Sketch Signal: (t-4)[u(t-2)-u(t-4)]

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Discussion Overview

The discussion revolves around how to sketch the signal (t-4)[u(t-2)-u(t-4)], focusing on the interpretation of the components involved, particularly the effects of the ramp function (t-4) and the unit step functions (u(t-2) and u(t-4)). The scope includes conceptual understanding and graphical representation of the signal.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants note that (t-4) represents a ramp function with a slope of 1, starting from the point (4,0).
  • Others explain that u(t-2) - u(t-4) creates a pulse of amplitude 1 that extends from t=2 to t=4, acting as a window over the ramp function (t-4).
  • One participant suggests sketching u(t-2) and u(t-4) separately and then subtracting them graphically to aid in understanding the overall signal.
  • Another participant introduces a different question about sketching the signal u(t) - 2u(t-2) + u(t-5), seeking clarification on that topic.
  • A later reply provides a method for sketching the latter signal by summing step functions with specified amplitudes and starting points.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the original signal, with some clarity on the components but no consensus on the overall sketching process. The discussion remains unresolved as different approaches and interpretations are presented.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the ramp and pulse functions, as well as the lack of detailed mathematical steps for sketching the signals.

DanielleL5432
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The question says to sketch the signal (t-4)[u(t-2)-u(t-4)].
I know that the inner part is a delay of two and a delay of four, but I don't know what to do with the (t-4)...does it have anything to do with the slope?
 
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DanielleL5432 said:
The question says to sketch the signal (t-4)[u(t-2)-u(t-4)].
I know that the inner part is a delay of two and a delay of four, but I don't know what to do with the (t-4)...does it have anything to do with the slope?

t-4 is a ramp with slope 1 passing by the point (4,0).
u(t-2)-u(t-4) is a pulse of amplitude 1 extending from t=2 to t=4. It acts as a window over the function t-4.
 
Sketch U(t-2). Then sketch U(t-4). Now subtract the two graphically. Does that help?
 
hello! could someone please explain to me how u(t)-2u(t-2)+u(t-5) is sketched?
 
eleni_p said:
hello! could someone please explain to me how u(t)-2u(t-2)+u(t-5) is sketched?
+1 anyone?
 
You should sum a step of amplitude 1, starting at t = 0, with a step of amplitude -2 starting at t = 2 and a step of amplitude 1 starting at t = 5.
 

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