Digital Signals Lecture Notes

Overview

• Focus on digital signals, contrasting with analog and discrete time signals.
• Digital signals require discretization of both time and magnitude.

Key Concepts

Discretization

• Time Axis: Divide time into equal intervals.

  • Example of interval calculation:

    ( \Delta t = t1 - t0 )

    ( \Delta t = t2 - t1 )

    ( \Delta t = t_n - t_{n-1} )
• Magnitude Axis: Must also be discretized.
  • Fixed number of levels for measurement.

Example: Temperature Measurement

Discrete Time Signals

• Temperature measurements at different time intervals:
  • T1: 9°C
  • T2: 38°C
  • T3: 24°C
  • T4: 15°C
  • T5: 45°C
• Values can be any within the range (0 to 45°C).

Digital Signals

• Discretized magnitude levels: 0, 15, 30, 45.
• Measurements:
  • T1: 9°C → 0°C (choosing lower value)
  • T2: 38°C → 30°C
  • T3: 24°C → 15°C
  • T4: 15°C → 15°C (allowed value)
  • T5: 45°C → 45°C
• Key Takeaway: Digital signals can only take specific discrete values.

Example: Voltage Measurement

• Voltage allowed values: 0 volts and 5 volts.
• At T1: 2 volts → 0 volts (lower value selected).
• Error Calculation:
  • Initial error: 2 volts.

Reducing Error by Increasing Levels

• By dividing the range into more levels (e.g., 0, 1.25, 2.5, 3.75, 5):
  • At T1: 2 volts → 1.25 volts (lower value selected).
  • New error: 0.75 volts.
• Further increasing levels (e.g., 0 to 5 incrementally):
  • At T1: can measure as 2 volts → error of 0 volts.
  • Conclusion: Increasing levels reduces measurement error.

Conclusion

• Discussion on the need for digital signals in the next lecture.
• Question posed: Why do we need digital signals?
• Call for students to provide answers in the comments.