Signal

Signals

Signals are essential in telecommunications and data transmission, characterized by three primary components: Amplitude, Frequency, and Phase.

Amplitude

• Amplitude refers to the height of the wave above or below a reference point.
• It is typically measured in volts.

Frequency

• Frequency indicates how many times a signal completes a cycle in a specific time frame, measured in Hertz (Hz), or cycles per second.
  • Period is calculated as ( \text{Period} = \frac{1}{\text{Frequency}} ).
• The spectrum represents the range of frequencies a signal spans, from its minimum to maximum values.
• Bandwidth is defined as the absolute difference between the lowest and highest frequencies of a signal.

Example: Average Voice

• The average voice operates within a frequency range of approximately 300 Hz to 3100 Hz.
  • The spectrum would be 300 – 3100 Hz.
  • The bandwidth would be 2800 Hz.

Phase

• Phase describes the position of a waveform concerning a specific moment in time or relative to time zero.
• Phase can change by any angle between 0 and 360 degrees, with common phase angles being 45, 90, 135, etc.

Phase and Signal Transmission

• If a signal can demonstrate two different phase angles, 1 bit can be transmitted with each signal change (or baud).
• If it can exhibit four different phase angles, then 2 bits can be transmitted with each change.
• The relationship can be expressed mathematically as: $$\text{Number of bits transmitted}={\log }_2(\text{Number of different phase angles})$$
• This principle also applies to amplitude levels or frequency levels.

Decibels (dB)

• The decibel (dB) is a logarithmic unit used to express the ratio of two values, commonly in power.
• The formula for calculating decibels is: $$\text{dB}=10\times {\log }_{10}\left(\frac{P_2}{P_1}\right)$$ where $P_1$ is the initial power level, and $P_2$ is the final power level.

Loss of Signal Strength (in dB)

• To determine the impact of a signal loss:
  • If a signal loses 3 dB, how significant is that?
  • For a signal starting at 100 watts and ending at 50 watts, the dB loss can be calculated as follows:
  $$\text{dB}=10\times {\log }_{10}\left(\frac{50}{100}\right)=10\times {\log }_{10}(0.5)\approx 10\times -0.3=-3.0$$
• Therefore, a 3 dB loss indicates that the signal has lost half of its power.

Understanding these fundamentals of signals is crucial for effective communication and data transmission in various technological applications.