Step Signal:
- A step signal represents an instantaneous change from one value to another. It jumps from zero to a constant value at a specific time (usually
).
- Mathematical representation:
for
, and
for
, where
is a constant.
- Applications: Step signals are used to test the transient response of systems (how quickly a system reacts to sudden changes).
Example: A switch that turns on a light instantly at .
Ramp Signal:
- A ramp signal is a steadily increasing linear signal that starts at zero and increases linearly over time.
- Mathematical representation:
for
, and
for
, where
is the slope of the ramp.
- Applications: Ramp signals model systems that experience constant acceleration or uniformly increasing values (e.g., charging a capacitor).
Example: A vehicle that accelerates steadily over time.
Impulse Signal:
- An impulse signal (also called Dirac delta function) represents an idealized signal that occurs at a single instant of time with infinite amplitude and zero duration, but with a finite area under the curve.
- Mathematical representation:
is zero everywhere except at
, where it is infinitely high, and its integral is 1.
- Applications: Used to test system behaviour by analysing the system’s response to a sudden input.
Example: A brief spike of energy, such as a lightning strike.
Sinusoidal Signal:
- A sinusoidal signal is a smooth periodic oscillation that can represent many physical systems, especially in AC power systems and communications.
- Mathematical representation:
, where
is amplitude,
is angular frequency, and
is phase.
- Applications: Common in alternating current (AC) circuits, wave propagation, and signal modulation in communication systems.
Example: The voltage of a standard AC power supply oscillates sinusoidally over time.
Square Signal:
- A square signal alternates between two levels (usually high and low) with a 50% duty cycle, producing a periodic, non-sinusoidal waveform.
- Mathematical representation:
switches between
and
at regular intervals.
- Applications: Widely used in digital electronics and pulse-width modulation (PWM) for signal processing.
Example: A digital clock signal, switching between 0 and 1.
Sawtooth Signal:
- A sawtooth signal rises linearly over time and then sharply drops to its initial value, creating a shape resembling the teeth of a saw.
- Mathematical representation:
- The signal increases linearly and resets after a period.
- Applications: Commonly used in audio synthesizers, signal generators, and timing circuits.
Example: The scanning signal in analog televisions or oscilloscopes.
Comparison of Signals:
| Signal | Shape | Characteristics | Applications |
| Step | Sudden jump from 0 to a constant value | Instantaneous change | System response testing |
| Ramp | Linear increase over time | Continuous growth | Acceleration modeling |
| Impulse | Sharp spike at | Infinitely high at one point | Testing system responses |
| Sinusoidal | Smooth oscillations | Periodic and continuous | AC power, communication signals |
| Square | Alternates between two levels | Sudden changes, periodic | Digital signals, PWM |
| Sawtooth | Linear rise, sudden drop | Periodic, non-smooth | Audio synthesis, signal generation |