Digital Signal Processing Reference
In-Depth Information
1
0.5
0
−0.5
−1
0
2
4
6
8
10
12
14
16
(a) Cosine−Correlated Coefficients, X−axis = Frequency
1
0.5
0
−0.5
−1
0
2
4
6
8
10
12
14
16
(b) Sine−Correlated Coefficients, X−axis = Frequency
Figure 4.8:
(a) Coefficients of cosine-correlated components (scaled according to the synthesis formula);
(b) Coefficients of sine-correlated components (scaled according to the synthesis formula).
a description of the contents of Volume II). In Volume II, the theoretical basis for both the Real and
Complex DFTs will be taken up; our brief foray into the Real DFT has served to illustrate the basic
underlying principle of standard frequency transforms such as the DFT, which is correlation between the
signal and orthogonal correlator pairs of various frequencies.
4.4 USING ORTHOGONALITY IN SIGNAL TRANSMISSION
The property of orthogonality of sinusoids, i.e., that
N
−
1
cos
(
2
πnF/N)
sin
(
2
πnF/N)
=
0
n
=
0
can be put to remarkable use in encoding and transmitting signals. For example, suppose it is desired to
transmit two real numbers
A
and
B
simultaneously within the same bandwidth. The numbers can be
encoded as the amplitudes of
sine
and
cosine
functions having the same frequency
F
, where
F
cannot be
equal to 0 or
N/
2:
