Analysis of Continuous Time Signals

Study Notes

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.

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.

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.

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

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