HW in linear system

HW in linear system.(Electrical Engineering Major),need step by step solutions with disscusion.

ECE 350 – HW #1 Name ____________________________ Fall 2013
Due date: 9/12/2013

1. Find the zero-state response of a system with impulse response h(t) = t[u(t) – u(t – 1)], if the input is

x(t) =

2[u(t) – u(t – 2)].

2. Evaluate

∞∞∞
a. ∫δ(t−2)e−tdt b. ∫δ(2t−1)e−tdt c. ∫δ(t+3)(t2 +1)dt

−∞ −∞ −∞

3. For systems described by the following differential equations, classify the systems as (i) linear or non-linear and (ii) time-varying or time-invariant: (Explain why)

a.  dy 2 + 2 dy + 5y(t) = x(t)  dt  dt

b. d2y+3tdy+2ty(t)=x(t) dt2 dt

4. A differential equation of a system with x(t) as an input and y(t) as an output is

defined as:
5. Find the system response to unit step function, x(t)= 2u(t), where

y(0) = 0, and y(0) = −2. 5.1) Specify ZIR

5.2) Specify ZSR
5.3) What is unit impulse response of this system? (h(t)=?) 6. If signal x(t) is defined as:

2-t 0≤t≤2

y(t)+7y(t)+10y(t)=3x(t)

x(t) =

0 otherwise

ECE 350 – HW #1 Name ____________________________ Fall 2013
Due date: 9/12/2013
Sketch each of the following continuous time signals, specify if they are:

• Causal or Non-causal
• Periodic (specify period) or Aperiodic • Odd or Even

a) x(t+3) b) x(t/2)
c) x(t/2+1) d) x(-t-2) e) x(-2t+1)