yt=∫−∞∞
V
ω
t−τhτd
τ
=∫−∞∞hτeiω(t−τ)d
τ
=eiωt∫−∞∞hτe−(iωτ)d
τ
=Hωeiωt
y
t
τ
V
ω
t
τ
h
τ
τ
h
τ
ω
t
τ
ω
t
τ
h
τ
ω
τ
H
ω
ω
t

(1)
where

Hω
H
ω
is the

eigenvalue (scale factor) and

eiωt
ω
t
is

V
ω
t
V
ω
t
, which is the

eigenfunction.

Summary: Figure 2.

Hω=|Hω|ei∡Hω
H
ω
H
ω
∡
H
ω

(2)
where

|Hω|
H
ω
changes the amplitude of

eiωt
ω
t
and

ei∡Hω
∡
H
ω
changes the phase of

eiωt
ω
t
.

output=|Hω|ei(ωt+∡Hω)
output
H
ω
ω
t
∡
H
ω

(3)