814 Chapter 24
AZ. The maximum required charge in voltage per sam-
ple is therefore
(24-9)The value of 'V relative to the maximum amplitude
A defines the amplitude resolution of the system. The
SNR is proportional to the sampling frequency and
inversely proportional to the signal bandwidth. When
presented with a fixed input, the delta modulator will
hunt for the value by changing the output between 1 and
0 every sample. The resulting output is a tone of magni-
tude 'V at the sampling frequency and is called the
idling noise.
Delta modulation is more immune to errors in stor-
age or transmission than PCM. A single-bit error in the
output has a resulting error in the analog signal of 'V. In
a PCM system a single-bit error could cause an error of
up to half the full-scale value. When compared to a
PCM system in term of bits per second, delta modula-
tion will have comparable dynamic range but a smaller
frequency range. At lower bit rates, delta modulation
can have a better SNR and dynamic range than a PCM
system and this has implications for delay lines, where
the total number of bits that must be stored can be
reduced for the same quality of signal.
24.5.3 Sigma-Delta Modulation
By reorganizing the sequence of operations, the delta
Modulator becomes a sigma-delta modulator. A first-
order SDM as shown in Fig. 24-19, has one low-pass
filer integrator in the signal path and a direct feedback
path to a summing point that produces an analog error
signal. The comparator of the delta modulator is
replaced with a quantizer, which is a comparator against
a fixed zero reference. Demodulation is accomplished
using a low-pass filter as in delta modulation.
Both delta modulators and sigma-delta modulators
use sampling frequencies much larger than the Nyquist
frequency, typically of the order of 100 times. This
places the quantization noise energy at very high fre-
quencies where it can easily be removed by filtering.24.5.4 DecimationThe process of sampling well above the required
Nyquist frequency is called oversampling. The objec-
tive is to cause the modulation noise inherent in the
sampling process to appear at frequencies further
removed from the audio signal so that it can be more
easily removed by filtering. The high SNR of an over-
sampled system can be preserved while reducing the
overall bit rate by the process of decimation.
The quantization noise from PCM encoding
decreases by 6 dB for every bit added but decreases by
only 3 dB for every doubling of the sample rate. Deci-
mation of the oversampled PCM data can result in a
large reduction in the overall bit rate. Decimation filters
are used to achieve this and can be thought of as per-
forming an interpolation on the existing data to fill in
the additional bits in the output.
A sigma-delta modulator can have as much as a
15 dB SNR improvement for a doubling of the sample
rate. Decimation of the SDM signal can be used to con-
vert the single bit data stream to a multibit PCM format
suitable for storage in RAM and processing by DSP.'VA= Z't