A sinusoidal carrier wave with amplitude \( A_c \) and frequency \( f_c \) is amplitude modulated with a message signal \( m(t) \) having frequency \( 0<f_m \ll f_c \) to generate the modulated wave \( s(t) \) given by \[ s(t) = A_c[1 + m(t)]\cos(2\pi f_c t) \] The message signal that can be retrieved completely using envelope detection is _________
A periodic function \( f(x) \), with period 2, is defined as \[ f(x) = \begin{cases} -1 - x & \text{for } -1 \leq x&t;0 \\ 1 - x & \text{for } 0 \leq x \leq 1 \end{cases} \] The Fourier series of this function contains _________