Quality Improvement of Speech Signals. Using LPC Analysis

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1 Adv. tudie Theor. Phy., Vol., 008, o. 4, Qulity Imrovemet of eech igl Uig LPC Alyi N. Efdi d E. Nderejd, Ghemhhr Brch, Ilmic Ad Uiverity Ghemhhr, Ir N_efdi@yhoo.com Dertmet of Comuter Egieerig, Fculty of Egieerig Mdr Ititute of Techology No-Govermetl P.O. Box: 744, Bbol, Ir eh_der@it.c.ir Abtrct Thi er, rooe ew method for eech igl ehcemet bed o ectrl ubtrctio, Ivere Fourier Trform. We ue the Lier Predictive Codig LPC lyi for oie etimtio d extrctio, d the we comre the rooed method with the reviou oe d re ble to recover the eech igl much better th the reviou method. Keyword: eech igl, Noie, eech ehcemet, ectrl ubtrctio, multi-bd ectrl ubtrctio, LPC lyi. Itroductio Noie reductio i imortt iue i eech igl roceig ytem, lie eech igl codig, eech recogitio. Thu my method hve bee rooed for oie reductio i eech igl, ome of which re method bed o ectrl ubtrctio be & Multi-Bd [5, 6, 7, 8], dtive filterig [], Wvelet trform [0,, 3, 4, 5]. I the ectrl ubtrctio method, 3 coditio hould be met;. Noie mut be dditive. b. Noie d the igl mut be ucorrelted. c. A cl mut be cceible.

2 674 N. Efdi d E. Nderejd Although the be ectrl ubtrctio method i very imle d efficiet, it dd ew oie med muicl oie. For reducig thi oie, the ectrl ubtrctio method lyig ectrl floor d over-ubtrctio, c be ued [6]. Lter, w rooed the multi-bd ectrl ubtrctio method i [5]. I thi method, the corruted eech igl i iitilly divided ito everl frequecy bd, the the ectrl ubtrctio method i lied to ech bd. A metioed before, i thi roch it i uoed tht the igl d oie re ucorrelted, but ctully thu umtio relly he i eech igl. Hece, the ivere Fourier ectrl ubtrctio method h bee reet, which i the me the ectrl ubtrctio method, but here, the ubtrctio, i lied to the ivere Fourier trform. I thi method, the roblem of the correltio betwee the igl d oie i olved to ome extet. Alo, there re ome other method lie ceetrl ubtrctio, wvelet trform [0,, 3, 4, 5] for oie reductio or elimitio de-oiig. I thi er, firt, we decribe the be ectrl ubtrctio, multi-bd ectrl ubtrctio, d ivere Fourier ectrl ubtrctio method, the we etimted the oie from the eech igl uig the LPC lyi [,, 3, 4]. At lt, we ly the etimted oie to the multi-bd ectrl ubtrctio, d ivere Fourier ectrl ubtrctio method d we ee oticeble imrovemet i thee method.. Power ectrl ubtrctio P We uoe tht the igl d oie re dditive, o corruted eech igl c be exreed bellow: x + where x i the corruted eech igl, i the cle ectrl igl, d i rdom oie igl. Accordig to the ecod umtio, the igl d oie re ucorrelted, o we c write: [] R τ D0δ τ R, τ 0 3 where D 0 i cott, R τ i the uto-correltio of the rdom oie igl, d R, τ i the cro-correltio fuctio of the d igl. Accordig to the reltio bove d by uoig tht the d igl re ttiory, we c write: Γ ω Γ ω + Γ ω 4 x Where Γ x, Γ, Γ re Power Deity ectrum PD of x,,, reectively. Followig eq.4 by etimtig the PDF of the rdom oie igl, the PDF of the cle eech igl c be etimted exreed below: ˆ ω Γ ω Γˆ ω Γ 5 x

3 Qulity imrovemet of eech igl uig LPC lyi 675 ˆ ˆ where Γ ω, Γ ω re Etimtio of the Γ ω, Γ ω. Equtio 4 d 5 re true oly whe the cle eech igl d the oie re ttiory, but ctully thi i ot lwy true. ice the cle eech igl re loclly ttiory i hort-time frme, d dditiolly the umtio tht oie i ttiory i more ccetble i hort time itervl, widowig i lied to the corruted eech igl. The the ectrl ubtrctio i lied to ech frme by coiderig m the widow umber, we hve: x ; ; + ; 6 R τ ; D0δ τ 7 R, τ ; 0 8 Where x ; i the widowed igl of the eech igl x. By clcultig the PDF for both ide of eq. 6 we hve: Γ ω; Γx ω; Γ ω; 9 Alo we ow tht []: x * X ω; X ω; ω ; N X ω; N Γ 0 where N i the widow legth ie d X i the eech igl. The fctor N c be imly eglected, ice X ω; i the more bigger th the deomitor: Γ ω ; x ω; x The followig reltio c be chieved uig the reltio, 9: ω; X ω; N ω; where X ω; i the mgitude of Fourier trform for the widowed x; ω ; d N ω ; re the mgitude of the Fourier trform for the widowed cle eech igl d widowed oie igl, reectively. A c be ee from the eq, to comutig the mgitude of the Fourier trform of the cle igl, we eed the mgitude of the rdom oie, hece the rdom oie igl i etimted from the ilece. There i o eech igl i the ilece rt. Now, for chieve the cle eech igl i the time domi, it i ecery to clculte the mgitude of the Fourier trform well it i he, d by hort time ft Fourier trform t.fft get the eech igl i time domi. I ll rcticl lictio, the he of the cle eech ig c be coidered equl to the he of the corruted eech igl [8]. ϕ ϕ 3 ω; X ω;

4 676 N. Efdi d E. Nderejd Thi me tht the effect of oie o the he of the eech igl i ot eible for hum er. Accordig to the equtio, 3, the cle eech igl c be etimted below: ω; ω; ex iϕ { } ω; X ω; N ω; ex iϕ { } ω; Where ω;, N ω; re the fourier trform of the etimted cle igl d fourier trform of the etimted oie igl, reectively. 4 Noiy eech Widowig FFT Phe Iformtio Γ ; ω Ehced eech Overl & Add IFFT Fig. digrm bloc of Power ectrl ubtrctio P The bove method i clled the Power ectrl ubtrctio P method. Fig.. Becue the ecod order of the mgitude of the fourier trform, which idicte the ower of the igl, i beig ued, uully they ue other ower fctor other th, i the ectrl ubtrctio method, the mgitude of which i chieved uig otimiig techique. The method metioed bove i clled the geerl ectrl ubtrctio G method. { iϕ } ω; ω; X ω; N ω; 5 ex But, imortt roblem i the ectrl ubtrctio method i the egtive vlue of the fourier trform of the cle igl. I order word, we c't certily ume the fourier trform of the cle eech igl i ech of the reltio 4 d 5, oitive vlue. There re two method for correctig thee egtive vlue []: hlf-wve correctio : ω; ω; 0 if ω; elewhere > 0 6

5 Qulity imrovemet of eech igl uig LPC lyi 677 b Full-wve correctio : ω ; m bc ω ; m 7 3. Ivere Fourier ectrl ubtrctio IF I the ectrl ubtrctio method [5, 6, 7, 8], it i umed tht the oie d the igl re ucorrelted. Thi coditio c be met by lyig the utocorreltio fuctio to both ide of equtio. Now, if the ccurcy of the reltio 4 or 9 i reduced, the ccurcy of the u correltio betwee the igl d oie would become le coequetly. I the ivere Fourier ectrl ubtrctio method, ubtrctio i lied to the ivere Fourier trform of the mgitude of the Fourier trform of the corruted igl d the etimted oie igl. It c be evidetly id tht i the ivere Fourier ubtrctio method, the ubtrctio i erformed i the time domi i which the u correltio betwee the igl d oie h le ccurcy. Becue uully oie i dded to the igl i the time domi where it' ot certily ucorrelted, but dditio i the frequecy domi eed ucorreltio. I thi method, the etimted cle eech igl i clculted ccordig to fig 3. Noiy eech Widowig FFT IFFT Phe Iformtio IFFT N ω ; Ehced eech Overl & IFFT FFT Fig3. digrm bloc of Ivere Fourier ubtrctio 4. Multi-bd ectrl ubtrctio MB A metioed before, i the be ectrl ubtrctio method, it i uoed tht the effect of oie i the me for ll the igl rg. However ctully thi i ot ctully the ce. Thi i becue, i dditio to the exitig of differet oie ource, there i other fct d tht i the effect of oie o the eech igl deed o the frequecy [7]. Thi deedece of the oie o frequecy, led u to the fct tht the effect of oie o the voice d u-voice letter igl i ot the me [7]. Fig. how the NR i ech frme d i four frequecy bd for the exreio " oe four eve three " id by wom. Becue of the roblem metioed before, mth d loiou [5] hve rooed the ue of ectrl ubtrctio method of berouti [6] i everl

678 N. Efdi d E. Nderejd frequecy bd, o tht they divided ech eech frme ito everl bd i the frequecy domi d the they hve lied the reltio 5, 9 the widowed igl I ech frequecy bd.

6 678 N. Efdi d E. Nderejd frequecy bd, o tht they divided ech eech frme ito everl bd i the frequecy domi d the they hve lied the reltio 5, 9 the widowed igl I ech frequecy bd. I thi method, the mout of the muicl oie i reduced well. The imortt thig i thi method i the wy the NR i comuted i ech frme d i ech bd of tht ech frme. The mout of NR i ech frme d bd i clculted below: i w bi NRi, j 0log e N ω; m e i w bi X ω; m i i th Where NR i, j i the NR i the j bd of the i th frme, X ω ; mi i the qure of the mgitude of the fourier trform of the corruted eech igl i the i th frme, i N ω; m i the qure of the mgitude of the fourier trform of the etimted oie i the i th frme, d b i d e i re the iitil d the ed th frequecie of the j bd. Fig. NR i four frequecy bd, i oe frme 5. Lier Predictio Coefficiet LPC Becue i our rooed lgorithm, LPC lyi [,, 3] i ued for oie etimtio, i thi ectio we decribe thi lyi. The LPC i oe of the troget tool i eech igl roceig. The geerl ide of thi lyi i tht ech mle of the eech ig c be exreed lier equtio of reviou iut d outut: + bl u l 4 l 0 q Where d b l re the deomitor d omitor of the filter, reectively, d

7 Qulity imrovemet of eech igl uig LPC lyi 679 u i the iitil igl which i imule burt for voice d i trig of rdom oie for uvoice [,,3,4]. The trform fuctio of the ytem c be chieved by lyig the Z trform to the equtio 4: q l l l b U H 0 5 A ll ole model i very good etimtio for the trform fuctio H [] for eech igl d c be exreed : A H 6 For hum lryx, P i iteger umber i the rge of 4 0. The imortt oit i comutig the LPC i tht thee coefficiet c be directly drive from the eech igl for thi reo d becue of the deedece of the eech igl o time firt, widowig i doe the igl the the LPC coefficiet, re clculted i hort frme []. 4.. Noie Etimtio Accordig to the dicuio bove, ech mle of the eech igl c comuted with good ccurcy jut uig P reviou mle of tht igl without uig their reviou P mle []: 7 the error igl i ctully the differece betwee the mi eech igl d the eech igl etimte from P reviou mle: e 8 If we ly Z trform o both ide of the reltio bove we hve: A E 9 Fig4. digrm bloc of clcultio of error fuctio e x + -

8 680 N. Efdi d E. Nderejd where, i the trform of the error igl d h the E chrcteritic of oie, ie lier filter erte the ucorrelted. Prt of the igl the mot of which i oie for rovig thi clim, it' eough to clculte the uto-correltio fuctio of the igl e. I fig.5, the uto-correltio of the error, igl which belog to eech igl from the Timit dtbe, i lotted. A c be ee, the igl e h the chrcteritic of oie, ice it' uto-correltio igl i the me the utocorreltio fuctio of the rdom oie igl. I our rooed lgorithm, we hve ued thi igl for oie etimted tht h reulted i gret imrovemet i the NR of the corruted eech igl comred to the exitig method. Fig5. Auto-correltio fuctio of the error igl. Although the igl e i ot the oie igl dded to the cle eech igl, it h mot it' chrcteritic. O the other hd, ome of the ucorrelted igl relted to the eech igl exit i the outut of the filter A, which i egligible comred to oie. 6. Imlemettio d comrio of exerimetl reult I thi rt we y to imlemettio of P, IF d MB ectrl ubtrctio method. After imlemettio, with electio of cle eech igl from TIMIT dtbe d oiig it with white Gu I oie we roduce degrded eech igl. Now, we ly degrded eech igl iut to ech of u imlemettio ytem d we coider the outut for uroe of igl to oie rtio NR, triet tte grh d ectrogrm. I fter tge, we ue from LPC lyi. To thi lie tht we ly obtied outut from u ytem iut to LPC ytem, tht i thi coditio LP, LPIF d LPMB ytem re roducig. With coiderig mout of NR, triet tte grh d ectrogrm of ew ytem with LPC we ee tht reult re imroved reltive to rior tte without LPC.

9 Qulity imrovemet of eech igl uig LPC lyi 68 Tble : Tet reult without LPC Meuremet tye : igl to oie rtio db Cle igl :mled cle eech igl from TIMIT dtbe Added oie to cle igl : White Gui oie Iut NR Ehcemet Method 5 db 0 db 5 db P IF MB Tble : Tet reult with LPC Meuremet tye : igl to oie rtio db Cle igl :mled cle eech igl from TIMIT dtbe Added oie to cle igl : White Gui oie Iut NR Ehcemet Method LP 5 db db db LPIF LPMB

10 68 N. Efdi d E. Nderejd b c d

Qulity imrovemet of eech igl uig LPC lyi 683 e f g Fig5: Triet tte grh cle eech

with IF method e Ehced eech igl with MB method f Ehced eech igl with LP method g

11 Qulity imrovemet of eech igl uig LPC lyi 683 e f g Fig5: Triet tte grh cle eech igl b degrded eech igl NR5db c Ehced eech igl with P method d Ehced eech igl with IF method e Ehced eech igl with MB method f Ehced eech igl with LP method g Ehced eech igl with LPIF method Fig6: ectrogrm cle eech igl b degrded eech igl NR5db c Ehced eech igl with P method d Ehced eech igl with IF method e Ehced eech igl with MB method f Ehced eech igl with LP method g Ehced eech igl with LPIF method

12 684 N. Efdi d E. Nderejd 8. Cocluio I thi er, we rooed ew method for eech igl ehcemet bed o ivere fourier trform ectrl ubtrctio. By tudyig thee eech imrovig method, we hve how their wee i the ccurte etimtio of oie. For olvig thi roblem, the ide of uig the LPC lyi for oie etimtio w rooed. By tudyig thee method, we udertood tht i ll the method, there' eed for oie etimtio or ome of it rmeter. A reult, we tried to fid method which i ble to give better d more ccurte etimtio of oie. I the LPC lyi, we re looig for filter d model for the lryx tht h ll the lryx chrcteritic d by lyig oie to it' iut, we get eech igl t it outut. o, if we ly the eech igl to the ivere model filter, we mut get oie igl t it' outut. ice, the u correlte rt of the oie eech igl er t the filter outut tht becue of the filter lierity, mot of it i oie. We hve lied thi oie i the eech igl ehcemet d ued it to imrove the method bove. By comrig the rooed d the exitig method, we hve ee tht the rooed method imroved the NR of the ehced igl Referece [] J. R. Deller, J. H. L. He, J.G. roi, Dicrete-time roceig of eech igl. d editio, IEEE re, 000. [] L. R. Rbier, R. W. chfer. Digitl roceig of eech igl. Pretice Hll, 978. [3] J. Tierey A tudy of LPC lyi of eech i dditive oie, IEEE tr. Acout. eech d igl roce, AP-8,4, : Aug.980. [4] M.r. mbur, N.. Jyt LPC lyi/ythei from eech iut cotiig gutiig oie or dditive white oie, IEEE Tr. Acout. eech d igl roce. AP-4, 6, : Dec.976. [5]. Kmth P. Loiou, A Multi-bd ectrl ubtrctio method for Ehcig eech corruted by colored oie, roceedig of ICAP-00, Orldo, FL, My 00. [6] M. Berouti, R. chwrt, J. Mhoul, Ehcemet of eech corruted by coutic oie, roc. IEEE ICAP, Whigto DC, Aril 979, 08-.

13 Qulity imrovemet of eech igl uig LPC lyi 685 [7] Y. Ghbri, M. R. Krmi, B. Amelifrd, Imroved multi-bd ectrl ubtrctio method for eech ehcemet, Proceedig of the 6 th ITED Itertiol coferece IGNAL AND IMAGE PROCEING, :5-30, Agut 3-5, 004, Hoolulu, Hwii, UA. [8]. F. Boll, ureio of coutic oie i eech uig ectrl ubtrctio, IEEE Tr. O Acout. eech & igl roceig, vol. AP-7, Aril 979, :3-0. [9] P.. Whitehed, D.V. Adeo, M. A. Clemet, Adtive coutic oie ureio for eech ehcemet, IEEE Itertiol Coferece o Multimedi & Exo., July 003. [0] D. L. Dooho, De-oiig by oft-threholdig, IEEE Trctio o Iformtio Theory, vol. 4, No. 3, My 995, : [] K. Y. Lee, B. G. Lee,. A, Adtive filterig for eech ehcemet i colored oie, IEEE Tr. O igl Proceig Letter, Vol. 4, October 997, : [] Ig Y oo, oo Ngee Koh, Chi Lit Yeo, Wvelet for eech Deoiig, TENCON 97, Bribe, Autrli, 997, : [3] H.heihdeh, H. R. Abutlebi, A Imroved Wvelet-Bed eech Ehcemet ytem, i roc. 7 th Euroe Coferece o eech Commuictio d Techology Euroeech, Alborg, Demr, e. 00. [4] Y. Ghbri, M.R. Krmi, ectrl ubtrctio i the Wvelet Domi for eech Ehcemet, IJIT, vol., No., Augut 004 [5] Y.Ghbri, M.R. Krmi-Mollee A ew roch for eech ehcemet bed o dtive threholdig of wvelet cet eech commuictio [6] H. meti, H. heihdeh, Li Deg, R. L. Bre, HMM-Bed trtegie for Ehcemet of eech igl Embedded i Nottiory Noie, IEEE Trctio o eech d Audio Proceig, Vol. 6, No. 5, etember 998. Received: Februry 9, 008

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