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    Diskretizacija-Teorema O Odabiranju: F (T) - F (J)

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    sdmitar
    The document discusses the discretization theorem for sampling, which states that a continuous-time signal x(t) can be reconstructed from its samples if it is bandlimited and sampled at or above the Nyquist rate. Specifically: 1) A continuous-time signal x(t) is multiplied by a periodic sampling function s(t) to obtain samples Sn at intervals of τ seconds. 2) The Fourier transform of the sampled signal is equal to the Fourier transform of the original signal multiplied by sinc functions centered at integer multiples of the sampling frequency. 3) For perfect reconstruction, the signal must be bandlimited to less than half the sampling frequency to avoid aliasing, in accordance with the Nyquist sampling theorem

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    Attribution Non-Commercial (BY-NC)
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    Diskretizacija-Teorema O Odabiranju: F (T) - F (J)

    Uploaded by

    sdmitar
    20 views2 pages
    The document discusses the discretization theorem for sampling, which states that a continuous-time signal x(t) can be reconstructed from its samples if it is bandlimited and sampled at or above the Nyquist rate. Specifically: 1) A continuous-time signal x(t) is multiplied by a periodic sampling function s(t) to obtain samples Sn at intervals of τ seconds. 2) The Fourier transform of the sampled signal is equal to the Fourier transform of the original signal multiplied by sinc functions centered at integer multiples of the sampling frequency. 3) For perfect reconstruction, the signal must be bandlimited to less than half the sampling frequency to avoid aliasing, in accordance with the Nyquist sampling theorem

    Original Description:

    Digitala obrada signala Diskretizacija redavanja

    Original Title

    DISKRETIZACIJA

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    © Attribution Non-Commercial (BY-NC)

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    The document discusses the discretization theorem for sampling, which states that a continuous-time signal x(t) can be reconstructed from its samples if it is bandlimited and sampled at or above the Nyquist rate. Specifically: 1) A continuous-time signal x(t) is multiplied by a periodic sampling function s(t) to obtain samples Sn at intervals of τ seconds. 2) The Fourier transform of the sampled signal is equal to the Fourier transform of the original signal multiplied by sinc functions centered at integer multiples of the sampling frequency. 3) For perfect reconstruction, the signal must be bandlimited to less than half the sampling frequency to avoid aliasing, in accordance with the Nyquist sampling theorem

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    20 views2 pages

    Diskretizacija-Teorema O Odabiranju: F (T) - F (J)

    Uploaded by

    sdmitar
    The document discusses the discretization theorem for sampling, which states that a continuous-time signal x(t) can be reconstructed from its samples if it is bandlimited and sampled at or above the Nyquist rate. Specifically: 1) A continuous-time signal x(t) is multiplied by a periodic sampling function s(t) to obtain samples Sn at intervals of τ seconds. 2) The Fourier transform of the sampled signal is equal to the Fourier transform of the original signal multiplied by sinc functions centered at integer multiples of the sampling frequency. 3) For perfect reconstruction, the signal must be bandlimited to less than half the sampling frequency to avoid aliasing, in accordance with the Nyquist sampling theorem

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    of 2

    DISKRETIZACIJA- TEOREMA O ODABIRANJU

    |F(j
    )|

    f(t)
    t
    s(t)

    -T

    Sn

    -
    /2
    /2

    -
    /2
    /2

    -
    0

    x(t)
    -T

    -
    m

    2
    0

    |X(j
    )|
    |

    |S-1|

    |S0|

    |S1|

    |S2|

    -
    2
    -
    m
    0
    0
    0
    m 0
    -

    0
    m
    0
    m
    Sn =

    E sin( n 0 / 2)
    T
    n 0 / 2

    X ( j) =

    x(t ) e

    jt

    s (t ) =

    Sn e jn t
    0

    n =

    n =

    dt = f (t ) s (t ) e jt dt = S n F [ j ( n0 )]

    E = 1/ , 0 Sn = 1/ T

    1 sin2f t n
    X ( j ) = nF [ j ( m n20f m) ]

    f (t ) = T
    f n =
    n =

    f0 2 fm

    2 fm

    n
    2f m 1 t 1
    T = 2 fm
    f0

    2 fm

    USKOPOJASNO ODABIRANJE

    f(t) )|
    |X(j
    |

    + x(t) >

    ~
    ~

    f(t)

    T
    1/T
    x(t )
    s(t)|
    fm

    -
    2
    -
    m
    0
    0
    0
    m 0

    0-
    m
    0-
    m

    |X(j
    )|
    (n+1)
    0

    n
    0

    |F2(j
    )|

    -
    -

    1+n
    0
    1
    2
    2+(n+1)
    0

    -
    -
    2
    1

    1 + n 0 1

    2 + (n + 1) 0 2
    2 2 21

    n +1
    n

    MINIMALNA
    U^ESTANOST
    ODABIRANJA

    KRITI^NA
    U^ESTANOST
    ODABIRANJA

    |F1(j
    )|

    2 2
    2
    0 1
    n +1
    n

    0 min

    0c

    1
    2 1

    2 2
    n +1

    2 2
    1
    + 1
    2
    1`

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