Signals and Sys...

The Fourier series coefficient for the periodic signal x(t) = sin²t is

The Fourier series coefficient of signal x(t) is c_k­, then the Fourier series coefficient of the signal x(0.5t) + x(t – 0.5) + x(2t) will be:

Consider a periodic signal x[n] with period N and Fourier series coefficients c_k. The Fourier Series coefficients d_k of the signal y[n] = (-1)ⁿ x[n] will be:

What is the amplitude of the second harmonic component of the signal x(t) given below?

\(x\left( t \right) = \cos \left( {\frac{{2\pi }}{3}t} \right) + 2\cos \left( {\frac{{5\pi }}{3}t} \right)\)

Consider a real periodic signal x[n] with period N and FS coefficient c_k. If N is even then which of the following statements is true?

Consider a periodic signal x(t) whose Fourier series coefficient is defined as below

\({c_n} = \left\{ {\begin{array}{*{20}{c}} {2\;\;\;\;\;\;\;\;,\;\;\;\;\;\;\;\;n = 0}\\ {j{{\left( {\frac{1}{2}} \right)}^{\left| n \right|}},\;\;\;otherwise} \end{array}} \right.\)

Which of the following is true?