ECE 301 Homework 4
Systems in the time domain
Q1.
For the circuit depicted below, find the differential equation relating
outputs y
1
(t) and y
2
(t) to the input f(t).
Q2.
1)
Please state the definition for
causality
.
2)
The following are the impulse responses of some discrete-time LTI
systems. Please determine whether each system is causal or not and
justify your answers.
(a)
ℎ[𝑛] = (
1
5
)
𝑛
?[𝑛]
(b)
ℎ[𝑛] = (0.8)
𝑛
?[𝑛 + 2]
(c)
ℎ[𝑛] = (
1
2
)
𝑛
?[−𝑛]
(d)
ℎ[𝑛] = (−
1
2
)
𝑛
?[𝑛] + (1.01)
𝑛
?[𝑛 − 1]
Q3
.
1)
Please state the definition of
time-invariant
.
2)
Determine
whether each of the following systems is time-invariant or
not. Justify your answers. (In each question, y[n] denotes the system