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    Documents - Ecet310 w5 Homework51sol

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    Ruth Abendan
    This document discusses digital transmission and pulse code modulation (PCM). It includes examples of: - Calculating Nyquist sampling rates for different maximum analog input frequencies - Determining the dynamic range and number of bits for given PCM codes - Calculating voltages for different linear PCM codes - Finding resolution and quantization error of PCM codes - Determining the voltage ranges for different 12-bit PCM codes - Calculating the output voltage of a μ-law compression encoder for a given input voltage.

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    Documents - Ecet310 w5 Homework51sol

    Uploaded by

    Ruth Abendan
    53 views4 pages
    This document discusses digital transmission and pulse code modulation (PCM). It includes examples of: - Calculating Nyquist sampling rates for different maximum analog input frequencies - Determining the dynamic range and number of bits for given PCM codes - Calculating voltages for different linear PCM codes - Finding resolution and quantization error of PCM codes - Determining the voltage ranges for different 12-bit PCM codes - Calculating the output voltage of a μ-law compression encoder for a given input voltage.

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    This document discusses digital transmission and pulse code modulation (PCM). It includes examples of: - Calculating Nyquist sampling rates for different maximum analog input frequencies - Determining the dynamic range and number of bits for given PCM codes - Calculating voltages for different linear PCM codes - Finding resolution and quantization error of PCM codes - Determining the voltage ranges for different 12-bit PCM codes - Calculating the output voltage of a μ-law compression encoder for a given input voltage.

    Copyright:

    © All Rights Reserved
    Download as DOC, PDF, TXT or read online from Scribd
    Download as doc, pdf, or txt
    53 views4 pages

    Documents - Ecet310 w5 Homework51sol

    Uploaded by

    Ruth Abendan
    This document discusses digital transmission and pulse code modulation (PCM). It includes examples of: - Calculating Nyquist sampling rates for different maximum analog input frequencies - Determining the dynamic range and number of bits for given PCM codes - Calculating voltages for different linear PCM codes - Finding resolution and quantization error of PCM codes - Determining the voltage ranges for different 12-bit PCM codes - Calculating the output voltage of a μ-law compression encoder for a given input voltage.

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    of 4

    HW51

    DIGITAL TRANSMISSION

    1. Determine the Nyquist sample rate for a maximum analog input frequency of :

    (a) 4 KHz
    (b) 10 KHz

    (a) fN = 2(4KHz) = 8 KHz

    (b) fN = 2(10KHz) = 20 KHz

    2. Determine the dynamic range for a 10-bit sign-magnitude PCM code.

    2n = DR + 1

    DR = 2n -1 = 29 – 1 = 511

    3. Determine the minimum number of bits required in a PCM code for a


    dynamic range of 80 dB. What is the coding efficiency?

    2n = DR + 1

    2n = log-1(80/20) + 1 = 10 000 + 1 = 10001

    n = log(10001)/log(2) = 13.28

    = 15 bits including the sign bit

    Coding efficiency = (14.28 / 15) (100) = 95.2 %

    1
    4. For a resolution of 0.04 V, determine the voltages for the following linear seven-
    bit sign magnitude PCM codes.

    (a) 1001011

    (b) 0101101

    (a) + ( 23 + 21 + 20)(0.04) = = 0.44 V

    (b) - (( 25 + 23 + 22 + 20)(0.04) = -( 32 + 8 + 4 + 1 )(0.04) = -1.8V

    5. Determine the resolution and quantization error for an-eight bit linear sign-
    magnitude PCM code for a maximum decoded voltage of 1.27 V.

    Resolution = 1.27 / (27 – 1) = 0.01 V

    Qe = Resolution/2 = 0.005 v

    2
    6. For a 12-bit linear PCM code with a resolution of 0.02 V, determine the voltage
    range that would be converted to the following PCM codes.

    (a) 100000000001
    (b) 000000000000
    (c) 110000000000
    (d) 01000 0000000
    (e) 100100000001
    (f) 101010101010

    (a) (1)(0.02) = 0.02 V

    Range = 0.02 V – 0.01V to 0.02 V + 0.01V = 0.01V to


    0.03 V

    (b) (0) (0.02) = -0V

    Range = 0 – 0.01V to 0 + 0.01V = -0.01V to 0.01V

    (c) (1024)(0.02)= 20.48 V

    Range = 20.48 – 0.01V to 20.48 + 0.01V= 20.47V to 20.49 V

    (d) (- 1024)(0.02) = - 20.48 V

    Range = - 2048 – 0.01V to - 2048V + 0.01V


    = -20.49V to -20.47 V

    (e) (257)(0.02) = 5.14 V

    Range = 5.13 V to 5.15 V

    (f) (682)(0.02) = 13.64V

    3
    Range = 13.63V to 13.65 V
    7. A µ-law compression encoder has:

    Vi(max) = 8 V, vi(max) = 1V, µ = 255

    Determine the output voltage for an input voltage of 2 V.

    m vin
    vo (max) ln(1 + )
    vi (max)
    vo = for vi �0
    ln(1 + m )

    (0)(2)
    (1) ln(1 + )
    = 8 = 0.752
    ln(1 + 0)

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