nal, 'T
the v Probality
e distribution
: = of signal
e Clean signal Noisy signal values
S
e ee —
rm > [7177
e Oo
the 2
the e
luce «c J
an
pe op s >
y, 1) 2 3 1
a en 1 0 Area is proportional to
3 T + probality of being in |
0 0 ee a À the first level above correct |
|] € 0 ; : |
© + + -+ — Area is proportional to
EA m Ya ie me - probality of being in
the d 0 1 0 the correct level
O fp il ————————Ááám—À—)—oiÜ
"o 0 T Area is proportional to
nce v ah [s2+12142<QL probality of being in
Most the first level below correct
significant
) bit
fig. 6.1
For a clean signal contaminated with noise there will be a nonzero
probability of assigning an incorrect digital level in the analogue
the digital conversion ( after Billingsley, 1975 |.
The probability distribution of signal and noise can be found by
convolving the distribution of the signal with that of the noise. The
probability of correct digitizing is found by integrating the joint
distribution between limits representing the quantization interval
boundaries. A graphic representation of these probabilties as a
function of B is given in fig. 6.2.
rom The analysis can be carried further ( Fulz, 1965) to provide for
red determination of quantization within + N levels of the correct value.
nal This probability is given by the expression
te
e n pe CEN) z (N«1) erf((n«1)a]-N erf(Na)-(exp(-N a? )-expL- (N«1)^a7 )) /a/v
to
( 6.1 )
ps. where a=quantizing step size/o/2 and N denotes the number of levels
ven from the correct level. If N=0 the expression reduces t the
nal probability of correct classification and erf(x) - 2//w f exp(-t ) dt
we is evaluated from 0 to x.
of
bi-
tep
149