[Signals and Systems] What's the signinfance of negative time?

In summary, the conversation discusses the physical significance of representing signals in negative time, particularly in terms of practical usage and mathematical calculations. Negative time can be useful for setting up a reference frame and distinguishing regions of interest in a system. It also has a notable effect in the frequency domain, taking the conjugate of signal phase vectors.
  • #1
snshusat161
214
1
Hello all,
This one thought came to my mind just now. What's the physical significance of signal representation in negative time, i mean second and third quadrant.

So for example, sin(t) and sin(t).u(t) aren't they same for all practical purposes?

I know, mathematically they are different. But I'm trying to visualize the difference in terms of practical usage.
 
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  • #2
Not sure if this is along the lines of what you are asking.
But when we covered this material the prof mentioned that while you can physically have negative time in a system (obviously) but the inclusion of negative time made the calculations of much of the math vastly easier.
 
  • #3
It is useful for setting up a reference frame for looking at the impulse response of your system. The negative time could represent anything transient which has occurred before a time frame of interest. the step function u(t) multiplied by a function makes everything before equal to zero allowing the system's reference frame to begin, you can easily delay when this occurs by looking at u(t-delay) by some delayed period. It is pretty much a convention to distinguish regions which we care about and it represents that the system is causal and done not depend on past inputs which is a requirement for many systems.
 
  • #4
Representing a signal in negative time, reversed time order, has a simple elegant effect in the frequency domain.
It takes the conjugate of the signal phase vectors.
 
  • #5


The concept of negative time in signal and system representation is a fundamental aspect of understanding and analyzing various physical phenomena. It allows us to represent and study the behavior of systems and signals over a wide range of time, not just in the present or future, but also in the past.

One of the main significance of negative time is its application in modeling and analyzing systems that exhibit memory. This means that the output of a system at any given time depends not only on the present input, but also on past inputs. By representing signals in negative time, we can capture this memory aspect and better understand the behavior of these systems.

Moreover, negative time also allows us to study the behavior of signals and systems in the time domain, which is essential for practical applications such as signal processing and control systems. This is because many physical systems exhibit behavior that is time-varying, and by representing signals in negative time, we can analyze and manipulate them in a more comprehensive manner.

Furthermore, negative time also has applications in communication systems, where signals can travel in both forward and backward directions. By representing signals in negative time, we can study their propagation and interactions in a more complete way.

In conclusion, the significance of negative time in signal and system representation lies in its ability to capture the memory aspect of systems, study time-varying behavior, and analyze the propagation and interactions of signals. It is a crucial concept in the field of signal and system analysis and has numerous practical applications in various fields of science and engineering.
 

1. What is negative time in signals and systems?

Negative time refers to the time before a specific event or starting point. In signals and systems, it is used to describe the behavior and characteristics of a system or signal before the starting point or initial condition.

2. Why is negative time important in signals and systems?

Negative time allows us to analyze and understand the behavior of a system or signal before a specific event or starting point. This information is crucial in predicting and controlling the behavior of a system, and can also help in identifying any potential issues or errors.

3. How is negative time represented in signals and systems?

Negative time is typically represented by using a negative sign (-) in front of the time variable. For example, if the starting point is t = 0, then negative time would be represented as t = -1, t = -2, and so on.

4. Can negative time have physical significance in signals and systems?

In some cases, negative time can have physical significance in signals and systems. For example, in electronic circuits, negative time can represent the time it takes for a signal to reach the output after a change in the input. However, in most cases, negative time is used as a mathematical concept to understand and analyze systems and signals.

5. How is negative time related to causality in signals and systems?

Negative time is closely related to causality in signals and systems. A system or signal is considered causal if the output depends only on the present and past inputs, not on future inputs. Negative time allows us to analyze the behavior of a system or signal before the present moment, which is important in determining causality.

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