I have trouble solving the following question related to signals and systems, and I need to plot its graph:

(2t/5) * [u(t) - u(t-6)]

The tools provide a solution, but I want to understand the logic behind how it is plotted.

If anyone knows and can help, it would be greatly appreciated.


thanks..

 

I don't recognize this formula. It might help a lot if you defined the two variables and describe the function of the formula.

 

I don't recognize this formula. It might help a lot if you defined the two variables and describe the function of the formula.

this m(t) function is actually a mathematical expression of the unit digit function. and the graph of this is drawn according to this equation. but I'm trying to learn your logic

 

That is purely theoretical mathematics. That's not my speciality but I am sure someone here can help.

 

That is purely theoretical mathematics. That's not my speciality but I am sure someone here can help.

thank u for your concern

 

Not my speciality either but most of the signals and systems transformations have their origin in the: Heaviside step function

This is a good history other than the stupid, Tesla invented radio (the radio part of the EM spectrum was discovered, not by Tesla), comments. Heaviside was the real genius.

 

how is u(t) defined?

 

u(t) is the unit step function. It is 0 for t < 0 and 1 for t ≥ 0
By analogy u(t-6) is 0 for t - 6 < 0, and 1 for t - 6 ≥ 0, so it is a translated version of u(t).

 

u(t) is the unit step function. It is 0 for t < 0 and 1 for t ≥ 0
By analogy u(t-6) is 0 for t - 6 < 0, and 1 for t - 6 ≥ 0, so it is a translated version of u(t).

how do we express the expression 2t/5 when drawing a graph? can you draw and show this with pencil and paper

 

how do we express the expression 2t/5 when drawing a graph? can you draw and show this with pencil and paper

would it help to write:

\( \cfrac{2t}{5},\text{ as }0.4t \)

 

would it help to write:

\( \cfrac{2t}{5},\text{ as }0.4t \)

unfortunately, I didn't quite understand

 

So u(t)-u(t-6) must be a pulse of length 6.
multiplying it by t makes it into a sawtooth ramp.

 

So u(t)-u(t-6) must be a pulse of length 6.
multiplying it by t makes it into a sawtooth ramp.

hmm, I understand you now. when multiplied by t, it becomes a gear, but what about if there were 3 [u(t) - u(t-6)], would there be gears again? or how would it be?

 

hmm, I understand you now. when multiplied by t, it becomes a gear, but what about if there were 3 [u(t) - u(t-6)], would there be gears again? or how would it be?

Wouldn't that just be a rectangular pulse of height 3 and length 6?

 

unfortunately, I didn't quite understand

You don't understand that

\( \cfrac{2}{5}\;=\;0.4 \)

That's just a bit hard to believe.

 

u(t) - u(t-6) is impulse with amplitude 1 and length(duration) 6.
If you multiply the amplitude with 0.4... you get a pulse with amplitude ____ (fill the blank) and duration ____ (fill the blank).

I dont understand what you mean by gear.

 

u(t) - u(t-6) is impulse with amplitude 1 and length(duration) 6.
If you multiply the amplitude with 0.4... you get a pulse with amplitude ____ (fill the blank) and duration ____ (fill the blank).

I dont understand what you mean by gear.

I think he means sawtooth. That particular profile on an actual gear would male pretty crappy one at that.

 

See

 

You are right.. I focused on:

And I did not notice it also multiplies with t before the brackets.

so you have a linear function 0.4t with length of 6.

 

See
View attachment 345496

thank you so much, now I can understand and see some things better. your help is honored!