Let x(t) be a periodic function with period T = 10. The Fourier series coefficients for this series are denoted by ak, that is:\(x\left( t \right) = \mathop \sum \limits_{k = - \infty }^\infty {a_k}{e^{jk\frac{{2\pi }}{T}t}}\)The same function x(t) can also be considered as a periodic function with period T′ = 40. Let \(b_k\) be the Fourier series coefficients when the period is taken as T’. If \(\mathop \sum \limits_{{\rm{k}} = - \infty }^\infty \left| {{{\rm{a}}_{\rm{k}}}} \right|=16{\rm{\;}}\), then \(\mathop \sum \limits_{{\rm{k}} = - \infty }^\infty \left| {{{\rm{b}}_{\rm{k}}}} \right|{\rm{\;}}\)is equal to

• A. 256
• B. 64
• C. 16
• D. 4