Digital Signal Processing Reference
In-Depth Information
1
0
−1
0
5
10
15
20
25
30
(a) Weighted Cosine−Correlated Components of Signal; X−Axis = Sample
1
0
−1
0
5
10
15
20
25
30
(b) Weighted Sine−Correlated Components of Signal; X−Axis = Sample
2
0
−2
0
5
10
15
20
25
30
(c) Signal (circles); Synth from Coeffs (stars); X−Axis = Sample
Figure 4.9:
(a) Cosine-correlated components, each weighted with its respective coefficient (plotted
as continuous functions for ease of visualization); (b) Sine-correlated component, weighted with its
coefficient (plotted as continuous function for ease of visualization); (c) Sum of all components, plotted
as stars, atop unknown signal's samples, plotted as circles.
S
=
A
cos
(
2
πnF/N)
−
B
sin
(
2
πnF/N)
At the receiving end, because the two carrier waves cos
(
2
πnF/N)
and sin
(
2
πnF/N)
are orthog-
onal, it is possible to separately recover the amplitudes of each by multiplying
S
separately by each, and
summing the products (i.e., computing the CZL).
N
−
1
S
R
1
=
S
·
cos
(
2
πnF/N)
n
=
0
N
−
1
S
R
2
=
S
·
sin
(
2
πnF/N)
n
=
0
