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    TakeHome - A1 July Dec 2024 IET

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    Rochelle Quadros

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    TakeHome - A1 July Dec 2024 IET

    Uploaded by

    Rochelle Quadros
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    TakeHome_A1 July Dec 2024 IET

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    3 views2 pages

    TakeHome - A1 July Dec 2024 IET

    Uploaded by

    Rochelle Quadros

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    DEPARTMENT OF E&C

    FIFTH SEMESTER B.TECH. (E&C)


    Take Home Assignment (September 2024)
    Analog and Digital Communication (ECE 3121)
    Submission Date: On or before 9-September 2024 (4.30PM)
    Answer any 5 full questions.
    MAX.MARKS: 5
    Q. Questions CLO AH Bloo
    No.
    LEP ms
    1. a) Define Chi-Square (χ2) Random Variable and give its PDF. 5 1,2 3
    Also compute its mean and variance.

    b) What is a Rayleigh Random Variable? Give its PDF. Also


    compute its mean and variance.

    2 a) Suppose X is a random variable uniformly distributed over 5 1,2 3


    the interval [0,99]. Find the expected value and variance.
    b) Suppose X is a random variable uniformly distributed over
    the interval [3,15]. Find the PDF and CDF of X. Also, find the
    probability that X is between 4 and 6.

    3. Let X be a Gaussian random variable with mean μ=2 and 5 1,2 3


    variance equal to 4. Calculate the following:
    1. The probability density function (PDF) of X.
    2. The probability that X takes a value less than 1.

    4 Consider a message signal m(t) of unit amplitude containing 1 1,2 4


    frequency components 0.1KHZ, 0.2KHZ and 0.4KHZ. The
    signal is applied to a SSB modulator together with a carrier of
    100KHZ with only upper side band retained. The local
    oscillator used at coherent detector to recover m(t) delivers a
    frequency of 100.02KHZ.
    (i)Write down the expression of Susb(t).
    (ii)Determine the expression for output of multiplier V0(t).
    (iii)Determine the LPF output V(t).
    (iv)Determine the frequency components at detector output.
    5 Evaluate the output and channel signal to noise ratio for an 1 1,2 3
    AM DSBSC receiver using coherent detection. Also obtain
    the figure of merit (FOM).
    6 Design an Armstrong FM modulator for the generation of 1 1,2 4
    WBFM signal with ∆𝑓 = 20𝐾ℎ𝑧 𝑎𝑛𝑑 𝑓𝑐 = 96𝑀ℎ𝑧, using the
    narrow band carrier as 200Khz and frequency deviation 10Hz
    and mixer oscillator frequency as 12.4Mhz.
    7 Consider a composite wave obtained by adding a non- 1 1,2 3
    coherent carrier 𝐴𝑐 𝑐𝑜𝑠(2𝜋𝑓𝑐 𝑡 + ∅) to a DSBSC wave. This
    composite wave is applied to an ideal envelope detector. Find
    the resulting detector output and evaluate this output for ∅ =
    0
    8 Find the frequency multiplication ratios of a two-stage 1 1,2 3
    frequency multiplier (for FM generation) if frequency at the
    first stage and second stage as 0.1MHz and 9.5MHz
    respectively. The 100Hz will limit the frequency deviation to
    20Hz and the 15KHz will limit the frequency deviation to
    75KHz. The carrier frequency is 100MHz.
    9 A signal that is sometimes used in communication system is 1 1,2 4
    a raised cosine pulse. The figure QNo. 17 shows a signal gp(t)
    that is a periodic sequence of these pulses with equal spacing
    between them. Determine the first three terms in the fourier
    series expansion of gp(t).

    Figure : Question No. 9

    10 Evaluate the output and channel signal to noise ratio for an 1 1,2 3
    AM envelope detector. Also obtain the figure of merit (FOM)
    for a special case of single tone AM modulation, where, the
    message signal is a sinusoidal signal with frequency fm and
    amplitude Am.

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