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In-Depth Information
Fig. 1.
Ambiguity function of an “oscillator”signal
Fig. 2.
Ambiguity function of a random signal
Fig. 3.
Ambiguity function of a chirp signal
In Figures 1, 2, and 3, the ambiguity function of a signal from the oscillator
system is compared with that of a random signal and a typical chirp.
The oscillator system can be extended to a much larger system
S
E
, consisting
of order of
p
5
signals if one is willing to compromise Properties 1 and 2 for a
weaker condition. The extended system consists of all signals of the form
M
w
L
τ
ϕ
for
τ, w
S
E
)=
p
2
p
5
.
∈
F
p
and
ϕ
∈
S
O
. It is not hard to show that # (
·
#(
S
O
)
≈
As a consequence of (1) and (2) for every
ϕ
=
φ
∈
S
E
we have
4
√
p
.
|
ϕ, φ
| ≤
