Digital Signal Processing Reference
In-Depth Information
where Var[
n
i
] is the variation of the number of quantizing pulses falling within
the time interval being measured. In the case of uncorrelated
t
i
, the random
error can be written as
t
β
(Var[
t
])
1
/
2
(19.29)
Although this time-interval estimation scheme is simple and practical, the mean
value
q
of the time intervals between the quantizing pulses or, in other words,
the mean repetition rate of these pulses, should be stabilized, which is certainly
a disadvantage.
The second time-interval estimation scheme, shown in Figure 19.11(b), does
not have this disadvantage. This improvement is achieved by organizing the esti-
mation process in such a way that the unknown input time intervals are compared
with some constant time intervals
T
, rather than with the parameter
q
of the pulse
sequence used for quantizing. Therefore, in this case, it is the time reference pulse
duration
T
that has to be stabilized. These time reference pulses are generated
whenever a time interval to be quantized appears at the input. The reference and
input time intervals are quantized in parallel by means of the same quantizing
pulse sequence. The quantization results
m
i
and
n
i
are entered into the respective
counters 1 and 2. It can be written that
ε
=
.
r
=
t
i
q
T
q
.
E
[
n
i
]
and
E
[
m
i
]
=
Therefore
E
[
n
i
]
E
[
m
i
]
T
t
=
and the estimate
t
of the time interval
t
, obtained by averaging
N
quantization
results, is given as
i
=
1
n
i
N
N
T
t
=
.
(19.30)
i
=
1
m
i
t
can be carried out until either
N
or the sum of
m
i
reaches
some preset value
m
. The second approach is preferable and, if it is applied,
An estimation of
N
T
m
t
=
n
i
.
(19.31)
=
i
1
In order to carry out the averaged quantizing of time intervals according to Equa-
tion (19.31), the capacity of counter 1 should be set equal to
m
and quantizing
