Digital Signal Processing Reference
In-Depth Information
Figure 15.2
Illustration of the impact sampling irregularities on the errors when estimating
the Fourier coefficients
components. In fact, the irregularities of the sampling point stream leads to cross-
interference between the signal components. This phenomenon can be observed
if filtering of a nonuniformly sampled signal with two or more components is
studied. It can be seen that each signal component impacts on the parameter es-
timation of all other signal components and that this impact directly depends on
the specific nonuniformities present in the involved sampling process. To observe
this phenomenon, the experiment should be repeated. Exactly the same sampling
point process should be used for the signal sampling and a sine function at fre-
quency
f
m
should be added to the previously used cosine function with gradually
increased amplitude. The results obtained in this case are displayed as line 3 in
Figure 15.2. It can be seen that the presence of the irregularly sampled com-
ponent at frequency
f
m
adds to the estimation error. However, the value of the
coefficient
A
1
C
1
remains the same; it is not changed by the second component.
Therefore it seems that in this second case
a
b
m
(
A
1
S
m
), where the
coefficient
A
1
S
m
indicates the strength of the impact of the sinusoidal signal com-
ponent at frequency
f
m
on the estimation of the coefficient
a
1
when the signal
is sampled in that particular way. The impact of the specific nonuniformities of
the sampling point process can be characterized by constant coefficients. Thus
it seems that these coefficients characterizing the cross-interference between the
=
a
(
A
1
C
1
)
+
