ECE 220
Spring 2005
Homework 3 Solutions
1.
(a) y[n] = 2x[n1] + 4x[n2] – x[n4]
(b)
direct form
(c)
transposed direct form
2. (a)
n
0
1
2
3
4
5
6
7
8
9
10
y[n]
0
5
20
7
3
1
4
2
2
2
2
(b) h[n] = 5
δ
[n]  3
δ
[n2]
3.
(a) linear, not time invariant, causal
(b) linear, time invariant, causal
(c) not linear, time invariant, causal
(d) linear, time invariant, not causal
4. y[n] =
δ
[n] +
δ
[n1] 
δ
[n2] 
δ
[n3]
5. (a) x[n] =
δ
[n1] +
δ
[n2] +
δ
[n3]
(b) h[n] =
δ
[n] 
δ
[n1]
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6. (a) y[n] = 1/3(
δ
[n] 
δ
[n1] +
δ
[n2] 
δ
[n3] +
δ
[n4] 
δ
[n5])
(b) y[n] = 1/3(x[n] + x[n2] + x[n4])
7. (a) B = 2Asin(
ω
/2)
θ
=
φ

ω
/2 +
π
/2
ω
=
ϖ
(b) not expressible in form
(c) let H(e