# Time Variant System: y(t) = x(-t)

• jaus tail
In summary, the conversation is discussing whether a given system is time variant or time invariant. The condition for time invariance is discussed, which involves applying a delay to the input and checking the output. The attempt at a solution involves using an example with sequences and applying the delay to both the input and the system. Ultimately, it is determined that the system is time variant based on differences in the output at different time steps.
jaus tail

## Homework Statement

Is the system: y(t) = x(-t) time variant or time invariant?

## Homework Equations

Condition for time invariant:
1) Apply delay to input and check output as Y1
2) Apply input to system without delay and apply delay to output and name it as Y2

If Y1 = Y2, system is Time invariant.

## The Attempt at a Solution

We have y(t) = x(-t)
So I tried with example:
T -3 -2 -1 0 1 2 3
x(t) 1 2 3 4 5 6 7
y(t) 7 6 5 4 3 2 1

At time t = 2
First apply delay to input.
Delay of 1
So time becomes 1
x(1) = 5
y(1) = x(-1) = 3-----equation 1

Now at time t = 2
Apply this to system
y(2) = x(-2) = 2
Apply delay of 1
y(1) = 3-----equation 2

Equation 1 and equation 2 are same.
So this is time invariant.
Book says it's time variant equation.
How?

If I go by red line (first delay and then system)
or if I go by blue line (first system and then delay) I get same answer,
so how is this time variant?

#### Attachments

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jaus tail said:

## Homework Statement

Is the system: y(t) = x(-t) time variant or time invariant?

## Homework Equations

Condition for time invariant:
1) Apply delay to input and check output as Y1
2) Apply input to system without delay and apply delay to output and name it as Y2

If Y1 = Y2, system is Time invariant.

## The Attempt at a Solution

We have y(t) = x(-t)
So I tried with example:
T -3 -2 -1 0 1 2 3
x(t) 1 2 3 4 5 6 7
y(t) 7 6 5 4 3 2 1

At time t = 2
First apply delay to input.
Delay of 1
So time becomes 1
x(1) = 5
y(1) = x(-1) = 3-----equation 1

Now at time t = 2
Apply this to system
y(2) = x(-2) = 2
Apply delay of 1
y(1) = 3-----equation 2

Equation 1 and equation 2 are same.
So this is time invariant.
Book says it's time variant equation.
How?

View attachment 219783
If I go by red line (first delay and then system)
or if I go by blue line (first system and then delay) I get same answer,
so how is this time variant?
I don't quite follow your logic with the red and blue arrows.

Code:
T       -3    -2     -1     0      1      2      3
x(t)     1     2      3     4      5      6      7
y(t)     7     6      5     4      3      2      1

Delay the "y(t)" above to obtain your Y2

Now write out x(t-1).

Then write out y(t-1) based on what you just did with x(t-1). From that you have your Y1.

At this point, compare your Y1 to Y2.

Okay. Let's take time = 3.
Apply x(3) to system.
We get output:
y(3) = 1
Delay it by 1 to get y(2) and we get 2.

Now delay time. So t = 3 - 1 = 2.
Apply x(2) to system and we get output:
y(2) = 2.
They still turn out to be same.

jaus tail said:
Okay. Let's take time = 3.
Apply x(3) to system.
We get output:
y(3) = 1
Delay it by 1 to get y(2) and we get 2.

Now delay time. So t = 3 - 1 = 2.
Apply x(2) to system and we get output:
y(2) = 2.
They still turn out to be same.

Code:
T      -3  -2  -1   0   1   2   3
x(t)    1   2   3   4   5   6   7
x(t-1)  0   1   2   3   4   5   6

Now what's y(t-1)?

jaus tail

Is this right? I'm still not sure.
Row 4 and 6 are different so it's time variant.

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jaus tail said:
View attachment 219860
Is this right? I'm still not sure.
Row 4 and 6 are different so it's time variant.
Yeah, I think that's the right idea.

(For what it's worth, I appreciate the confusion though. Personally, I think this problem is a little ambiguous in what is actually meant by "y(t) = x(-t)" and exactly how that is accomplished in the system. That said, demonstrating that rows 4 and 6 are different is probably what your instructor/coursework is expecting.)

jaus tail
The coursework actually requires using x(t)--->y(t)---->y(t-to)
and then x(t)---> replace all t by t-t0 and then find out y(t-to)
Even google suggested replacing t by t-t0 in which I never understood how the minus sign spreads.
That's why I prefer the above method of making rows and columns.

## 1. What is a Time Variant System?

A Time Variant System is a type of system in which the output is dependent on the input at different times. This means that the output of the system will change over time, even if the input remains the same.

## 2. How is a Time Variant System different from a Time Invariant System?

A Time Variant System is different from a Time Invariant System in that the output of a Time Invariant System remains constant over time, regardless of changes in the input. This is not the case for a Time Variant System, as the output will vary based on the input at different times.

## 3. What is the significance of the equation y(t) = x(-t) in a Time Variant System?

The equation y(t) = x(-t) represents a Time Variant System, where the output at time t is equal to the input at time -t. This means that the output is dependent on the input at a different time, making it a Time Variant System.

## 4. How can a Time Variant System affect a scientific experiment?

A Time Variant System can affect a scientific experiment by introducing variability in the output, making it difficult to accurately measure and analyze the results. This can lead to inconsistencies and uncertainties in the findings of the experiment.

## 5. Are there any practical applications of Time Variant Systems?

Yes, Time Variant Systems have various practical applications in fields such as signal processing, control systems, and communication systems. They are also commonly used in modeling and analyzing real-world phenomena that are subject to changes over time.

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