engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Fourier Series Forms of Fourier Series
Let f(x) be a real, periodic function satisfying f(-x) = -f(x). The general form of its Fourier series representation would be
1
\(f\left( x \right) = {a_0} + \mathop \sum \limits_{k = 1}^\infty {a_k}\cos \left( {kx} \right)\)
2
\(f\left( x \right) = \mathop \sum \limits_{k = 1}^\infty {b_k}\sin \left( {kx} \right)\)
3
\(f\left( x \right) = {a_0} + \mathop \sum \limits_{k = 1}^\infty {a_{2k}}\cos \left( {kx} \right)\)
4
\(f\left( x \right) = \mathop \sum \limits_{k = 0}^\infty {a_{2k}} + \sin \left( {2k + 1} \right)x\)