Digital Signal Processing Reference
In-Depth Information
Digital to Analog Converter Section
10
Successive Approximation Register
1
1
1
1
0
0
20
6
X
(a) Sample
X
3
+
11.25
X
1.5
15
Compare
X
0.75
11.25
6
3
1.5
0.75
Binary Weight Generator
Set the 2
0
bit to 1
Conversion Value for Sample 12 is 1 1 1 1
15
10
5
0
0
5
10
15
20
25
30
(b) Sample
Figure 3.23:
A schematic arrangement of an ADC having LSB = 0.75 volt, using the Offset method
with no bias to the input signal; (a) Analog signal (solid), sample being quantized (circle); (b) Quantized
samples.
effectively no quantization error, there will still be a very large stairstep component in the DAC output
which was not in the original analog signal. Referring to a sine wave, for example, the amplitude of the
stairstep component is large when the number of samples per cycle of the sine wave is low, and decreases
as the number of samples per cycle increases.
Fortunately, the frequencies comprising the stairstep component all lie above the Nyquist limit
and can be filtered out using a lowpass reconstruction filter designed especially for zero-order hold
reconstruction (LPF in Fig. 3.20). Quantization noise, on the other hand, has components below the
Nyquist limit, and thus cannot be eliminated with lowpass filtering. Zero-order hold conversion acts like
a gently-sloped lowpass filter, so a special reconstruction filter must be used that cuts off at the Nyquist
limit but emphasizes higher frequencies in the passband. Details may be found in [2].
3.16
CHANGING SAMPLE RATE
There are many different standard sample rates in use, and from time to time it is necessary to convert
one sequence sampled at a first rate to an equivalent sequence sampled at a different rate. It might, for
example, be necessary to add two sequences together, one of which was sampled at 11.025 kHz, and the
