1. What is a Signal?

A system is a process or device that takes an input signal and produces an output signal. It can be a mathematical model or a physical device (e.g., amplifiers, filters, communication channels).

Types of Systems

  1. Linear and Non-Linear Systems:

    • Linear: Follows the principle of superposition and scaling.
    • Non-Linear: Does not follow superposition (e.g., power amplifiers).

  2. Time-Invariant and Time-Variant Systems:

    • Time-Invariant: System properties do not change with time.
    • Time-Variant: System behavior changes over time (e.g., aging circuits).

  3. Causal and Non-Causal Systems:

    • Causal: Output depends only on present and past inputs.
    • Non-Causal: Output depends on future inputs (used in predictive systems).

  4. Stable and Unstable Systems:

    • Stable: Produces bounded output for bounded input.
    • Unstable: Output grows uncontrollably for a bounded input.

Basic Operations on Signals

  1. Time Shifting: Moves the signal in time.

    • x(t−T)x(t - T) shifts the signal right byTTT.
    • x(t+T)x(t + T) shifts the signal left byTTT.

  2. Time Scaling: Changes the speed of the signal.

    • x(2t)x(2t)x(2t) compresses the signal.
    • x(t/2)x(t/2)x(t/2) expands the signal.

  3. Time Reversal: Flips the signal around the y-axis.

    • x(−t)x(-t)x(−t) is the time-reversed version.

Importance of Signals and Systems

  • Communication: Transmission of audio, video, and data signals.
  • Control Systems: Automation, robotics, and feedback control.
  • Image and Speech Processing: Used in medical imaging and voice recognition.
  • Electronics and Circuits: Design of filters, amplifiers, and communication device