt na, brng bp sng chnh stng ln gp i tng ng.Hnh 1.2-4 chra

p ng tn sca ca sHamming 160 im v 80 im.Hnh 1.2-5 minh ha

phng thc to ca sca gii thut c ngh.


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Hnh 1.2-4 p ng tn sca cc ca sHamming khc nhau.

Hnh 1.2-5 Phng thc to ca sca gii thut hiu chnh.

1.2.4

FFT

Trong bc ny strnh by tnh phca mi sub-frame.Hnh 1.2-6 chra

mt sub-frame 80 im c ca s ha v ph ca n c chuyn i thnh

FFT 256 im v 128 im tng ng. phn gii tn sca mt phFFT

256 im chtt hn mt t so vi mt phFFT 128 im, nhng n yu cu


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khi lng tnh ton gn nh l gp i bin i FFT 128 im v khi lng tnh

ton tlvi NNlog vi N l sim FFT.

22

log2

log

NN

NN

(Error! No

text of

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in

document..16)

Hnh 1.2-6 Phca tn hiu tcc FFT khc nhau


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Chng ta sdng FFT 128 im trong gii thut mi bi v nhng l do

trn. Hn thna, do tnh cht i xng ca mt phnn chc 64 im u

tin c dng cho cc bc tnh ton tip theo.

Sau khi bin i FFT, bin ca 64 im phc u tin c tnh ton

bng thut ton c lng, thut ton ny tnh ton rt nhanh bin ca mt s

phc gn nh chnh xc so vi cch tnh bin bng cch ly cn bc 2. Cho s

phc I+jQ, thut ton c lng bin nh sau:

QIQIM ,min,max (Error! No

text of

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document..17)

Php tnh gi trtuyt i gii hn phm vi sphc trong tm t0 n 090 ,

sau cc php tnh max, min sgii hnsphc trong tm t0 n 045 . Trong

gii hn ca tm ny, skt hp tuyn tnh ca I v Q t c xp xtt vbin

. Trong hthng ny, chng ti sdng 1 v 41 . Php tnh xp xny

gim bt khi lng tnh ton vi sai sc thchp nhn c.

1.2.5

Mel Frequency Filter Bank

Chng ta sdng cng mt phng php nh tho lun trong phn1.1.5,

nhng thay v sdng blc hnh tam gic, trong gii thut mi ny chng ti s

dng b lc hnh chnht. Theo nh nhng nghin cu trc y, mt bng b

lc c thdng cho nhn dng ting ni nu p ng tn skhi kt hp cc blc

thnh phn ca n l phng trn ton bdy tn smong mun. V vy bng b

lc hnh ch nht tha yu cu ny tt hn bng b lc hnh tam gic thng

thng.Hnh 1.2-7, Hnh 1.2-8 minh ha p ng xung ca bng blc hnh tam

gic v hnh chnht tng ng.


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Hnh 1.2-7 Bng blc hnh tam gic thng thng (a) v p ng tn skhi kt hp ccblc vi nhau (b).

Hnh 1.2-8 Bng blc hnh chnht ngh(a) v p ng tn skhi kt hp cc blc vi nhau (b).


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(Bin ca tt ccc blc hnh chnht u bng 1 nhng dquan

st trong hnh trn ta vbin cc blc khc 1)

Trong phng php thng thng, ng ra FFT c nhn vi cc hsca

cc blc hnh tam gic to ra cc gi tr ng ra blc. Sau , tt ccc gi tr

ng ra ca mt b lc c ly tng to ra h s cng sut ca b lc . Tuy

nhin, nu chng ta sdng cc blc hnh chnht thay thcc blc hnh

tam gic khi php ton nhn v cng n gin chl cc php ton cng v

khng cng bi v h sng ra ca b lc hnh chnht hoc l 1 hoc l 0.

Trong thut ton mi th khng yu cu php ton nhn trong bc ny.

1.2.6

OverlappingQu trnh chng lp trong gii thut mi c minh ha Hnh 1.2-9.

Trong nf v 1nf i din cho cc frame thng thng (chiu di mi frame l

160 im) thnv thn+1 vi 50% chng lp,n

sf v 1nsf i din cho cc sub-

frame trong gii thut mi (chiu di mi sub-frame l 80 im) thnv thn+1

tng ng.nk

FS l hscng sut c to ra bi blc thkca sub-frame th

n. Cc ng rank

FS v knFS 1 ca bng blc c cng vi nhau to ra hs

cng sut nkS , h s cng sut knS 1 c c bng cch ly tng cc ng ra

knFS 1 v knFS 2 ca b lc. iu c ngha l nkS bng vi nkFS cng vi

knFS 1 v knS 1 bng vi knFS 1( cng vi knFS 2 . Bng cch cng ng ra hin

ti vi ng ra trc ca bng blc, chng ta lp li 50% chng lp ging nh

trong thut ton thng thng.


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Hnh 1.2-9 Qu trnh chng lp trong thut ton ngh

Mt frame thng thng nf bao gm hai sub-frame l nsf v 1nsf , nng

lng ca n bng vi tng nng lng ca hai sub-frame thnh phn, hoc trong

ton bbng thng (t0 n 4 KHz) hoc trong mt khong bng thng c bit

no (blc thktrong bng blc). V vy, trongHnh 1.2-9, nkS chra hs

cng sut thkca frame thng thng nf v knS 1 chra hscng sut thk

ca frame thng thng 1nf .

1.2.7

Cepstral Analysis

Tnh ton cc h s cepstrum cng tng t nh trong gii thut thng

thng


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PpK

pkSC

K

nknp...,,2,1,5.0coslog

1k

(Error! No

text of

specified style

indocument..18)

Php ton logarithm th tnh ton rt kh trong cphn mm ln phn cng.

Bi v gi tr nkS khng thbit trc v chng ta cn tnh logarithm nhanh v gn

ng, v vy n gin chng ti tnh xp xlogarithm bi thut ton Mitchell

[19]. Gi N l sc cho bi:

i

k

i

izN

0

2 (Error! No

text of

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in

document..19)

vi iz bng 0 hoc 1. Gis kz bng 1 ktbit c trng scao nht (MSB) ca z.

Khi N c vit li nh sau:

1

22k

oii

ik zN (Error! No

text of

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in

document..20)

Bng cch t hsk

2 lm nhn tchung, ta c:


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i

k

i

kik zN1

0

212 (Error! No

text of

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indocument..21)

Ly 2log hai v, ta c:

i

k

i

ki zkN1

022

21loglog (Error! No

text of

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in

document..22)

V ki nni

k

i

ki z

1

0

2 sthuc khong t0 n 1, chng ta k hiu gi tr

ca tng ny bng m. Khi phng trnh(Error! No text of specified style in

document..22) c vit li nh sau:

1,1loglog 22 mmkN (Error! Notext of

specified style

in

document..23)

Mitchell xp xgi tr thc ca m1log 2 bi phng trnh ng thng

bam . n gin, Mitchell sdng 1a v 0b trong phng trnh ng

thng xp x


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mkN 2log (Error! No

text of

specified style

indocument..24)

V d, chng ta tnh gn ng 39log 2 , c ngha l N=39. Biu din N di

dng s nh phn ta c N=100111. Trong trng hp ny, 5k v

200111.0m . Chng ta vit li N di dng 3900111.012 25 N , bng

cch sdng phng trnh (Error! No text of specified style in document..24)

tnh xp x 222 00111.10100111.0539log , gi tr xp x ny bng5.21875, gi trthc sca 2854.539log 2 .

Sai sca php ton gn ng l:

mmerror 1log2 (Error! No

text of

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in

document..25)

Khi sai s ln nht bng 0.086071 vi m=0.442695 bng cch ta tnh

o hm cp 1 theo mnh sau:

12ln

1

12ln1

1

0

1log2

m

m

mmrerro

(Error! No

text of

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in

document..26)


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1.2.8 Energy Calculation

Nng lng ca mi frame c tnh l logarithm ca tng nng lng 2

sub-frame ktip nhau (mi sub-frame c chiu di l 80 im). N c tnh bi

phng trnh(Error! No text of specified style in document..27),trong nlsf chnh l mu thltrong sub-frame thn.

80

1

80

1

2

1

2loglogl l

lnnln ssE

(Error! No

text of

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in

document..27)

Trong thut ton mi ny th nng lng cng c tnh c lp trc khi

pre-emphasis v windowing nh trong thut ton thng thng. Php ton tnh

logarithm c tnh gn ng nh tho lun trong phn1.1.7

1.2.9

Delta Coefficient

Trong php ton tnh h s delta, chng ti nhn biu thc ca phng

trnh(Error! No text of specified style in document..14) vi 10. Tt ccc hsdelta u c nhn vi 10, iu ny skhng nh hng n cht lng nhn

dng bi v hm phn phi khng i. Vic nhn cc hsdelta vi 10 slm cho

vic thc thi phn cng trnn n gin hn nhiu v khng c php chia trong

tnh ton.


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1122

1122

2

1010

2

nnnn

nnnn

n

cccc

ccccd

(Error! No

text of

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indocument..28)

1.2.10

Nhng thun li ca gii thut hiu chnh

Phn cng thc thi bnhn tiu tn nhiu din tch v cng sut tiu th

hn cc phn cng thc thi cc php ton khc. V vy tit kim ngun ti

nguyn phn cng, chng ta cn gim bt slng php ton nhn ti u ha

thut ton. Trong thut ton trch c trng MFCC thng thng c trnh bytrong phn1.1,vi mt frame c chiu di 160 im cn phi tnh 160 php ton

nhn trong bc windowing, 256log128 2 php ton nhn trong vic tnh FFT,

khong 256 php nhn trong tnh ton cng sut v 1227 php ton nhn trong

bc tnh DCT. Tng cng cn 1764 php nhn cho trch c trng mt frame.

Bng cch sdng thut ton trch c trng mi c nghtrong phn

1.2,tng sphp nhn dng cho trch c trng mt frame chcn 804, trong

bao gm 80 php ton nhn trong bc windowing, 128log64 2 php ton nhn

trong vic tnh FFT v 1223 php ton nhn trong bc tnh DCT.

Cc c trng c trch bi phng php mi cha ng nhng thng tin

tng tnh phng php thng thng bi v chng cng c tnh ton tcc

hscng sut ca frame l ng ra ca bng blc tn sthang Mel ging nh

nhng c trng thng thng. Nhng slng php ton nhn trong thut ton

mi c gim i mt na, phn ln php nhn c gim bt trong bc tnh

FFT. Hn na, php nhn trong tnh ton FFT th phc tp hn 4 ln php nhn

dng trong cc khi khc, bi v tnh FFT yu cu php nhn sphc. Kt qul

khi thc thi phn cng th thut ton mi sdng t din tch v tiu thcng sut


29/29

t hn mc d chnh xc ca kt qunhn dng chthp hn mt t so vi thut

ton thng thng.

1.2.11Kt lun

Bng cch sdng thut ton tnh trch c trng MFCC mi, mt frame

bao gm 2 sub-frame c chuyn thnh vect MFCC 26 phn t, gm 1 h s

nng lng, 12 hscepstral v 13 hsdelta (o hm cp 1 ca hscepstral

theo thi gian). Vi n sub-frame, ta c n-1 frame thng thng v svect c

trng l n-5.

thuật toán trích Đặc trưng mfcc

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