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  • X L S TN HIU Digital Signal Processing

    Ging vin: Ths. o Th Thu Thy

    1

    TRNG I HC CNG NGHIP TP.HCM

    CNDT_O TH THU THY

  • Chng 4:

    TN HIU V H THNG TRONG MIN TN S LIN TC

    CNDT_O TH THU THY 2

  • CNDT_O TH THU THY 3

    Chng 4:

    TN HIU V H THNG TRONG MIN TN S LIN TC

    4.1 PHN TCH TN S CA CC TN HIU LIN TC

    THI GIAN

    4.2 PHN TCH TN S CA CC TN HIU RI RC THI

    GIAN

    4.3 CC TNH CHT CA BIN I FOURIER

    4.4 QUAN H GIA BIN I FOURIER & BIN I Z

    4.5 PHN TCH H THNG LTI RI RC TRONG MIN

    TN S

  • CNDT_O TH THU THY 4

    4.1 PHN TCH TN S CA CC TN HIU LIN TC THI GIAN

    Phn tch Fourier ca mt tn hiu cho ta thy cu trc tn s (ph) ca tn hiu.

    V d: Ph ca nh sng trng :

  • CNDT_O TH THU THY 5

    4.1 PHN TCH TN S CA CC TN HIU LIN TC THI GIAN

    4.1.1 Khai trin Fourier (chui Fourier)

    p dng cho tn hiu tun hon

    4.1.2 Bin i Fourier (tch phn Fourier)

    p dng cho cc tn hiu khng tun hon.

  • CNDT_O TH THU THY 6

    4.1.1 Khai trin Fourier (tn hiu tun hon)

    Mt dng sng tun hon c th phn thnh v hn cc thnh phn sin c tn s l bi s nguyn ca tn s tun hon ca dng sng.

    -Tp Tp 0

    x(t)

    t

    X(f)

    F0 -F0

  • CNDT_O TH THU THY 7

    4.1.1 Khai trin Fourier

    x(t) tun hon c chu k To, tn s gc o=2/To v fo = 1/To c 3 dng khai trin Fourier:

    - Khai trin lng gic

    - Dng bin v pha

    - Dng m phc (sin phc)

  • CNDT_O TH THU THY 8

    a. Khai trin lng gic

    0 n 0 n 0n 1 n 1

    x(t) a a cosn t b sinn t

    /

    /

    ( )

    To

    To

    a x t dtT

    2

    00 2

    1

    /

    /

    ( )cos

    To

    n

    To

    a x t n tdtT

    2

    00 2

    2

    /

    /

    ( )sin

    To

    n

    To

    b x t n tdtT

    2

    00 2

    2

    ao: thnh phn trung bnh (mt chiu). a1cosot + b1sinot: thnh phn cn bn hay gi l hi th nht. a2cos2ot + b2sin2ot: hi th hai a3cos3ot + b3sin3ot: hi th ba v.v..

  • CNDT_O TH THU THY 9

    b. Dng bin v pha (ph 1 bn)

    ( ) cos( )n nn

    x t c c n t

    0 01

    , , ...

    ar

    o o

    n n n

    nn

    n

    c a

    c a b n

    bctg

    a

    2 21 2 3

    co: thanh phn trung binh

    c1cos(0t +1)

    : thanh phn cn ban

    c2cos(20t +2)

    : hai th 2

    Ph bin la bin thin ca cc h s gc co, cn theo tn s

    Ph pha la bin thin ca pha ban u n theo tn s

    Ph chi hin hu nhng tn s ri rac no nn la ph ri rac

    hay ph vach

  • CNDT_O TH THU THY 10

    c. Dng m phc (sin phc) (ph 2 bn)

    ( ) ojn t

    n

    n

    x t X e

    njn n nn

    X a c

    a jb cX e

    0 0 0

    2 2

    Cc h s ca khai trin m phc l:

    /

    /

    ( ) 02

    0 2

    1To

    jn tn

    To

    X x t e dtT

  • CNDT_O TH THU THY 11

    Cng sut ca tn hiu tun hon

    n

    n

    P X

    2

  • CNDT_O TH THU THY 12

    1. Tm khai trin Fourier ca dng sng vung i xng.

    V ph bin v ph pha

    a. Khai trin lng gic

    b. Khai trin Fourier dng bin v pha

    c. Dng m phc

  • CNDT_O TH THU THY 13

    ( ) sin sin sin ...o o oA

    x t t t t

    4 1 13 5

    3 5

    b. Ph bin va pha:

    ( ) cos ( ) oo

    n

    Ax t n t

    n

    1

    4 12 1 90

    2 1

    a. Cc hai chn bng khng, cc hai l c bin giam

    tng i nhanh nhng chi bng khng tn s ln v

    han

  • CNDT_O TH THU THY 14

    2. Tm khai trin Fourier ca dng sng sin chnh lu

    ton k bin nh A. V ph bin v ph pha.

    x(t)=A|sin t|

    t

    x(t)

    A

    0 2 3

  • CNDT_O TH THU THY 15

    /

    /

    ( ) sin cos

    2

    00 02 0

    1 1 2To

    To

    A Aa x t dt A tdt t

    T

    /

    /

    ( )cos sin os

    2

    0 00 2 0

    2 2To

    n

    To

    a x t n tdt A tc n tdtT

    sin( ) sin( )0

    2 1 2 1nA

    a n t n t dt

    os( ) os( )

    0 0

    2 1 2 1

    2 1 2 1n

    A c n t c n ta

    n n

    2

    2 2 4 1

    2 1 2 1 4 1n

    A Aa

    n n n

  • CNDT_O TH THU THY 16

    ( ) cos2

    1

    2 4 12

    4 1n

    A Ax t nt

    n

    ( ) cos cos cos ......2 4 1 1 1

    2 4 63 15 35

    A Ax t t t t

  • CNDT_O TH THU THY 17

    3. Cho khai trin dng lng gic nh sau. Tm khai

    trin hai dng kia. V ph tn hiu v tm cng sut

    ca tn hiu

    4. Tm khai trin Fourier ca chui xung Dirac u

    ( ) cos sino ox t t t 10 8 6

    -2T -T 0 T 2 T 3T

    1

    n

    x(t)

  • CNDT_O TH THU THY 18

    Gii bi 4

    x(t) l chui xung Dirac u chu k T0 hay tn s f0=1/T0

    V x(t) tun hon nn ta c khai trin Fourier ca x(t):

    ( ) ( ) 02

    0ojn t j nf t

    n n

    k k k

    x t t kT X e X e

    /

    /

    ( ) 02

    20

    0 02

    1 1To

    j nf tn

    To

    X t e dt fT T

    ( ) ( ) ( )02

    00 0

    1 1j nf t

    k n

    x t e X f f nfT T

  • CNDT_O TH THU THY 19

    Vy mt chui xung dirac trong min thi gian cho mt chui xung dirac trong min tn s

    -2T0 -T0 0 T0 2 T0 3T0

    1

    t

    x(t)

    -2f0 -f0 0 f0 2 f0 3f0

    f0

    f

    X(f)

  • CNDT_O TH THU THY 20

    4.1.2 Bin i Fourier

    (tn hiu khng tun hon)

    X()

    2/ -2/

    x(t)

    -/2 t

    /2

  • CNDT_O TH THU THY 21

    ( )( ) ( ) j fX f X f e

    Bin thin ca |X(f)| theo f la ph bin ( ln)

    Bin thin ca (f) theo f la ph pha (con c vit

    argX(f) hay X(f))

    b. Ph bin v ph pha

    a. Cp bin i Fourier x(t) X(f):

    ( ) ( ) ( ) j ftX f F x t x t e dt

    2

    ( ) ( ) ( ) j ftx t F X f X f e df

    1 2

  • CNDT_O TH THU THY 22

    ( ) ( ) ( ) cos sinj ftX f x t e dt x t ft j ft dt

    2

    2 2

    ( ) ( )cosRX f x t ftdt

    2Thanh phn thc ao la:

    Khi x(t) thc

    ( ) ( )sin 2IX f x t ftdt

    Bin va pha ca X(f) la:

    ( ) ( ) ( )R IX f X f X f 2 2

    ( )( )

    ( )

    I

    R

    X ff arctg

    X f

  • CNDT_O TH THU THY 23

    Nng lng ca tn hiu khng tun hon

    ( ) ( )E x t dt X f df

    2 2

  • CNDT_O TH THU THY 24

    CC TNH CHT BIN I FOURIER

  • CNDT_O TH THU THY 25

    CC TNH CHT BIN I FOURIER

  • CNDT_O TH THU THY 26

    CC TNH CHT BIN I FOURIER

  • CNDT_O TH THU THY 27

    CC TNH CHT BIN I FOURIER

  • CNDT_O TH THU THY 28

    CC TNH CHT BIN I FOURIER

  • CNDT_O TH THU THY 29

    MT S BIN I FOURIER C BN

  • CNDT_O TH THU THY 30

    MT S BIN I FOURIER C BN

  • CNDT_O TH THU THY 31

    MT S BIN I FOURIER C BN

  • CNDT_O TH THU THY 32

    Chng 4:

    TN HIU V H THNG TRONG MIN TN S LIN TC

    4.1 PHN TCH TN S CA CC TN HIU LIN TC

    THI GIAN

    4.2 PHN TCH TN S CA CC TN HIU RI RC THI

    GIAN

    4.3 CC TNH CHT CA BIN I FOURIER

    4.4 QUAN H GIA BIN I FOURIER & BIN I Z

    4.5 PHN TCH H THNG LTI RI RC TRONG MIN

    TN S

  • CNDT_O TH THU THY 33

    4.2 PHN TCH TN S CA CC TN

    HIU RI RC THI GIAN

    4.2.1 KHAI TRIN FOURIER RI RC THI GIAN

    (tn hiu ri rc tun hon)

    4.2.2 BIN I FOURIER RI RC THI GIAN

    (tn hiu ri rc ko tun hon)

    4.2.3 IU KIN TN TI BIN I FOURIER

  • CNDT_O TH THU THY 34

    4.2.1 KHAI TRIN FOURIER RI RC THI GIAN

    DFS (tn hiu ri rc tun hon)

    Tn hiu x(n) ri rc, tun hon vi chu k N mu.

    1

    0

    /2)(N

    k

    Nknj

    kecnx

    1

    0

    /21N

    n

    Nknj

    k enxN

    c

    Tn hiu x(n) ri rc tun hon vi chu k N mu th ph ck ca n cng tun hon vi chu k N

  • CNDT_O TH THU THY 35

    x(n) tun hoan chu k N Tnh DFS ca

    x(n) c(k)

    0 N

    xp(n)

    N-1 n L-1 n

    |c(k)|

    k 0 N -N

  • CNDT_O TH THU THY 36

    V d: Tm khai trin Fourier ri rc ca tn hiu x(n)=cosn0 khi a. b. 0 = /3 Gii

    0

    2 2 1

    2 2 2 2

    0 2

    0 2a. Khi

    th

    V 0 /2 khng phi s hu t nn x(n) khng tun hon khng c khai trin Fourier

    b. Khi 0=/3 th chu k tun hon ca tn hiu cosn/3 l:

    /N

    26

    3

    Cc thanh phn ph la: /j knkn

    c x n eN

    5

    2 6

    0

    1

    Hoc ta pht biu x(n) theo m phc

    / / / /( ) os j n j n j n j nn

    x n c e e e e 2 6 2 6 2 6 2 5 6

    2 1 1 1 1

    6 2 2 2 2

    Cc thanh phn ph la: c0=0, c1=1/2, c2=c3=c4=0, c5=1/2

    Chu k ph nay c lp lai lin tc

  • CNDT_O TH THU THY 37

    K hiu:

    x(n) X() hay X() = F{x(n)}

    X() x(n) hay x(n) = F-1{X()}

    4.2.2 BIN I FOURIER RI RC THI GIAN

    (tn hiu ri rc ko tun hon)

    F

    1

    F

    Trong : - tn s ca tn hiu ri rc, = Ts

    - tn s ca tn hiu lin tc

    Ts - chu k ly mu

    Bin i Fourier ri

    rc thi gian ca x(n):

    n

    njenxX

    )()(

  • CNDT_O TH THU THY 38

    b. X() biu din di dng modun & argument:

    Nhn thy X() tun hon vi chu k 2, tht vy:

    )()()(

    jeXX

    Trong : )(X - ph bin ca x(n)

    )](arg[)( X - ph pha ca x(n)

    n

    njenxX

    )2()()2(

    )()( Xenxn

    nj

    p dng kt qu:

    0 :0

    0:2

    k

    kdk