The following problems relate to the periodicity of signals: (a) Determine the frequency 0 in rad/sec,

The following problems relate to the periodicity of signals:

(a) Determine the frequency Ω_­0 in rad/sec, the corresponding frequency f₀ in Hz, and the fundamental period T₀ sec of these signals defined in −∞< t< ∞,

(i) cos(2πt),                

(ii) sin(t –π/4),           

(iii) tan(πt)

(b) Find the fundamental period Tof z(t) =1 + sin(t) + sin(3t), −∞ < t < ∞.

(c) If x(t) is periodic of fundamental period T₀ = 1, determine the fundamental period of the following signals

(i) y(t) = 2 + x(t),       

(ii) w(t) = x(2t),           

(iii) v(t) = 1/x(t)

(d) What is the fundamental frequency f₀, in Hz, of

(i) x(t) = 2 + cos(t),     

(ii) y(t) = 3 cos(2πt + π/4),            

(iii) c(t) = 1/cos(t)

(e) If z(t) is periodic of fundamental period T₀, is z_e (t) = 0.5[z(t) + z( − t)] also periodic? If so determine its fundamental period T₀. What about z_o (t) = 0.5[z(t) − z(−t)]?