engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Fourier Series Properties of Fourier Series
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/are true?
1
x(t) is a real-valued signal
2
x(t) is an even signal
3
\(\frac{{dx\left( t \right)}}{{dt}}\) is an even signal
4
None of the above