B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

496 RANDOM PROCESSES AND SPECTRAL ANALYSIS
This is shown in Fig. 9.23b. Thus, the quadrature representation of a bandpass process
is not unique. An infinite number of possible choices exist for the center frequency, and
corresponding to each center frequency is a distinct quadrature representation.
Example 9. 14 A bandpass white noise PSD of an SSB channel (lower sideband) is shown in Fig. 9.24a.
Represent this signal in terms of quadrature components with the carrier frequency W e .
The true center frequency of this PSD is not w e ; but we can still use W e as the center
frequency, as discussed earlier,
n(t) = n e (t) cos W e t + n5(t) sin W e t (9.74)
The PSD Sn/f ) or Sn/f) obtained by shifting S 0 (f) up and down by j [see Eq. (9.73)1 is
shown in Fig. 9.24b,
lf l S B
lf l > B
(9.75)
Figure 9.24
A possible form
of quadrature
component
representation of
noise in SSB.
N
2
0
(a)
(b)
From Fig. 9.24a it follows that
n 2 =/VB
(9.76a)
Similarly, from Fig. 9.24b we have
n = n; =NB
(9.76b)
Hence,
n 2 = n 2 = n 2 = NB
C S
(9.76c)