Question
Download Solution PDFIntegration of unit ramp function gives
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFRamp input:
It is a standard input signal that consists of a constant rate of change in input.
The ramp is a signal, which starts at a value of zero and increases linearly with time
\(r\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {At;t \ge 0}\\ {0;else\;where} \end{array}} \right.\)
If amplitude A=1, it is called Unit Ramp Input.
The integration of the unit ramp is a parabolic signal
\(p\left( t \right) = \smallint t\;dt = \frac{{{t^2}}}{2}\)
A parabolic signal is expressed as
\(p\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{{t^2}}}{2};t \ge 0}\\ {0;else\;where} \end{array}} \right.\)
Important points:
|
Standard signal functions |
Integral of standard signal |
|---|---|
|
Impulse function - δ(t) |
Step function - u(t) |
|
Step function - u(t) |
Ramp function - r(t) |
|
Ramp function - r(t) |
Parabolic function - p(t) |
Last updated on Mar 26, 2025
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