Signals and Sys...

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:

What is the exponential Fourier series coefficient of x(t) = cos² 8t + sin² 4t

Consider a real-valued function f(t) such that \(f\left( t+2\pi \right)=f\left( t \right)\) for all t ≥ 0. Such a signal f(t) can be represented as

\(f\left( t \right)=\frac{{{a}_{0}}}{2}+\underset{n=1}{\overset{\infty }{\mathop \sum }}\,\left[ {{a}_{n}}\cos \left( nt \right)+{{b}_{n}}\sin \left( nt \right) \right]\)

If f(t) = cos (3t) + sin (4t), then the coefficient a₄ in the summation series, as indicated above is

For the given Fourier series co-efficient x[k] = j δ [k - 1] – j δ [k + 1] + δ [k - 3] + δ [k + 3] and ω₀ = 4π, find the time domain signal.