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6-6 Digital Coding of Audio Signals

can be applied to a signal having no higher frequency components than 6.75 MHz. If studio
equipment exceeds this limit—and many cameras and associated amplifiers do—a low-pass fil-
ter must be inserted in the signal path before the conversion from analog to digital form takes
place. A similar band limit must be met at 3.375 MHz in the chrominance channels before they
are digitized in the NTSC system. If the sampling occurs at a rate lower than the Nyquist limit,
the spectrum of the output analog signal contains spurious components, which are actually
higher-frequency copies of the input spectrum that have been transposed so that they overlap the
desired output spectrum. When this output analog signal is displayed, the spurious information
shows up in a variety of forms, depending on the subject matter and its motions [1]. Moiré pat-
terns are typical, as are distorted and randomly moving diagonal edges of objects. These aliasing
effects often cover large areas and are visible at normal viewing distances.

Aliasing may occur, in fact, not only in digital sampling, but whenever any form of sampling

of the image occurs. An example long familiar in motion pictures is that of vehicle wheels (usu-
ally wagon wheels) that appear to be rotating backward as the vehicle moves forward. This
occurs because the image is sampled by the camera at 24 frames/s. If the rotation of the spokes of
the wheel is not precisely synchronous with the film advance, another spoke takes the place of
the adjacent one on the next frame, at an earlier time in its rotation. The two spokes are not sepa-
rately identified by the viewer, so the spoke motion appears reversed. Many other examples of
image sampling occur in television. The display similarly offers a series of samples in the verti-
cal dimension, with results that depend not only on the time-vs.-light characteristics of the dis-
play device but also, and more important, on the time-vs.-sensation properties of the human eye.

6.1.3

The A/D Conversion Process

To convert a signal from the analog domain into a digital form, it is necessary to create a succes-
sion of digital words that comprise only two discrete values, 0 and 1 [1]. Figure 6.1.1 shows the
essential elements of the analog-to-digital converter. The input analog signal must be confined to
a limited spectrum to prevent spurious components in the reconverted analog output. A low-pass
filter, therefore, is placed prior to the converter. The converter proper first samples the analog
input, measuring its amplitude at regular, discrete intervals of time. These individual amplitudes
then are matched, in the quantizer, against a large number of discrete levels of amplitude (256
levels to convert into 8-bit words). Each one of these discrete levels can be represented by a spe-
cific digital word. The process of matching each discrete amplitude with its unique word is car-
ried out in the encoder, which, in effect, scans the list of words and picks out the one that matches

Figure 6.1.1 

Basic elements of an analog-to-digital converter. (

From [1]. Used with permission.)

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Analog/Digital Signal Conversion

Analog/Digital Signal Conversion 6-7

the amplitude then present. The encoder passes out the series of code words in a sequence corre-
sponding to the sequence in which the analog signal was sampled. This bit stream is, conse-
quently, the digital version of the analog input.

The list of digital words corresponding to the sampled amplitudes is known as a code. Table

6.1.1 represents a simple code showing amplitude levels and their 8-bit words in three ranges: 0
to 15, 120 to 135, and 240 to 255. Signals encoded in this way are said to be pulse-code-modu-
lated. Although the basic pulse-code modulation (PCM) code sometimes is used, more elaborate
codes—with many additional bits per word—generally are applied in circuits where errors may
be introduced into the bit stream. Figure 6.2.2 shows a typical video waveform and several quan-
tized amplitude levels based on the PCM coding scheme of Table 6.1.1.

The sampling rate, even in analog sampling systems, is crucial. Figure 6.1.3a shows the spec-

tral consequence of a sampling rate that is too low for the input bandwidth; Figure 6.1.3b shows
the result of a rate equal to the theoretical minimum value, which is impractical; and Figure
6.1.3c shows typical practice. The input spectrum must be limited by a low-pass filter to greatly
attenuate frequencies near one-half the sampling rate and above. The higher the sampling rate,
the easier and simpler the design of the input filter becomes. An excessively high sampling rate,
however, is wasteful of transmission bandwidth and storage capacity, while a low but adequate
rate complicates the design and increases the cost of input and output analog filters.

Analog signals can be converted to digital codes using a number of methods, including the

following [3]:

Table 6.1.1 Binary Values of Amplitude Levels for 8-Bit Words 

(

From [1]. Used with permis-

sion.)

Amplitude

Binary Level

Amplitude

Binary Level

Amplitude

Binary Level

0

00000000

120

01111000

240

11110000

1

00000001

121

01111001

241

11110001

2

00000010

122

01111010

242

11110010

3

00000011

123

01111011

243

11110011

4

00000100

124

01111100

244

11110100

5

00000101

125

01111101

245

11110101

6

00000110

126

01111110

246

11110110

7

00000111

127

01111111

247

11110111

8

00001000

128

10000000

248

11111000

9

00001001

129

10000001

249

11111001

10

00001010

130

10000010

250

11111010

11

00001011

131

10000011

251

11111011

12

00001100

132

10000100

252

11111100

13

00001101

133

10000101

253

11111101

14

00001110

134

10000110

254

11111110

15

00001111

135

10000111

255

11111111

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Analog/Digital Signal Conversion

6-8 Digital Coding of Audio Signals

•

 Integration

•

Successive approximation

•

Parallel (flash) conversion

Figure 6.1.2 

Video waveform quan-

tized into 8-bit words.

(

a)

(

b)

(

c)

Figure 6.1.3

 Relationship between sampling rate and bandwidth: (

a) a sampling rate too low for

the input spectrum, (

b) the theoretical minimum sampling rate (F

s

), which requires a theoretically

perfect filter, (

c) a practical sampling rate using a practical input filter.

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Analog/Digital Signal Conversion 6-9

•

Delta modulation

•

Pulse-code modulation

•

Sigma-delta conversion

Two of the more common A/D conversion processes are successive approximation and parallel
or flash. Very high-resolution digital video systems require specialized A/D techniques that often
incorporate one of these general schemes in conjunction with proprietary technology.

6.1.3a

Successive Approximation

Successive approximation A/D conversion is a technique commonly used in medium- to
high-speed data-acquisition applications. One of the fastest A/D conversion techniques, it
requires a minimum amount of circuitry to implement. The conversion times for successive
approximation A/D conversion typically range from 10 to 300 

µs for 8-bit systems.

The successive approximation A/D converter can approximate the analog signal to form an

n-bit digital code in n steps. The successive approximation register (SAR) individually compares
an analog input voltage with the midpoint of one of n ranges to determine the value of 1 bit. This
process is repeated a total of n times, using n ranges, to determine the n bits in the code. The
comparison is accomplished as follows:

•

The SAR determines whether the analog input is above or below the midpoint and sets the bit
of the digital code accordingly.

•

The SAR assigns the bits beginning with the most significant bit.

•

The bit is set to a 1 if the analog input is greater than the midpoint voltage; it is set to a 0 if the
input is less than the midpoint voltage.

•

The SAR then moves to the next bit and sets it to a 1 or a 0 based on the results of comparing
the analog input with the midpoint of the next allowed range.

Because the SAR must perform one approximation for each bit in the digital code, an n-bit code
requires  n approximations. A successive approximation A/D converter consists of four main
functional blocks, as shown in Figure 6.1.4. These blocks are the SAR, the analog comparator, a
D/A (digital-to-analog) converter, and a clock.

6.1.3b

Parallel/Flash

Parallel or flash A/D conversion is used in high-speed applications such as video signal process-
ing, medical imaging, and radar detection systems. A flash A/D converter simultaneously com-
pares the input analog voltage with 2

n

 – 1 threshold voltages to produce an n-bit digital code

representing the analog voltage. Typical flash A/D converters with 8-bit resolution operate at 100
MHz to 1 GHz.

The functional blocks of a flash A/D converter are shown in Figure 6.1.5. The circuitry con-

sists of a precision resistor ladder network, 2

n

 – 1 analog comparators, and a digital priority

encoder. The resistor network establishes threshold voltages for each allowed quantization level.
The analog comparators indicate whether the input analog voltage is above or below the thresh-
old at each level. The output of the analog comparators is input to the digital priority encoder.
The priority encoder produces the final digital output code, which is stored in an output latch.

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Analog/Digital Signal Conversion

6-10 Digital Coding of Audio Signals

Figure 6.1.4

 Successive approximation A/D converter block diagram. (

After [4].)

Figure 6.1.5

 Block diagram of a flash A/D converter. (

After [5].)

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Analog/Digital Signal Conversion