Linear Signals & Systems: Time Shift/Scale

Thread Starter


Joined Jan 22, 2016
Okay, so my teacher has been super theoretical in his explanations about time functions, and he didn't work any example problems that pertained to scaling time functions. This homework is due on Monday. I've given it my best shot thus far, and I'd like some feedback on a few problems. I've attached links to the assignment and to my work.

From what I've gathered there's a definite order of operations regarding these problems. Please tell me if this is correct or not.
1) Shift
2) Scale
3) Apply the sign of the scale (if it is negative, reflect across the y axis)

Problem 3 (b):
Here, I pulled a (-1) out from the (2-t), giving me (-1)(t-2). On this step, I don't know whether or not I should factor out the (-1). If I factor it out, I shift right, and then flip the function across the y-axis. If I don't, I'll shift left and then flip across the y-axis. Is factoring out the -1 the wise thing to do here?

Problem 3 (c):
Here, I shifted the function left one, and applied the coefficient of t which is 2. To the best of my understanding this effectively halves all values of t0.

Problem 3 (d):
I am aware of what a delta function is to a certain extent. I know that it has a value of 0 at all values of t other than t0 at which it will have a value of 1 multiplied by the value of x(t) at that t0. If I applied the function, would I graph two impulses, one at t=-3/2 where y(t) = 1, and the other at t=3/2?

I am interested in fully understanding how to do this, not just getting the right answers on my homework. If anyone could point me in the direction of a learning source for this material, it would be greatly appreciated.

Thanks in advance!

Links to my solutions and the assigned work:


Joined Nov 13, 2010
Your definition of the delta (or impulse) function seems to be giving some trouble. For discrete time systems the delta function (also called Kronecker delta) equals 1 at t equal to zero, and equals zero at t not equal to zero. But for continuous time systems, which seems to be the case here, delta(0)=infinity while being zero otherwise. The step function is the integral of the delta, the ramp function is the integral of the step.

For time shifting, just realize what happens with the function at t=0. If you need that to happen sooner (before t=0), then add a time shift (t+a). If you need it to happen later (after t=0), then subtract a time shift (t-a).

When the function you are trying to construct has a vertical jump in amplitude, you need to add a step function at that point. When the function has a change in slope, add a ramp at that point. Some points in the construction may need both a step and a ramp.

Scaling just means adjusting the amplitude of the unit step or unit ramp. Have no idea what you mean by factoring and flipping. (Unless flipping means making the function amplitude negative?)