engineering recuitment GATE EE 2023-24 Test Series Signals and Systems Fourier Series Definition of Fourier Series
Signal \({\rm{x}}\left( {\rm{t}} \right)\) has following information given about it.
1) \({\rm{x}}\left( {\rm{t}} \right)\) is real and odd.
2) \({\rm{x}}\left( {\rm{t}} \right)\) is periodic with period \({\rm{T}} = 2\) and Fourier coefficients \({{\rm{a}}_{\rm{k}}}\) .
3) \({{\rm{a}}_{\rm{k}}} = 0{\rm{\;for\;}}\left| {\rm{k}} \right| > 1\)
4) \(\frac{1}{2}\mathop \smallint \limits_0^2 {\left| {{\rm{x}}\left( {\rm{t}} \right)} \right|^2}{\rm{dt}} = 1\)
Then the value of \(\left| {{{\rm{a}}_{ - 1}}} \right|\) is _______.
Enter numerical value using the virtual keypad. Round off where necessary.