Expression as an Integral
The unit ramp function is the integral of the unit step function μ(t), so can be expressed as the following integral:
The unit ramp function can also be obtained by integrating the unit impulse function twice.
Values of the Unit Ramp Function
The function can be expressed mathematically as:
Or, alternatively, by angles. The unit ramp is horizontal with one shift (in an anticlockwise direction) at t = 0 where the function takes on a 45 degree angle to infinity (Singh et. al, 2013).
Shifted Unit Ramp Function
The unit ramp function usually starts at zero. However, it can also shift along the x-axis (in the positive direction). This function is called a delayed ramp function, because of the delay in the start time, at t = a. The function’s values will obviously not be zero, as in the above definition. Instead, the shifted unit ramp is defined as (Bakshi, 2009):
- f(t) = (t – a), for t ≥ a
- f(t) = 0, for t < a.
Bakshi, U. (2009). Circuit Theory. Technical Publications Pune.
Singh, S. (2013). Proof of Sp’s… Ramp Function with the Help of Examples. International Journal of Engineering and Innovative Technology (IJEIT) Volume 2, Issue 7, January 2013
Stephanie Glen. "Unit Ramp Function" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/unit-ramp-function/
Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!
Comments? Need to post a correction? Please Contact Us.