EE422

Solution to Homework #1

1a) x(t) = -5r(-t-3) +5u(-t-1) -5u(t+1) -5r(t-2)+5r(t-3)

b) dx/dt = 5u(-t-3) -5d (-t-1) -5d (t+1) -5u(t-2)+5u(t-3)

c) Determine if the following signals are periodic, then find the fundamental period:

i) Periodic!! T = 1/2 sec

ii) Periodic!! n₁T₁ = n₁ (2/15) = n₂T₂ = n₂ (2/10). Therefore, n₁/n₂ = T₂/T₁ = 3/2 so n₁ = 3 and T = n₁T₁ = 2/5 sec

iii) NOT Periodic!! (ratio of T₁/T₂ is not a ratio of integers)

d) Classify the following as power or energy signals:

i)

Therefore it is a POWER SIGNAL!!

ii)

Therefore it is a POWER SIGNAL!!

iii)

Therefore it is an ENERGY SIGNAL!!

d) i) T= p seconds and P_AVE = 10²/2 = 50 W

ii) w ₀ = 1 rad/sec, therefore T= 1/2p seconds and P_AVE = 5² + 10²/2 + 10²/2 + 20²/2 +40²/2 = 1125 W

iii) T= 20 seconds and

Thus, the system is BIBO stable (assuming R/L > 0)