Power/Energy Signal Homework: u[n] - u[n-4]

In summary, the conversation was about determining whether the signal u[n] - u[n-4] is a power or energy signal. The formula |u[n] - u[n-4]|2 was mentioned as a way to determine this. After some discussion and calculations, it was concluded that u[n] - u[n-4] is an energy signal with an energy value of 4. The significance of the value 4 was also explained.
  • #1
smart_worker
131
1

Homework Statement


Determine whether u[n] - u[n-4] is a power or energy signal.

Homework Equations


form.PNG


The Attempt at a Solution


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I am stuck here. I don't know how to simply further. Please help.
 
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  • #2
You could tell by inspection based on the definitions of "energy signal" and "power signal". If you want to use that formula, what can you say about the equivalence of u[n] - u[n-4] and |u[n] - u[n-4]|2 ?
 
  • #3
lewando said:
You could tell by inspection based on the definitions of "energy signal" and "power signal". If you want to use that formula, what can you say about the equivalence of u[n] - u[n-4] and |u[n] - u[n-4]|2 ?

I think u[n] - u[n-4] = 1 for n=0,1,2,3 and 0 elsewhere.
So, Ex becomes 4. So, it's an Energy Signal. Am I right?
 
  • #4
smart_worker said:
I think u[n] - u[n-4] = 1 for n=0,1,2,3 and 0 elsewhere.
So, Ex becomes 4.
That is exactly right.
So, it's an Energy Signal.
You might want to indicate (for others who might want to follow your logic) what is so special about "4" that leads you to classify the signal as you have. What if the result was "5"?
 

1. What is a power signal?

A power signal is a type of signal that has a finite power value, meaning that the energy of the signal is spread over an infinite period of time. It is represented by the formula P = lim T->∞ (1/T ∫ |x(t)|² dt), where P is the power value and T is the length of the signal. A common example of a power signal is an alternating current (AC) signal.

2. What is an energy signal?

An energy signal is a type of signal that has a finite energy value, meaning that the signal has a finite duration and the energy is concentrated within that duration. It is represented by the formula E = ∫ |x(t)|² dt, where E is the energy value and t is the time variable. A common example of an energy signal is a pulse signal.

3. What does the notation u[n] - u[n-4] represent?

The notation u[n] - u[n-4] represents a discrete signal that is equal to 0 for n < 0, 1 for 0 ≤ n < 4, and 0 for n ≥ 4. In other words, it is a unit step function that is delayed by 4 units.

4. How do you calculate the power and energy values of u[n] - u[n-4]?

To calculate the power value, we can use the formula P = lim N->∞ (1/N ∑ |x[n]|²), where N is the length of the signal. In this case, the length is 4, so the power value will be 1/4. To calculate the energy value, we can use the formula E = ∑ |x[n]|², where n ranges from -∞ to ∞. In this case, the energy value will be 4.

5. What is the significance of the signal u[n] - u[n-4]?

The signal u[n] - u[n-4] has a finite power and energy value, making it a power and energy signal. It is a commonly used signal in signal processing and is often used as a test signal in systems analysis. It is also used in the analysis of linear systems and control systems.

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