Mathematical Solution for Unit Time Step Signal with Plotted Coordinates

In summary, the conversation is about solving the unit time step equation using mathematical methods and plotted signals. The approach described involves identifying important times and plotting the individual step functions on a time axis to see how they will sum up. The result should be a signal that varies with time.
  • #1
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Homework Statement




Solvinf the unit time step equation mathematically.

Homework Equations




x(t) = u(t+1) - 2u(t) + u(t-1)

The Attempt at a Solution



How can i solve this signal mathemtically :( and using plotted signals , i couldn't understand,

here is my approach and I'm not sure it is correct,

i simply wrote the coordiantes of each signal,

u(t+1) = (-1,1)

-2ut = (0,-2)

u(t-1) = (1,1)

and then added them which give answer = '0' :(

is this the way of solving the signals ?
please help
 
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  • #2
The result should be a signal that varies with time. You've identified the important times where "interesting things" take place -- the various unit step functions change value at these times.

If you were to draw several time axes stacked one over the other and plot the individual step functions, one per time axis, you might be able to see how the functions will sum up.
 

1. What is a unit time step signal?

A unit time step signal is a mathematical representation of a signal that starts at zero and increases by one unit at a specific time interval. It is often used in signal processing and control systems to simulate a step change in a system.

2. What are plotted coordinates in the context of a unit time step signal?

Plotted coordinates refer to the graphical representation of a unit time step signal. The x-axis represents time, and the y-axis represents the amplitude of the signal at that specific time. The coordinates are plotted as discrete points, with the value of the signal increasing by one unit at each time interval.

3. How is a unit time step signal with plotted coordinates solved mathematically?

A unit time step signal with plotted coordinates is typically solved using the Heaviside step function. This function is defined as 0 for negative values and 1 for positive values. By multiplying this function with the desired amplitude of the signal, the unit time step signal with plotted coordinates can be obtained mathematically.

4. What is the importance of using a unit time step signal with plotted coordinates in mathematical solutions?

A unit time step signal with plotted coordinates is a useful tool in mathematical solutions as it allows for the simulation of a step change in a system. This can help in understanding and predicting the behavior of a system in response to a sudden change. It is also an important concept in digital signal processing and control systems.

5. Are there any limitations to using a unit time step signal with plotted coordinates in mathematical solutions?

While a unit time step signal with plotted coordinates is a useful tool, it is not always a perfect representation of real-world systems. In some cases, the sudden step change may not accurately reflect the gradual changes that occur in a system. Additionally, the signal may not always be applicable to systems with nonlinear behavior.

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