{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

StepFunctions

# StepFunctions - Step Functions To deal effectively with...

This preview shows pages 1–3. Sign up to view the full content.

Step Functions To deal effectively with functions having jump discontinuities, it is very helpful to introduce a function known as the unit step function or Heaviside function . This function is denoted by u c where c 0, and it is defined by: u c (t) = 0 if t < c 1 if t > c ! " # When c = 0, we have u 0 (t) = 1 Notice u 0 (t) ! u c (t) = 1 if 0 < t < c 0 if t > c " # \$

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A variety of so-called step functions can be expressed as a linear combination of unit step functions. Example : 1) f(t) = 0 if 0 < t < 3 5 if t > 3 = 5 0 if 0 < t < 3 1 if t > 3 = 5u 3 (t) ! " # ! " # 2) g(t) = 3 if 0 < t < 7 9 if t > 7 ! " # = 3 + 0 if 0 < t < 7 6 if t > 7 = 3 + 6 0 if 0 < t < 7 1 if t > 7 ! " # ! " # = 3u 0 (t) + 6u 7 (t) 3) h(t) = 0 if 0 < t < 1 2 if 1 < t < 3 1 if t > 3 = 0 if 0 < t < 1 2 if t > 1 + 0 if 0 < t < 3 ! 1 if t > 3 = " # \$ " # \$ " # % \$ % 2 0 if 0 < t < 1 1 if t > 1 ! 0 if 0 < t < 3 1 if t > 3 = " # \$ " # \$ 2u 1 (t) ! u 3 (t) 4) p(t) = 2 if 0 < t < 3 ! 3 if 3 < t < 5 6 if t > 5 = 2 " # \$ % \$ + 0 if 0 < t < 3 ! 5 if 3 < t < 5 4 if t > 5 = 2 + 0 if 0 < t < 3 ! 5 if t
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

StepFunctions - Step Functions To deal effectively with...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online