Relationship Between Signals
Given below are some Relationship between signals :
Relationship Between Step Signal u(t) and Ramp Signal r(t)
X(t) = t for t ⋿ R
X(t) u(t) = t ; for t>= 0
0 ; for t<0
so , t u(t) = r(t)
Graphically, it can be represented as
Relationship Between Step Signal u(t) and Impulse Signal δ(t)
Where sudden change or Discontinuity is present at that point Impulse signal will be present.
Expression :[Tex] \frac{d u(t)}{dt} = \space \delta(t) or \int_{z=-\infty}^{t}\delta(z)dz = \space u(t) [/Tex]
Relationship Between Step Signal u(t) and Parabolic signal p(t)
Expression :[Tex] \frac{d^2 p(t)}{dt} = \space u(t) or p(t) \space = \space \frac{t^2}{2}u(t)[/Tex]
Relationship Between Ramp Signal r(t) and Parabolic signal p(t)
Expression :
[Tex] \frac{d p(t)}{dt} = \space r(t) or \int_{z=-\infty}^{t}r(z)dz = \space p(t) [/Tex]
Standard Test Signals
The standard signals are often used in control systems, signal processing, communication and various engineering applications. These are predefined signals with known characteristics. To clarify standard test signals, their uses and application in the control systems.
In this article, we will be going through standard signals. First of all, we will discuss the basic concepts of signals, and then we will go through 4 standard test signals that are mainly used in control systems followed by definitions, mathematical expressions, representation, properties, real-life examples, and relationships between all 4 standard test signals. At last, we will conclude our article with some interesting FAQs.
Table of Content
- Signal
- Standard Test Signals
- Step Signal
- Ramp Signal
- Impulse Signal
- Parabolic Signal
- Relation-Ship Between Signals