Analysis of Continuous Time Signals

Definition of Signals

• Signals represent a physical quantity (e.g., sound, temperature) that changes over time or space.
• They are single-valued functions carrying information through amplitude, frequency, and phase.
• Common examples include voice signals and video signals.

Classification of Signals

• Signals can be classified based on the number of dimensions into:
  • One Dimensional (1-D): Function of one variable; examples include audio and biomedical signals.
  • Two Dimensional (2-D): Function of two variables; represented by image signals where intensity varies with spatial coordinates.
  • Three Dimensional (3-D): Function of three variables; represented by video signals depending on spatial coordinates and time.

Types of Signals by Nature

• Continuous Time Signal (CTS):

  • Values continually vary over time with an infinite set of values.
  • Represented as x(t), where t is a continuous variable.
  • Examples include electrical signals and temperature changes over time.

• Discrete Time Signal (DTS):

  • Contains a finite set of values at specific time intervals.
  • Created through sampling, which converts continuous signals into discrete form.
  • Represented as x[n], where samples are taken at regular intervals Ts, with the sampling frequency fs being the reciprocal of Ts.

Operations on Signals

• Addition, multiplication, scaling, shifting, and folding are fundamental operations performed on signals.

Definition and Classification of Systems

• Systems can be defined in continuous and discrete domains, characterized by attributes:
  • Linear vs. Non-Linear
  • Causal vs. Non-Causal
  • Stable vs. Unstable
  • Time Variant vs. Time Invariant

Linear Time-Invariant (LTI) Systems

• A category of systems that maintain linearity and consistency over time, crucial for signal processing analysis.

Convolution and Correlation

• Fundamental operations used in signal processing to analyze and manipulate signals effectively.