BeginnerTopic 6 of 101Signals, Control & Comms
Basic signals
Impulse, step, ramp, exponential and sinusoid are the building blocks of analysis.
In depth
Building blocks: unit impulse δ(t) (infinite spike with unit area), unit step u(t), ramp r(t)=t·u(t), rectangular pulse, real exponential e^{at}, complex exponential e^{jωt} and sinusoids. Arbitrary signals are sums or integrals of these; system response to them characterises behaviour.
Key points
- Sifting property of δ
- u(t) is integral of δ
- Sinc function
ExampleThe step response of a system is its reaction to a switch-on.
What is Basic signals?
Impulse, step, ramp, exponential and sinusoid are the building blocks of analysis.
Why is it important to understand basic signals?
These basic signals are the building blocks from which almost any input can be built, so they are used as standard test inputs.
What is the unit impulse?
A signal that is zero everywhere except at the origin, where it has unit area, and it is the idealised input for a short kick.
Why do engineers use the step so often?
It shows how a system reacts to a sudden change, which reveals speed, overshoot and settling in a single test.
How is Basic signals used in practice?
Typical applications include using a step input to test the response of a motor speed controller, applying an impulse to measure the ringing of a structure and using a ramp to check how a tracking system follows a steady change.
What should I learn before Basic signals?
Study "Energy and power signals" first (topic 5 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Basic signals?
Sifting property of δ. u(t) is integral of δ. Sinc function.
Can you give an example of Basic signals?
The step response of a system is its reaction to a switch-on.
What comes after Basic signals?
The next topic is "Signal operations", which builds directly on this one.
How difficult is Basic signals?
It is classed as Beginner in Signals, Control & Comms (topic 6 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.