Question 1
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Pass Ratio : 100%
What is the spectrum that is obtained when we plot |ck |2 as a function of frequencies kF0, k=0,±1,±2..?
Explanation: When we plot a graph of |ck|2 as a function of frequencies kF0, k=0,±1,±2… the following spectrum is obtained which is known as Power density spectrum.
Question 3
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The Fourier series representation of any signal x(t) is defined as ___________
Explanation: If the given signal is x(t) and F0 is the reciprocal of the time period of the signal and ck is the Fourier coefficient then the Fourier series representation of x(t) is given as \\(\\sum_{k=-\\infty}^{\\infty}c_k e^{j2Ï€kF_0 t}\\).
Question 4
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The equation of average power of a periodic signal x(t) is given as ___________
Explanation: The average power of a periodic signal x(t) is given as
Question 5
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What is the spectrum that is obtained when we plot |ck| as a function of frequency?
Explanation: We know that, Fourier series coefficients are complex valued, so we can represent ck in the following way.
Question 6
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Which of the following is the equation for the Fourier series coefficient?
Explanation: When we apply integration to the definition of Fourier series representation, we get
Question 7
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What is the equation of the Fourier series coefficient ck of an non-periodic signal?
Explanation: We know that, for an periodic signal, the Fourier series coefficient is
Question 8
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Which of the following is a Dirichlet condition with respect to the signal x(t)?
Explanation: For any signal x(t) to be represented as Fourier series, it should satisfy the Dirichlet conditions which are x(t) has a finite number of discontinuities in any period, x(t) has finite number of maxima and minima during any period and x(t) is absolutely integrable in any period.
Question 9
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Pass Ratio : 100%
Which of the following is the Fourier series representation of the signal x(t)?
Explanation: In general, Fourier coefficients ck are complex valued. Moreover, it is easily shown that if the periodic signal is real, ck and c-k are complex conjugates. As a result