Global Positioning System Reference
In-Depth Information
FIGURE 7.3
Acquisition through locally generated C/A and RF code.
accurate enough to be passed to the tracking program. More accurate frequency
measurement is needed, and this subject will be discussed in Section 7.10.
The above discussion is for one satellite. If the receiver is designed to perform
acquisition on 12 satellites in parallel, the above arrangements must be repeated
12 times.
7.7 CIRCULAR CONVOLUTION AND CIRCULAR CORRELATION
(
1
)
This section provides the basic mathematics to understand a simpler way to
perform correlation. If an input signal passes through a linear and time-invariant
system, the output can be found in either the time domain through the convolution
or in the frequency domain through the Fourier transform. If the impulse response
of the system is
h
(
t
), an input signal
x
(
t
) can produce an output
y
(
t
) through
convolution as
∞
∞
y(t)
=
x(t
−
τ)h(τ)dτ
=
x(τ)h(t
−
τ)dτ
(
7
.
2
)
−∞
−∞
The frequency domain response of
y
(
t
) can be found from the Fourier trans-
form as
∞
∞
τ)dτe
−
j
2
πf t
dt
Y(f)
=
x(τ)h(t
−
−∞
−∞
x(τ)
∞
−∞
τ)e
−
j
2
πf t
dt
dτ
∞
=
h(t
−
(7.3)
−∞
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