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

In summary: The resulting graph would be a downward sloping line from t = 0 to t = 2, a horizontal line from t = 2 to t = 5, and a downward sloping line from t = 5 onwards.In summary, the signal (t-4)[u(t-2)-u(t-4)] is a pulse of amplitude 1 from t=2 to t=4, acting as a window over the function t-4 with a slope of 1 passing through (4,0). To sketch u(t)-2u(t-2)+u(t-5), you would sum a step of amplitude 1, starting at t=0, with a step of amplitude -2 starting at t=
  • #1
DanielleL5432
2
0
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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  • #2
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.
 
  • #3
Sketch U(t-2). Then sketch U(t-4). Now subtract the two graphically. Does that help?
 
  • #4
hello! could someone please explain to me how u(t)-2u(t-2)+u(t-5) is sketched?
 
  • #5
eleni_p said:
hello! could someone please explain to me how u(t)-2u(t-2)+u(t-5) is sketched?
+1 anyone?
 
  • #6
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.
 

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

1. What is Sketch Signal?

Sketch Signal is a mathematical function that represents a signal. It is often used in signal processing and control systems.

2. What does (t-4)[u(t-2)-u(t-4)] represent?

This function represents a signal that starts at t=4 and remains at 0 until t=2, where it jumps to 1 and stays at 1 until t=4, where it jumps back to 0. This type of signal is known as a step function.

3. How do you graph Sketch Signal?

To graph Sketch Signal, you would first plot the function (t-4) on the x-axis. Then, at t=2, the function would jump up to 1 and stay there until t=4, where it jumps back down to 0. This would create a vertical line segment connecting the points (2,1) and (4,0).

4. What are the main applications of Sketch Signal?

Sketch Signal is commonly used in signal processing and control systems, such as in the design of filters and controllers. It is also used in digital signal processing to represent discrete-time signals.

5. How is Sketch Signal related to the unit step function?

The unit step function, denoted as u(t), is defined as 1 for t≥0 and 0 for t<0. Sketch Signal is a modified version of the unit step function, with the addition of the (t-4) term which shifts the function to the right by 4 units. This allows for more flexibility in representing different types of signals.

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