Digital Signal Processing Reference
In-Depth Information
Quantisation error
(noise)
"Noise-Shaping"
1-Bit-A/ D-Con verter
(Delta-modulator)
without oversampling
1-Bit-A/D-Wandler
(Sigma-Delta-Modulator)
with n-tuple oversampling
1-Bit-ADC with n-tuple oversampling
Frequenc
y
f
B
f
s =
2 f
B
(n*
f
s
) / 2
Decimation filter
1-Bit-ADC
0 1 1 0 0
analog
Output 1-Bit-ADC
0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0
4 x 0 3 x 1
=
0
3 x 0 4 x 1
=
1
2 x 0 5 x 1
=
1
4 x 0 3 x 1
=
0
4 x 0 3 x 1
=
0
"Decimation filter "
Output
Illustration 231:
Noise shaping and decimation filters
The upper half of the Illustration shows the distribution of quantisation noise in different cases over the
frequency domain. The frequency f
B
designates the bandwidth of the original and recovered signal, f
S
the
minimum sampling frequency of the source signal. In the case of
Σ−Δ−
modulation only the quantization
noise designated by the triangle is effective.
The decimation filter "decimates" the number of bit/s at the output of the D/A converter by an odd-number
factor. Within a block it is only checked which of the two symbols 0 or 1 occur most frequently. This then
appears at the output. If there are more 1s the signal rises within the block instantaneously “on average”.
If there are more 0s it falls.
