Question Description
I’m working on a electrical engineering question and need a sample draft to help me learn.
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7.1.8 For the quantizer of Example 7.6,
the difference Z = X – Y is the quantiza-
tion error or quantization “noise.” As in
Example 7.6, assume that X has a uniform
(-r/2, r/2) PDF.
(a) Given event B? that Y = Yi = A/2+iA
and X is in the ith quantization inter-
val, find the conditional PDF of Z.
(b) Show that Z is a uniform random var-
iable. Find the PDF, the expected
value, and the variance of Z.
=
=
Example 7.6
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The continuous uniform (-r/2,r/2) random var-
r12
iable X is processed by a b-bit uniform quantizer to
produce the quantized output Y. Random variable
X is rounded to the nearest quantizer level. With a
b-bit quantizer, there are n = 26 quantization levels.
X The quantization step size is A =r/n, and Y takes
A 2A 3A 7/2 on values in the set
Qy = {Y-n/2,9-n/2+1, … , Yn/2-1} (7.11)
where yi = A/2+iA. This relationship is shown for
b = 3 in the figure on the left. Given the event B; that Y = yi, find the conditional
PDF of X given Bi.
In terms of X, we observe that B; = {iA
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