Chap4 Sampling Lecture

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    April 16, 2013 Digital Signal Processing 1

    EEE & ECE DepartmentBITS-Pilani, Hyderabad campus

    Sampling &

    Reconstruction

    Digital Signal Processing

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    April 16, 2013 3Digital Signal Processing

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    April 16, 2013 4Digital Signal Processing

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    nT)-(t(nT)g(t)p(t)g(t)gn

    -n

    aap

    Since impulse is a periodic signal of period T, it

    can be expressed as trigonometric Fourier series.

    ............2cos32cos22cos1T1)()( ooo tttnTttp

    n

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    ............(t)cos32g

    (t)cos22g(t)cos2g(t)g

    T

    1)()()(

    oa

    oaoaa

    t

    tttptgtg ap

    The FT of gp(t) is Gp(j)

    ............)cos3(j2G)cos2(j2G)cos(j2G)(jG

    T1)(

    oa

    oaoaa

    t

    ttjGp

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    Recovery of The Signal

    The discrete time signal must pass through

    an analog lowpass filter.

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    Recovery of The Signal

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    Recovery of The Signal

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    ADC

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    DAC

    Recovery of The Signal

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    Recovery of The Signal

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    Recovery of The Signal

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    Recovery of The Signal

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    Recovery of The Signal

    Ideal DACoutput

    Practical DACoutput

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    Recovery of The Signal

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    Recovery of The Signal

    FT

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    Recovery of The Signal

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    Aliasing

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    Digital Signal Processing 31

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    Critical Sampling

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    Under Sampling

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    Over Sampling

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    Problem

    (1) A continuous time signal xa(t) is composedof a linear combination of sinusoidalsignals of frequencies 300 Hz, 500 Hz, 1.2kHz, 2.15 kHz and 3.5 kHz. The signal xa(t)

    is sampled at a 2.0 kHz rate and thesampled sequence is passed through anideal low pass filter with a cut-offfrequency of 900 Hz, genearting acontinuos time signal of ya(t)

    What are the frequency componentspresent in the output signal ?

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    Problem

    The continuous-time signal

    xa (t) = 4 sin (20t) 5 cos (24t) + 3 sin (120 t)

    + 2 cos (176

    t)

    is sampled at a 50 Hz rate, generating the

    sequence x[n].

    Determine the exact expression of x[n].

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    Filtering Using FDA tool

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    Filtering Using FDA tool

    M4.2 (SK. Mitra)

    Determine the lowest order of a lowpass

    Chebyshev Type I filter with a 0.25 dB passbandfrequency at 1.5 kHz and minimum attenuation

    0f 25 dB at 6.0 kHz.