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Unformatted text preview: ECE425 ' LAB 5 FALL 2006 QUANTIZATION AND DITHERlNG For this lab, you are asked to look at some details of the use of dithering to alleviate
certain problems with signal level quantization“ The approach will be to have you write
Matlab programs to approximately reproduce the results given on four pages of figures
used in lecture and in the Finite Wordlength Notes (also reproduced below). Your results
will differ of course because of the use of random signals, and .you will likely choose
different parameters of the signals and for low—pass filters“ Additional hints will be given in lecture” I Orig. Sins 15
Units 1
OK!
0 s
0 Fig. 4 A small
sinewave when
05 quantized shows
100 1 o 200 . .
0 5° _ 5 samples ~  ‘ harmonic dist
QuantOrigSine  FFT Orig ouant.  ortion. With the
15   addition of noise
_ C) prior to quantiza
ling 1 tion, the distort
. ion components
05 can be broken
up onto the
0 background
noise.
o.s o . .
0 so 100 150 zoo 0 0.5Ts
' samples ' .
Dithered Sine _ . FFT Ditherod
. so
f).
so
40
so
20
10
o _ .
0 so 100 150 200  0 0.5g
. '  samples 7 ’ '
1 Quant. Dithered Sine  FFT Dith. Guam.
.5 . . ~ _
9)
Units
on
0.5
o
os '
0 so 100 150 zoo
’ ‘ _ samples
Avg. Quant. Dit. Sine r FFT of Aver.
15
a . i)
Units 1
of Q
as
o .

.05 ' ...umnmt..........t.m..t ....... who“... .
0 so 100 150 zoo ‘ o ' 056 samples (9) Orig‘ Sine 100 150 200
, samples Quant.‘ Orig‘ Sine 100 150 200
samples bithered Sine 100 150 200
samples Quant Dithered Sine ‘ o 50 100 150 200 samples
Avg“ Quant.‘ Dit Sine
1.5
i)
Units 1
of Q
05
0
'05 o 50 100 150 200
samples ' 60
50
40
30
20 10 50 4O 30 20 10 FFT Orig Quant 0.135
N .Jhnnll‘ FFT Dithered FFT Dim“ Quant FFI' of Aver oust; 0.t5fS 1‘) 0er h) 051‘s Fig. 5 When
the frequency is
increased to
0‘.3f5, the
"harmonics" now
appear in aliased
form, and here
the third
harmonic looks
like a sub
harmonic. Dither
is effective in this
case as weiit. Units signal level below 0/2 0 50 100 150 200
, samples quantized to zero 0 50 1 00 1 50 200 , ‘
samples . ) 0i5fs Units signal with unity dither
of Q O 50 100 150 200 0 I ‘
samples ' 0 "5f3 dithered/quantized 0 50 100 150 200 .
 samples Fig. 7 A small signal '(a) quantiﬁes to zero (c,d) and is lost” With the addition of dither (e) the
signal now triggers the quantizer and is detected (g,h).i '(13) _ (:10 Perhaps the aspect of using dither that is of the most general importance is that of increased
resolution, the ability to achieve effective levels that are between available quantization levels.
Fig. 8a shows a dc level of 1.250, which is rounded to 0. With the addition of dither (Fig. 8b) of
amplitude 0, we see that now multiple quantization levels are reached: many more are Q and
fewer are 20 (Fig. 8d). Now by averaging (Fig. 8e), we can achieve an output that hovers about
1.25, the true value. Here we have averaged over 50 samples, so it is only the output samples from 50 to 200 in Fig. Be that represent a typical result. It is probably clear that nothing depended on our choosing 1.250. We might have chosen
1.260 or 1.72340, and we would still expect some useful trend toward that level. The exact
degree to which a quantizer achieves increased linearity and increased resolution by this
procedure depends on correct selection of dither amplitude and probability distribution shape. in most cases, the dither would be supplied by some pseudo—random digital method. 25 2 a) 2 1.250 with unity dither
1 5 dc level of 1 250 1 5
. Units 1 Units 1
of 0
0.5 0 5
o o
.0 5 ..
o 50 100 150 200 o 5 o 50 100 150 200
samples samples
2 5 m————————
2
. 1 5
Units Units
of 0 °' Q 1
0 5 quantized to 0 or 20
o
O 5
100 150 200 0 50 100 150 200
samples samples quantized and averaged over 50 Units I
of Q 0 50 1 00 1 50 200
samples Fi 1.9 8 Although 1 .'250 IS not an actual quantization level, through the uSe of dither, we can
approach the 1.250 level as an average. (14) ...
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