Consider the 2π-periodic signal x(t) de- fined as For small A, x(t) looks like a square wave; as A → π, x(t) resembles a type of sawtooth wave. (a) Determine the Fourier series X k for signal x(t)....

For small A, x(t) looks like a square wave; as A → π, x(t) resembles a type of sawtooth wave.

(a) Determine the Fourier series X_k
for signal x(t). Sketch the corresponding magnitude and phase spectra.

Next, synthesize x(t) using a truncated Fourier series xK(t), as given in Eq. (1.61). Using the following parameters, accurately plot xK(t) and comment on the approximation, with particular attention to Gibbs phenomenon.

(a) A = π/2 and K = 20

(b) A = π/2 and K = 100

(c) A = π/64 and K = 20

(d) A = π/64 and K = 100