7(0$ 6(f$/(6 6, 67(0$6<...

18
7HPD– Procesamiento de Señales Biomédicas $xR17 7(0$ 6(f$/(66,67(0$6< &2192/8&,21 PROCESAMIENTO DE SEÑALES BIOMÉDICAS BIOINGENIERÍA 2017

Upload: others

Post on 25-Jul-2021

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

7(0$����6(f$/(6��6,67(0$6�<�&2192/8&,21PROCESAMIENTO DE SEÑALES BIOMÉDICAS

BIOINGENIERÍA2017

Page 2: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

7(0$����6(f$/(6��6,67(0$6�<�&2192/8&,21��� 6(f$/(6/DV�VHxDOHV�VH��SURFHVDQ�SDUD�H[WUDHU�LQIRUPDFLyQ�~WLO �3URFHVDPLHQWR�GH�6HxDOHV�x (Q�HVWH�FXUVR WUDWDUHPRV�VHxDOHV�XQLGLPHQVLRQDOHV�TXH�SRVHHQ�FRPR�YDULDEOH�LQGHSHQGLHQWH�HO�WLHPSR�R�OD�IUHFXHQFLD�/D�FODVLILFDFLyQ�PDV�LPSRUWDQWH�GH��VHxDOHV�HV�$QDOyJLFDV��DPSOLWXG�FRQWLQXD�\�YDULDEOH�LQGHSHQGLHQWH�FRQWLQXD��SRU�HM��7LHPSR�'LVFUHWD��DPSOLWXG�GLVFUHWD�\�YDULDEOH�LQGHSHQGLHQWH�GLVFUHWD��SRU�HM��7LHPSR�&XDQWLILFDGD��DPSOLWXG�GLVFUHWD�\�YDULDEOH�LQGHSHQGLHQWH�FRQWLQXD������ 6HxDOHV�GH�WLHPSR�GLVFUHWRx 6LWXDFLRQHV�QDWXUDOHV��SRU�HM��5HJLVWUR�GLDULR�GH�WHPSHUDWXUDV�x 6HxDOHV�PXHVWUHDGDV��SRU�HM��9HORFLGDG�GH�XQ�PRWRU������ 2SHUDFLRQHV�FRQ�VHxDOHV�GH�WLHPSR�GLVFUHWRx 6XPD��[>Q@�\>Q@��VXPD�SXQWR�D�SXQWR�GH�[>Q@�H�\>Q@�x 3URGXFWR��[>Q@\>Q@��SURGXFWR�SXQWR�D�SXQWR�GH�[>Q@�H�\>Q@�x 'HVSOD]DPLHQWR�HQ�HO�WLHPSR��[>Q��@��UHWDUGD�[>Q@���XQLGDGHV�GH�WLHPSR�x ,QYHUVLyQ��[>�Q@��LQYLHUWH�OD�VHxDO�RULJLQDOx (VFDODPLHQWR�HQ�DPSOLWXG���[>Q@��PXOWLSOLFD�OD�VHxDO�RULJLQDO�SRU��x 'HVSOD]DPLHQWR�HQ�DPSOLWXG��[>Q@����VXPD�XQ�RIIVHW�GH�&&�GH���D�[>Q@�x 'HFLPDFLyQ��[>�Q@��FRPSULPH�[>Q@�HQ�XQ�IDFWRU����HOLPLQD�PXHVWUDV�DOWHUQDGDV�x ,QWHUSRODFLyQ��[>Q��@��DPSOLD�[>Q@�SRU�XQ�IDFWRU����LQWHUSROD�HQWUH�GRV�PXHVWUDV�VXFHVLYDV�x &RPELQDFLRQHV

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 3: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

,QWHUSRODU�XQD�VHxDO�SRU�XQ�IDFWRU�1�Æ PXHVWUHDU�FRQ�WV�1��$GHPiV�H[LVWHQ�GLVWLQWRV�WLSRV�GH�LQWHUSRODFLyQ��FHUR��HVFDOyQ�\�OLQHDO�/D�LQWHUSRODFLyQ�QR�HV�OD�LQYHUVD�GH�OD�GHFLPDFLyQ�[>Q@ ����������Æ GHF�Æ[>�Q@ ������ÆLQWHUS�Æ �����������/D�GHFLPDFLyQ�HV�OD�LQYHUVD�GH�OD�LQWHUSRODFLyQ[>Q@ ����������Æ LQWHUS�Æ[>Q��@ ����������� ����ÆGHF�Æ [>Q@ ���������

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 4: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

����� &ODVLILFDFLyQ�GH�VHxDOHV�EDVDGD�HQ�SHULRGLFLGDG�\�VLPHWUtDx 8QD�VHxDO�HV�SHULyGLFD�VL��[>Q@ [>Q�r N1@��FRQ�N ������������)R ��1��1�HV�XQ� HQWHUR�x 8QD�VHxDO�SRVHH�VLPHWUtD�� 3DU�VL� [H>Q@ [H>�Q@,PSDU�VL [R>Q@ �[R>�Q@x 3DUWHV�SDUHV�H�LPSDUHV�GH�XQ�IXQFLyQ��

[H ���^[>Q@�[>�Q@`� SDUWH�SDU� [R ���^[>Q@�[>�Q@` SDUWH�LPSDU

������&DWiORJR�GH�VHxDOHV�GH�WLHPSR�GLVFUHWDV)XQFLyQ�LPSXOVR�GH�WLHPSR�GLVFUHWRG>Q@ � Æ ����Qz�Æ ����Q �3URSLHGDGHV�GH�OD�IXQFLyQ�LPSXOVR3URGXFWR��[>Q@G>Q�N@ [>N@G>Q�N@'HVSOD]DPLHQWR�� > @ > @ > @N[NQQ[Q �¦f�f G ��([WUDH�HO�YDORU�GHVHDGR�GH�XQD�VHxDO�[>Q@�(VFDODPLHQWR��G>DQ@ G>Q@

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 5: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 6: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

(M��,PSXOVR�GH�WLHPSR�GLVFUHWR[>Q@ �Q� \>Q@ �G>Q��@D� ]>Q@ [>Q@\>Q@ ���� G>Q��@ ��G>Q��@E� > @ > @ ��� � ¦¦ f

�f f�f Q QQ QQ] G

F� G>�Q@ �G>Q@����� 5HSUHVHQWDFLyQ�GH�VHxDOHV�GH�WLHPSR�GLVFUHWR�SRU�LPSXOVRV�GH�WLHPSR�GLVFUHWR�

/DV�VHxDOHV�GH�WLHPSR�GLVFUHWR�[>Q@�VH�SXHGHQ�UHSUHVHQWDU�SRU�XQD�VXPD�GH�GHVSOD]DPLHQWRV�GH�LPSXOVRV�GH�WLHPSR�GLVFUHWR��G>Q�N@��GRQGH�[>N@FRUUHVSRQGH�DO�YDORU�GH�OD�VHxDO�HQ�Q N�;>Q@ ����[>��@�G>Q��@�[>�@�G>Q@�[>�@�G>Q��@���� � > @ > @NQQ[Q �¦f�f G/D�UHSUHVHQWDFLyQ�GHO�HVFDOyQ�GH�WLHPSR�GLVFUHWR�VHULD�X>Q@ � > @ > @ > @NQNQQX QQ � � ¦¦ f

f�f GG �

(M�� [>Q@ ^����������` ���G>Q��@���G>Q@��G>Q��@���G>Q��@����G>Q��@

�� � � � �

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 7: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

)XQFLyQ�VLQF�GH�WLHPSR�GH�GLVFUHWR/D�IXQFLyQ�VLQF�HV�XQD�GH�ODV�IXQFLRQHV�PDV�LPSRUWDQWHV�GHQWUR�GHO�3URFHVDPLHQWR�GH�VHxDOHV��\�HVWD�GHILQLGD�6LQF�Q�1� VHQ�QS�1���QS�1�2EVHUYDFLRQHV��x VLQF��Q�1� ���Q N1��N r ���r �����x VLQF��Q� �G>Q@([SRQHQFLDO�GH�WLHPSR�GLVFUHWR[>Q@ DQX>Q@� Æ D!��FUHFH��D!��GHFUHFH��D ��FWHÆ D����FUHFH��D!���GHFUHFH��D ��FWH

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 8: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

����� )UHFXHQFLD�GLJLWDO([LVWH�XQ�SDUiPHWUR�PX\�LPSRUWDQWH�HQ�HO�DQiOLVLV�GH�VHxDOHV�GH�WLHPSR�GLVFUHWR�GHQRPLQDGR�)UHFXHQFLD�'LJLWDO�\�OD�FXDO�VH�GHILQH�HQ�IXQFLyQ�GHO�SHUtRGR�GH�PXHVWUHR�XWLOL]DGR�SDUD�REWHQHU�OD�VHxDO�GLVFUHWD�D�SDUWLU�GH�XQD�VHxDO�FRQWLQXD�)UHFXHQFLD�GLJLWDO�) I�6IGRQGH�6I ��WV�HV�OD�IUHFXHQFLD�GH�PXHVWUHR��DGHPiV�: �S)�HV�OD�IUHFXHQFLD�GLJLWDO�DQJXODU������ 3HULRGLFLGDG�\�)UHFXHQFLD�GH�VHxDOHV�DUPyQLFDV�GH�WLHPSR�GLVFUHWR�(Q�VHxDOHV�GH�WLHPSR�GLVFUHWR�QR�WRGDV�ODV�DUPyQLFDV�GH�XQD�VHxDO�SHULyGLFD�VRQ�SHULyGLFDV�[>Q@ HM�S)Q ���[>Q�1@ �HM�S)�Q�1�� �HM�S)Q HM�S)1 ��VL�)1 HQWHUR3RU�OR�WDQWR�SDUD�TXH�H[LVWD�SHULRGLFLGDG�VH�GHEH�FXPSOLU�TXH�)1 N HQWHUR��ODV�DUPyQLFDV�GH�WLHPSR�GLVFUHWR�VRQ�SHULyGLFDV�VL�) I�6I�HV�XQD�IUDFFLyQ�UDFLRQDO�GH�OD�IRUPD�N�1�3RU�HM��x [>Q@ FRV��QS�����HV�XQD�VHxDO�SHULyGLFD�GH�SHUtRGR�1 ��x [>Q@ FRV�Q������QS) Q���Æ ) ���S��Q~PHUR�QR�UDFLRQDO��SRU�OR�WDQWR�[>Q@�HV�QR�SHULyGLFD�2EVHUYDFLRQHVx 6L�) QR�HV�IXQFLyQ�UDFLRQDO�QR�KD\�SHULRGLFLGDG����� 5DQJR�SULQFLSDO�GH�XQD�VHxDO6L�VH�FRQVLGHUD�XQD�VLQXVRLGH�GH�WLHPSR�GLVFUHWR�[>Q@ �FRV��S)�Q�T���FX\D�IUHFXHQFLD�GLJLWDO�WLHQH�XQD�SDUWH�HQWHUD�0�\�XQD�SDUWH�IUDFFLRQDO�)U�WDO�TXH�~)U~�����HQWRQFHV�

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 9: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

[>Q@ FRV>�S�0�)U�Q�T@ FRV��S )U�Q�T��VL�)U�HV�����[>Q@ �FRV���S )U�Q�T� �FRV��S )U�Q�T��Æ IDVH�UHYHUVLEOH�(M�D��[>Q@ FRV>�S������Q�T@����) �������0 ���)U �����[>Q@ FRV>�S�����Q�T@E��[>Q@ FRV>�S�����Q�T@����) ������0 ���)U ������[>Q@ FRV>��S�����Q�T@�[>Q@ FRV>�S�����Q�T@��� 6LVWHPDV8Q�VLVWHPD�ItVLFR�HV�XQD�LQWHUFRQH[LyQ�GH�GLVSRVLWLYRV�\�HOHPHQWRV�VXMHWRV�D�OH\HV�ItVLFDV�6LVWHPDV� Æ $QDOyJLFRVÆ 'LVFUHWRV6LVWHPDV��$QiOLVLV��0RGHORV�\�6tQWHVLV�������2SHUDGRUHV�GH�WLHPSR�GLVFUHWR(O�RSHUDGRU�GH�WLHPSR�GLVFUHWR�PDV�XWLOL]DGR�HV�HO�RSHUDGRU�UHWDUGR�]���]��[>Q@ \>Q@ [>Q��@(M���\>Q@ ��]� [�>Q@�� ��[>Q��@��

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 10: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

������&ODVLILFDFLyQ�GH�VLVWHPDV�GH�WLHPSR�GLVFUHWR

/RV�ILOWURV�GLJLWDOHV�SXHGHQ�VHU�FRQVLGHUDGRV�VLVWHPDV�GH�WLHPSR�GLVFUHWR��OD�H[SUHVLyQ�JHQHUDO�HV�\>Q@�$��\>Q��@�����$1�\>Q�1@ %��[>Q@�%��[>Q��@�����%0�[>Q�0@HVWD�HV�OD�H[SUHVLyQ�GH�XQ�ILOWUR�UHFXUVLYR�GH�RUGHQ�1��HO�FXDO�SRVHH�XQD�UHVSXHVWD�LPSXOVLYD�K>Q@GH�ORQJLWXG�LQILQLWD��,,5�

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 11: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

6L�WRGRV�ORV�FRHILFLHQWHV�$N�VRQ����VH�WUDQVIRUPD�HQ�OD�H[SUHVLyQ�GH�XQ�ILOWUR�QR�UHFXUVLYR�GHVFULWSWR�SRU�\>Q@ �%��[>Q@�%��[>Q��@�����%0�[>Q�0@(VWH�ILOWUR�SRVHH�XQD�UHVSXHVWD�LPSXOVLYD�ILQLWD��),5��DO�QR�H[LVWLU�UHFXUVLYLGDG�������5HVSXHVWD�LPSXOVLYD�GH�ILOWURV�GLJLWDOHV¢3RUTXp�HV�LPSRUWDQWH�OD�UHVSXHVWD�LPSXOVLYD�GH�XQ�VLVWHPD"([LVWHQ�GRV�IRUPDV�GH�UHSUHVHQWDU�XQ�VLVWHPD�ItVLFR��HQ�HO�GRPLQLR�GH�OD�IUHFXHQFLD�\�HQ�HO�GRPLQLR�GHO�WLHPSR��(Q�HO�SULPHU�FDVR�VH�WUDWD�GH�OD�UHVSXHVWD�HQ�IUHFXHQFLD��OD�TXH�YHUHPRV�PDV�DGHODQWH�FXDQGR�DQDOLFHPRV�OD�WUDQVIRUPDGD�GH�)RXULHU�\�HQ�HO�VHJXQGR�D�WUDYpV�GH�OD�UHVSXHVWD�DO�LPSXOVR�GH�XQ�VLVWHPD��6L�VH�VXPDQ�LQILQLWRV�WpUPLQRV�FRVHQRLGDOHV�FX\D�IUHFXHQFLD�YDULD�GH���DLQILQLWR��VH�REWLHQH�XQD�VHxDO�LPSXOVLYD��SRU�OR�WDQWR�DSOLFDU�XQ�LPSXOVR�D�OD�HQWUDGD�GH�XQ�VLVWHPD�HV�HTXLYDOHQWH�D�DSOLFDU�LQILQLWRV�FRVHQRV�FRQ�XQ�UDQJR�LQILQLWR�GH�IUHFXHQFLDV��HQWRQFHV�HO�UHVXOWDGR�TXH�VH�REWLHQH�HV�UHSUHVHQWDWLYR�GHO�VLVWHPD�ItVLFR�EDMR�HVWXGLR�¢$�SDUWLU�GH�FRQRFHU�OD�UHVSXHVWD�LPSXOVLYD�GH�XQ�VLVWHPD�SXHGR�FDOFXODU�OD�UHVSXHVWD�SDUD�FXDOTXLHU�HQWUDGD"6L��HIHFWLYDPHQWH�¢3RUTXp�\�FRPR"6HD�XQ�VLVWHPD�DO�TXH�LQJUHVD�OD�VHxDO�[�Q���\�VX�VDOLGD�VHD�OD�VHxDO�\�Q� 7>[�Q�@��GRQGH�7>�@�HV�XQD�IXQFLyQ�OLQHDO�GH�WUDQVIRUPDFLyQ�/D�VHxDO�[�Q��HV�� > @ > @ > @Q[NQQ[Q �G¦f�f \�VHD�K�Q��OD�UHVSXHVWD�D�OD�VHxDO�LPSXOVLYD�G�Q��R�VHD��K�Q� 7>G�Q�@�(QWRQFHV�\�Q� 7>[�Q�@ 7>� ¦f�f �GQ NQQ[ ���� @ > @¦f�f �GQ NQ7Q[ ���� ¦f�f �Q NQKQ[ ����3RU�OR�WDQWR�VL�FRQRFHPRV�OD�UHVSXHVWD�LPSXOVLYD�K�Q��\�OD�HQWUDGD�[�Q���SRGHPRV�FDOFXODU�OD�VDOLGD�GHO�VLVWHPD�\�Q�

6,67(0$[�Q���G�Q� \�Q���K�Q�

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 12: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

��������5HVSXHVWD�LPSXOVLYD�GH�ILOWURV�QR�UHFXUVLYRV8Q�ILOWUR�QR�UHFXUVLYR�GH�ORQJLWXG�0���VH�GHVFULEH�SRU�\>Q@ �%��[>Q@�%��[>Q��@�����%0�[>Q�0@6,�[>Q@ G>Q@��OD�UHVSXHVWD�LPSXOVLYD�HV�K>Q@ �%��G>Q@�%��G>Q��@�����%0�G>Q�0@��������5HVSXHVWD�LPSXOVLYD�GH�ILOWURV�UHFXUVLYRV�FDXVDOHV�/D�H[SUHVLyQ�JHQHUDO�GH�XQ�ILOWUR�UHFXUVLYR�HV�\>Q@�$��\>Q��@�����$1�\>Q�1@ %��[>Q@�%��[>Q��@�����%0�[>Q�0@/D�VROXFLyQ�SDUD�HVWH�WLSR�GH�VLVWHPD�VH�EDVD�HQ�HO�SULQFLSLR�GH�OLQHDOLGDG�\�VXSHUSRVLFLyQ�HO�FXDO�HV�VROR�DSOLFDEOH�D�VLVWHPDV�OLQHDOHV�LQYDULDQWHV�HQ�HO�WLHPSR��HO�FXDO�HV�QXHVWUR�FDVR�/RV�SDVRV�D�VHJXLU�VRQ��� &RQ�K>��@ K>��@ ��� K>�1@ ���HQFRQWUDU�K�>Q@�SDUD�HO�VLVWHPD�K�>Q@��$��K�>Q��@�����$1�K�>Q�1@ �G>Q@�� 8WLOL]DQGR�OLQHDOLGDG�\�VXVSHUSRVLFLyQ�K>Q@ �%��K�>Q@�%��K�>Q��@�����%0�K�>Q�0@(M��(QFRQWUDU�OD�UHVSXHVWD�LPSXOVLYD�GHO�VLJXLHQWH�VLVWHPD�\>Q@�����\>Q��@�����\>Q��@ ��[>Q@�[>Q��@SDVR����(QFRQWUDU�KR>Q@����KR>Q@�����KR>Q��@�����KR>Q��@ G>Q@OD�VROXFLyQ�GH�OD�HFXDFLyQ�KRPRJHQHD�HV��]������]����� ��Æ ]� �����]� ����

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 13: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

SRU�OR�WDQWR�KR>Q@� �.�������Q ��.��������Q ��&RQ�KR>��@ �KR>��@ ��VH�GHEH�UHVROYHU�UHFXUVLYDPHQWH�KR>�@ ����KR>��@�����KR>��@�G>�@ � .��.�KR>��@ � �.���.�SRU�OR�WDQWR�.� �����.� ���SDVR����$SOLFDQGR OLQHDOLGDG�\�VXSHUSRVLFLyQ�

K>Q@ �KR>Q@�KR>Q��@ ^��������Q����������� Q`�X>Q@� ^��������Q������������� Q�� `�X>Q��@������(VWDELOLGDG�GH�VLVWHPDV�OLQHDOHV�LQYDULDQWHV�HQ�WLHPSR�GLVFUHWR8Q�VLVWHPD�OLQHDO�LQYDULDQWH�HQ�WLHPSR�GLVFUHWR�HV�HVWDEOH�VL�ODV UDLFHV�GH�VX�HFXDFLyQ�FDUDFWHUtVWLFD�WLHQHQ�WRGDV�PRGXOR�PHQRU�D��

(M���\>Q@�����\>Q��@�����\>Q��@ [>Q@�6X�HFXDFLyQ�FDUDFWHUtVWLFD�HV��]������]����� ��&RQ�UDtFHV�]� �����]� �����SRU�OR�WDQWR�HO�VLVWHPD�HV�HVWDEOH�

��� &RQYROXFLyQ/D�FRQYROXFLyQ�VL�ELHQ HV�XQD�RSHUDFLyQ�PDWHPiWLFD�JHQHUDO��WLHQH�VX�JUDQ�DSOLFDFLyQ�HQ�HO�FDPSR�GHO�DQiOLVLV�GH�VLVWHPD��GHELGR�D�TXH�UHODFLRQD�ORV�GRPLQLRV�GHO�WLHPSR�\�GH�OD�IUHFXHQFLD�(Q�JHQHUDO�XQ�VLVWHPD�OLQHDO�LQYDULDQWH�UHVSRQGH�FRQ�VX�UHVSXHVWD�LPSXOVLYD�K�W��D�XQD�HQWUDGD�LPSXOVR�G�W�

3DUD�FXDOTXLHU�HQWUDGD�[�W���OD�VDOLGD�\�W� [�W� K�W�G�W� K�W�6,67(0$

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 14: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

(MHPSOR�GH�LQWHUSUHWDFLyQ�GH�OD�FRQYROXFLyQ)LOWUR�GH�VHxDO�SURPHGLR��VH�XWLOL]D�SDUD�VXDYL]DU�XQD�VHxDO�/D�HFXDFLyQ�GH�HVWH�ILOWUR�HV�� > @������� 7WXWX7WK �� �

³³ �ff� � W

7W [7WK[WKW[W\ ��������� ���� OOO SDUD�W!7

W�7 W O

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 15: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

(M��0RVWUDU�FRPR�OD�FRQYROXFLyQ�H[SOLFD�HO�PDQFKDGR��ERUURVR��GH�XQ�REMHWR�HQ�PRYLPLHQWR�HQ�XQD�IRWRJUDItD�

&RQVLGHUHPRV�OD�VHFFLyQ�$$�GH�OD�LPDJHQ�GHO�DXWR�HQ�OD�IRWRJUDItD��GRQGH�H[LVWD�XQ�IXHUWH�FRQWUDVWH�HQWUH�HO�FRORU�GHO�DXWR�\�HO�IRQGR��\�HQ�DXVHQFLD�GH�PRYLPLHQWR�GLEXMHPRV�OD�RVFXULGDG��WH[WXUD�GHO�DXWR��YHUVXV�OD�GLVWDQFLD��(Q�OD�ILJXUD�D��VH�KD�VXSXHVWR�TXH�HO�FXHUSR�SULQFLSDO�GHO�DXWR�WLHQH�XQ�FRQMXQWR�GH�QLYHOHV�GH�UHIOH[LyQ�GLVFUHWR�\�GRQGH�OD�DQWHQD�GD�XQ�PX\�DQJRVWR�SXOVR�UHFWDQJXODU��6L�OD�DQWHQD�IXHUD�LQILQLWDPHQWH�DQJRVWD�\�UHIOHMDUD�OD�PLVPD�FDQWLGDG�GH�OX]�HO�GLEXMR�VH�WUDQVIRUPDUtD�HQ�XQ�LPSXOVR��ILJXUD�E��6L�DKRUD�HO�DXWR�VH�PXHYH�XQD�GLVWDQFLD�VLJQLILFDWLYD�GXUDQWH�HO�WLHPSR�GH�H[SRVLFLyQ�GH�OD�IRWRJUDItD��HO�GLEXMR�GH�OD�WH[WXUD�YHUVXV�OD�GLVWDQFLD�VH�WUDQVIRUPD�HQ�OD�ILJXUD�F���3DUD�HO�FDVR�GHO�DXWR�PRYLpQGRVH�D�YHORFLGDG�FRQVWDQWH��OD�IXQFLyQ�LPSXOVR�FRUUHVSRQGLHQWH�D�OD�DQWHQD�VH�YXHOYH�XQ�UHFWDQJXOR��$Vt�OD�UHVSXHVWD�LPSXOVLYD�GHO�VLVWHPD�VH�SXHGH�FRQVLGHUDU�FRPR�XQD�IXQFLyQ�UHFWDQJXODU�GH�OD�WH[WXUD�YHUVXV�OD�GLVWDQFLD��(QWRQFHV�OD�RSHUDFLyQ�GH�FRQYROXFLyQ�HV�DSOLFDEOH��/HMRV�GH�OD�DQWHQD��OD�LPDJHQ�DFWXDO�HV�OD�LPDJHQ�YHUGDGHUD�FRQYROXFLRQDGD�FRQ�OD�IXQFLyQ�UHFWDQJXODU��(O�HIHFWR�HV�TXH�OD�LPDJHQ�VH�QXEOD�

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 16: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

������&RQYROXFLyQ�'LVFUHWD(Q�HVWH�FXUVR�QRVRWURV�SUHVWDUHPRV�HVSHFLDO�DWHQFLyQ�D�OD�FRQYROXFLyQ�GLVFUHWD�OD�FXDO�SRVHH�XQD�LQWHUSUHWDFLyQ�DQiORJD�D�OD�GHO�FDVR�FRQWLQXR��VROR�TXH�VH�DSOLFD�D�VHxDOHV�GH�WLHPSR�GLVFUHWR��HVWD�VH�GHILQH FRPR�\>Q@ [>Q@ K>Q@ ¦f�f N [>N@K>Q�N@(M��[>Q@ K>Q@ DQX>Q@��FRQ�D��\>Q@ � ¦f�f N DN DQ�N�X>N@�X>Q�N@ �¦ QN � DN DQ�N �DQ ¦ QN � � �DQ�Q���������&RUUHODFLyQ/D�FRUUHODFLyQ�HV�XQD�RSHUDFLyQ�VLPLODU�D�OD�FRQYROXFLyQ��OD�PLGH�HO�JUDGR�GH�GHSHQGHQFLD�HQWUH�GRV�VHxDOHV��&XDQGR�VH�WUDEDMD�FRQ�XQD�PLVPD�VHxDO�GHVSOD]DGD�HQ�HO�WLHPSR�VH�GHQRPLQD�DXWRFRUUHODFLyQ�\�FXDQGR�VH�WUDEDMD�FRQ�GRV�VHxDOHV�GLIHUHQWHV�VH�GHQRPLQD�LQWHUFRUUHODFLyQ�R�FRUUHODFLyQ�FUX]DGD�(Q�SURFHVDPLHQWR�GH�VHxDOHV�WLHQH�PDV�DSOLFDFLyQ�OD�FRUUHODFLyQ�FUX]DGD�OD�FXDO�UHYHOD�HO�JUDGR�GH�VLPLOLWXG�HQWUH�GRV�VHxDOHV�$O�LJXDO�TXH�OD�IXQFLyQ�FRQYROXFLyQ�OD�FRUUHODFLyQ�VH�SXHGH�GHILQLU�HQ�HO�FDPSR�FRQWLQXR�\�HQ�HO�FDPSR�GLVFUHWR��HQ�HVWH�FXUVR�WUDEDMDUHPRV�FRQ�OD�FRUUHODFLyQ�GLVFUHWD�'HILQLFLyQ�$XWRFRUUHODFLyQ��5[[ � ¦f�f N [>N@[>N�Q@��FXDQGR�NÆ��5[[�HV�Pi[LPD��FXDQGR�NÆ f��5[[�HV�PtQLPD�&RUUHODFLyQ�FUX]DGD��5[\ ¦f�f N [>N@\>N�Q@� �[>Q@ \>�Q@��Q ��r���r�����

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 17: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

(M��)XQFLyQ�FRUUHODFLyQ�FUX]DGD�SDUD�VHxDOHV�GH�GXUDFLyQ�ILQLWD�&RQVLGHUHPRV�GRV�PLFUyIRQRV�PRQWDGRV�DO�DLUH�OLEUH�FRQ�VDOLGDV�[�W��H�\�W��SURYLVWDV�SRU�XQD�PLVPD�IXHQWH�GH�VRQLGR�FRPR�VH�PXHVWUDQ�HQ�OD�ILJXUD�D��\�ODV�GRV�VHxDOHV�PXHVWUHDGDV�HQ�OD�ILJ��E��

6H�REVHUYD�HQ�OD�ILJXUD�TXH�ORV�GRV�FRQMXQWRV�GH�PXHVWUDV�VRQ�LGpQWLFRV�SHUR�GHVSOD]DGRV�HQ�HO�WLHPSR��(VWH�GHVSOD]DPLHQWR�SXHGH�FDXVDU�TXH�OD�FRUUHODFLyQ�VHD�PX\�SHTXHxD��3DUD�LQGLFDU�OD�VLPLOLWXG�HQWUH�ODV�GRV�VHxDOHV�QHFHVLWDPRV�GH�DOJ~Q�SDUiPHWUR�TXH�VHD�IXQFLyQ�GHO�UHWDUGR�HQWUH�HOODV�5[\ ¦f�f N [>N@\>N�Q@

7HPD���± Procesamiento de Señales Biomédicas � $xR���17

Page 18: 7(0$ 6(f$/(6 6, 67(0$6< &2192/8&,21dea.unsj.edu.ar/pdsbio/Apuntes/Tema_1-Apuntes_Catedra.pdf · 2017. 9. 25. · 7HPD – Procesamiento de Señales Biomédicas $xR 17 7(0$ 6(f$/(6

��

'RQGH�OD�VHFXHQFLD�\>Q@�HVWD�UHWDUGDGD�N�XQLGDGHV�UHVSHFWR�GH�[>Q@�\�VH�HYDO~D�OD�VXPD�GHO�SURGXFWR�GH�VXV�WpUPLQRV��6L�VH�UHDOL]D�SDUD�WRGRV�ORV�YDORUHV�GH�N��(Q�HO�FDVR�GH�OD�ILJXUD�E���DSDUHQWHPHQWH�SRU�LQVSHFFLyQ�OD�FRUUHODFLyQ�FUX]DGD�HV�PX\�SHTXHxD�SDUD�N ��SHUR�HV�JUDQGH�VL�N ���(VWR�HV�SRUTXH�[>Q@�HVWD�UHWDUGDGD�UHVSHFWR�\>Q@�HQ�FLQFR�SHUtRGRV�GH�PXHVWUHR��3RU�OR�WDQWR�OD�IXQFLyQ�FRUUHODFLyQ�FUX]DGD�QR�VROR�GD�XQD�LGHD�GH�OD�UHODFLyQ�HQWUH�ODV�VHxDOHV�VLQR�GHO�UHWDUGR�HQWUH�DPEDV�(M��,GHQWLILFDFLyQ�GH�VLVWHPDV8Q�UHTXHULPLHQWR�FRPXQ�HQ�HO�SURFHVDPLHQWR�GH�VHxDOHV�HV�FDUDFWHUL]DU�XQ�VLVWHPD�GHVFRQRFLGR��GHWHUPLQDQGR�VX�UHVSXHVWD�LPSXOVLYD���'H�FXDOTXLHU�PDQHUD�SDUD�REWHQHUOD�VHULD�QHFHVDULR�XQD�VHxDO�LPSXOVLYD�OD�FXDO�WLHQH�DPSOLWXG�LQILQLWD�\�DQFKR�FHUR��OR�FXDO�HV�ItVLFDPHQWH�LUUHDOL]DEOH��8QD�DOWHUQDWLYD�HV�DSOLFDU�XQ�UXLGR�DO�VLVWHPD�\�FDOFXODU�OD�FRUUHODFLyQ�FUX]DGD�HQWUH��OD�HQWUDGD�\�OD VDOLGD��&RQVLGHUHPRV�XQD�VHxDO��GH�UXLGR�Q�W��DSOLFDGD�DO�VLVWHPD�FRQ�UHVSXHVWD�LPSXOVLYD�K�W���OD�VDOLGD�\�W� Q�W� K�W�$�VX�YH]��5\Q \�W� Q��W� >Q�W� K�W�@ Q��W� 5QQ�W� K�W�6L�OD�HQWUDGD�GH�UXLGR�WLHQH�XQ�DQFKR�GH�EDQGD�PX\�JUDQGH��UXLGR�EODQFR�SDUD�HO�VLVWHPD�FRQVLGHUDGR���OD�DXWRFRUUHODFLyQ�5QQ�HV�XQ�SLFR�PXFKR�PDV�DQJRVWR�TXH�OD�UHVSXHVWD�LPSXOVLYD�GHO�VLVWHPD��GH�HVWD�IRUPD���5\Q�W� K�W�(VWR�VLJQLILFD�TXH�VL�VH�DSOLFD�XQ�UXLGR�EODQFR�DO�VLVWHPD�GHVFRQRFLGR��OD�UHVSXHVWD�LPSXOVLYD�GH�HVWH�VLVWHPD�VH�REWLHQH�FRPR�OD�FRUUHODFLyQ�FUX]DGD�GH�OD�HQWUDGD�\�OD�VDOLGD�

7HPD���± Procesamiento de Señales Biomédicas � $xR���17