Digital Signal Processing Reference
In-Depth Information
Figure 18.1
Expected mean value of a sinusoidal signal sampled periodically with jitter as a
function of the normalized frequency
coefficient deviations from their expected mean values. The consequences of
cutting off some part of a signal period prevail in the low-frequency range. They
are much more powerful than the fluctuations due to nonuniform sampling, which
dominate in a wide higher frequency range. Apparently these deviations of both
types overlap.
Consider a signal component at frequency
f
i
. Suppose that the Fourier coeffi-
cient
a
i
is estimated in the presence of a cosine at frequency
f
m
. The impact of
the frequency
f
m
on the estimation of the coefficient
a
i
is characterized by the
cross-interference coefficient
A
i
C
m
. Figure 18.2 illustrates how this coefficient
depends on the distance between them under the given signal sampling condi-
tions. While the frequency
f
i
is fixed in the indicated zero position, frequency
f
m
is varied and the value of
A
i
C
m
obtained for
N
254 is displayed as a function
of
f
m
. This diagram, although characterizing the cross-interference coefficient
A
i
C
m
, actually also reflects some typical tendencies observed at the estimation
of other cross-interference coefficients. It is shown in more detail in Figure 18.3.
Equation (18.13) describing the expected value
E
[
m
(
f
)] of a sine-wave signal
sampled periodically with jitter is used for approximation of the cross-interference
coefficient
A
i
C
m
values in this case. Attention is drawn to two points. Firstly, this
approximation is applicable for a wide variety of sampling process parameters. For
example, although it has been calculated for the periodic sampling point process
with jitter, it also fits well the curve obtained in the illustrated case under the
conditions of additive sampling. Secondly, the suggested function approximates
the cross-interference coefficient well in the
f
m
range close to frequency
f
i
.How
=
