Triangle Periodic Function: Determining f1 with Heavyside Step Functions

[BrianBrian]

Homework Statement

Consider the triangle periodic function where x=0 @ t=0; x=2 @ t=2; x=0 @ t=4; x=2 @ t=6 and x=0 @ t=8. Let f1 be the function that agrees with f on [0,4], and is zero elsewhere. Determine f1 in terms of Heavyside step functions.

Homework Equations

Determine f1 in terms of Heavyside step functions.

The Attempt at a Solution

No idea...please help??!

 

[LCKurtz]

If u(t) is the unit step (Heaviside) function and a < b, notice that

u(t-a) - u(t-b) is 1 between a and b and 0 elsewhere. Because of that, this difference is sometimes called a filter function. So if you multiply it by any function f(t), the resulting function will agree with f(t) on (a,b) and be 0 else where. So you can put a few of these together to build sections of your sawtooth function and have 0 outside of the filters.

 

[BrianBrian]

Ok. So you filter between the points where t=0 to t=4?

 

[LCKurtz]

Ok. So you filter between the points where t=0 to t=4?

I would guess that you would be expected to filter each of the 4 pieces on that range and add them up. So you need the equation of each of the four segments for the filters.