Digital Signal Processing Reference
In-Depth Information
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Figure 7.1
Signal sampling based on sine-wave crossings: (a) diagram illustrating realization;
(b) time diagram of the involved signal interaction
In general, two coordinates need to be given for each signal sample value taken
randomly. In the case of direct sampling randomization, the sampling instants
are pre-planned and to fully determine each signal sample only its value has to
be measured. At the threshold-crossing sampling, the input and reference signal
crossings occur randomly in time. Therefore it might seem that this type of indirect
sampling randomization suffers from the handicap of not knowing when the signal
sample values are taken. That is true, but on the other hand the sample value of the
reference function at the crossing instant actually indicates both coordinates of
the corresponding signal sample. Indeed, the time instant
t
k
of taking each signal
sample value
x
(
t
k
) (and equal reference sine-wave value) functionally depends
on the value of this sample. It simply has to be recovered from the corresponding
instantaneous value of the reference function
r
(
t
k
)
x
(
t
k
), where
A
r
is the amplitude of the reference sinusoid. In the case where this type of
sampling is realized on the basis of the scheme illustrated in Figure 7.1, there is
an uncertainty that has to be resolved. This is related to the fact that there are two
phase angle values (except the phase angles equal to
π
=
A
r
sin 2
π
f
r
t
k
=
4) corresponding
to each particular reading of the reference sine-wave value. The scheme shown in
/
4 and 3
π
/
