Calculating time period of cos(pi/8 n*n)

In summary, the conversation is about calculating the time period of the signal cos(pi/8 n*n) and the confusion regarding the term n square. The speaker is seeking help with this question and believes that the function may not be periodic. They suggest entering it into Wolfram Alpha to view the graph and writing out the first few terms to determine the periodicity.
  • #1
tina_singh
14
0
can some one please help me calculate the time period of the signal cos(pi/8 n*n).
 
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  • #2
actually what really confuses me is the term n square..i hav solved similar questions where cos was a function of n(t in continuous time).

please help me with this question..
i will be really greatful
 
  • #3
tina_singh said:
actually what really confuses me is the term n square..i hav solved similar questions where cos was a function of n(t in continuous time).

please help me with this question..
i will be really greatful

It seems like that this function is not periodic. Enter this in wolfram alpha, check out the graph.
 
  • #4
tina_singh said:
actually what really confuses me is the term n square..i hav solved similar questions where cos was a function of n(t in continuous time).

please help me with this question..
i will be really greatful

Write out the first dozen or so terms, then the periodicity will become apparent.
 
  • #5


The time period of a signal is the amount of time it takes for one complete cycle of the signal to occur. In the case of cos(pi/8 n*n), the signal is a cosine function with a frequency of pi/8. This means that the signal will complete one cycle every 8/pi units of time.

To calculate the time period, we can use the formula T = 2*pi/f, where T is the time period and f is the frequency of the signal. In this case, the frequency is pi/8, so the time period can be calculated as:

T = 2*pi/(pi/8) = 16/pi units of time.

Therefore, the time period of the signal cos(pi/8 n*n) is 16/pi units of time.
 

1. How do you calculate the time period of cos(pi/8 n*n)?

To calculate the time period of cos(pi/8 n*n), you can use the formula T = 2π/ω, where ω is the angular frequency. In this case, ω = pi/4. Therefore, the time period would be T = 2π/(pi/4) = 8 seconds.

2. What is the significance of pi/8 in the equation for calculating the time period of cos(pi/8 n*n)?

The value of pi/8 represents the angular frequency, which is the rate at which the angle of the cosine function is changing. It determines the number of cycles that occur per unit of time.

3. Can the formula for calculating the time period of cos(pi/8 n*n) be used for other trigonometric functions?

No, the formula T = 2π/ω is specific to cosine functions. For other trigonometric functions, different formulas may be used to calculate the time period.

4. How does the value of n affect the time period of cos(pi/8 n*n)?

The value of n does not have an effect on the time period of cos(pi/8 n*n). It only affects the amplitude of the cosine function.

5. Can the time period of cos(pi/8 n*n) be negative?

No, the time period cannot be negative as it represents a measurement of time. However, the cosine function itself can take on negative values depending on the input value of n.

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