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The complex exponential Fourier series representation of a signal f(t) over the interval (0,T) is
Find the sum of component of f(t) at n = 3 and n = -3
- a)0.084
- b)0.024
- c)0.064
- d)0.014
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The complex exponential Fourier series representation of a signal f(t...
To find the sum of the components of f(t) at n = 3 and n = -3 in the complex exponential Fourier series representation, we need to determine the Fourier coefficients for these values of n and calculate the sum.
The complex exponential Fourier series representation of a signal f(t) over the interval (0,T) is given by:
f(t) = ∑[cn * e^(j*n*ω0*t)]
Where:
- f(t) is the signal
- cn is the Fourier coefficient for each value of n
- e is the base of the natural logarithm
- j is the imaginary unit (√(-1))
- ω0 is the fundamental angular frequency (ω0 = 2π/T)
- t is the time variable
To find the Fourier coefficient cn, we can use the formula:
cn = (1/T) * ∫[f(t) * e^(-j*n*ω0*t) dt] from t = 0 to T
For n = 3:
cn = (1/T) * ∫[f(t) * e^(-j*3*ω0*t) dt] from t = 0 to T
Similarly, for n = -3:
cn = (1/T) * ∫[f(t) * e^(j*3*ω0*t) dt] from t = 0 to T
Once we have obtained the Fourier coefficients, we can calculate the sum of the components:
Sum = c3 + c(-3)
Let's evaluate the integrals and calculate the sum.
The complex exponential Fourier series representation of a signal f(t) over the interval (0,T) is given by:
f(t) = ∑[cn * e^(j*n*ω0*t)]
Where:
- f(t) is the signal
- cn is the Fourier coefficient for each value of n
- e is the base of the natural logarithm
- j is the imaginary unit (√(-1))
- ω0 is the fundamental angular frequency (ω0 = 2π/T)
- t is the time variable
To find the Fourier coefficient cn, we can use the formula:
cn = (1/T) * ∫[f(t) * e^(-j*n*ω0*t) dt] from t = 0 to T
For n = 3:
cn = (1/T) * ∫[f(t) * e^(-j*3*ω0*t) dt] from t = 0 to T
Similarly, for n = -3:
cn = (1/T) * ∫[f(t) * e^(j*3*ω0*t) dt] from t = 0 to T
Once we have obtained the Fourier coefficients, we can calculate the sum of the components:
Sum = c3 + c(-3)
Let's evaluate the integrals and calculate the sum.
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Community Answer
The complex exponential Fourier series representation of a signal f(t...
Comparing the given with the standard form
From the given from A cos nω0t
∴ n = 3
Component of f(t) at n = 3
Similarly when n = –3
Adding (1) and (2)
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