2. Sine wave is the fundamental periodic signal and can be represented by three

Question

2. Sine wave is the fundamental periodic signal and can be represented by three parameters. Name the three parameters that match the following statements a. Strength of signal typically measured in volts. b. Rate at which the signal repeats. c. Relative position in time within a single period of a signal 3. Shannon equation relates the maximum capacity (transmission bit rate) that can be achieved over a given channel with certain noise characteristics and bandwidth. In other words, Shannon's Theorem gives an upper bound to the capacity of a link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio of the link. a. What is the equation presented by Shannon for the maximum channel capacity? b. The signal-to-noise ratio (SN) is usually expressed in decibels (dB). Decibels is computed using logarithms so that very large and small ratios result in numbers that are easy to work with. Express a signal-to-noise ratio of 1000 in decibels. c. You would convent decibels to a standard signal-to-noise ratio before applying Shannon equation. True or False 4. A typical telephone line has a signal-to-noise ratio of 30dB and an audio bandwidth of 3kHz. Based on Shannon's theorem, what is the maximum data rate for this telephone line? 5. Nyquist theorem gives the maximum capacity of a noiseless channel. Based on Nyquist, what is the maximum capacity for a noiseless channel with a 3kHz bandwidth and four discrete signal levels?

Explanation / Answer

[2]
    [a] amplitude
    [b] phase
    [c] angular frequency

[3] [a]
      Shannon Equation relates to maximum data rate of:   C = B * log2(1+S/N)
       B is the bandwidth of the line
       S is the average signal power
       N is the average noise power
  
    [b]
      The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula:
                            = 10 * log10(S/N)
      so for example a signal-to-noise ratio of 1000 is commonly expressed as 10 * log10(1000) = 30 dB.

     [c] True.

[4] maximum data rate of:   C = B * log2(1+S/N)
The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula: 10 * log10(S/N)

C = 3000 * log2(1001)

which is a little less than 30 kbps.

[5]

   Nyquist’s formulae for multi-level signalling for a noiseless channel is : C = 2 * B * log M.
   B is the maximum bandwidth allowed by the channel
   M is the number of different signalling values or symbols and log is to the base 2.

    C = 2 * 3000 * log 4 = 6000* 2 = 12000 bps.

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