Relationship between transmission rates

  • bandwith

$$ = f_B $$

  • Binary data rate

$$ = R_s = \frac{1}{T_s} $$

  • Roll off factor

$$ f_B = \frac{1+\alpha}{2*T_s} $$

trade-off: An increase in a increase the required bandwidth but decrease the ISI, and vice versa.

Sample signal and ideal low-pass filter

$$ Example: \newline m(t) = 6cos(8,000\pi t) + 2cos(20,000\pi t) $$

Draw the portion of the amplitude of…

  • Sample rate

$$ = f_s > 2 * Highest \space Frequency \space component $$

Lind Coding

  • Types:

    • None-return-to-zero (NRZ)
    • Polar NRZ
    • Bipolar NRZ(AMI)
    • Manchester signaling (power efficiency)
    • HDBn

  • Properties of line codes:

    • timing content (Clock recovery)
    • Bandwidth
    • Error detection & correction capability
    • DC content
    • Power efficiency

Miltilevel Baseband Systems

Terminology

  • ASK: Amplitude Shift Keying
  • PSK: Phase Shift Keying
  • FSK: Frequency
  • QAM: Quadrature Amplitude Modulation

Formula

  • Minimum bandwidth of baseband

$$ = 0.5 * \frac{R_B}{\log_2 M} $$

  • Minimum bandwidth of passband *

$$ = 2 * bandwidth\space of\space baseband $$

  • Draw constellation pattern for M-ary ASK

Tap Equaliser *

Quantisation noise ratio *

Formula

$$ (\frac{S}{N_q})_{dB} = 1.76 + 6.02n $$

HDB3 provides transitions during long sequences of zeros (AMI doesn’t ), thus substantially improving timing information. It is possible to always extract the clock frim any HDB3 waveform whereas AMI RZ loses the clock signal if a long sequence of zeros occurs.