ANALOG DATA, DIGITAL SIGNALS

ANALOG DATA, DIGITAL SIGNALS

In this section we examine the process of transforming analog data into digital signals.

Strictly speaking, it might be more correct to refer to this as a process of converting

analog data into digital data, a process known as digitization. Once analog

data have been converted into digital data, a number of things can happen; the three

most common are

1. The digital data can be transmitted using NRZ-L. In this case, we have gone

directly from analog data to a digital signal.

2. The digital data can be encoded as a digital signal using a code other than

NRZ-L. Thus, an extra step is required.

3. The digital data can be converted into an analog signal, using one of the modulation

techniques discussed in Section 4.2.

This last, seemingly curious procedure is illustrated in Figure 4.11, which

shows voice data that are digitized and then converted to an analog ASK signal; this

allows digital transmission in the sense defined in Lesson 2. The voice data,

because they have been digitized, can be treated as digital data, even though transmission

requirements (e.g., use of microwave) dictate that an analog signal be used.

The device used for converting analog data into digital form for transmission,

and subsequently recovering the original analog data from the digital, is known, as

a codec (coder-decoder). In this section, we examine the two principal techniques

used in codecs, pulse code modulation, and delta modulation. The section closes

with a discussion of comparative performance.

Pulse Code Modulation

I

I Pulse Code Modulation (PCM) is based on the sampling theorem, which states

: If a signal f(t) is sampled at regular intervals of time and at a rate higher than

! twice the highest significant signal frequency, then the samples contain all the

information of the original signal. The function f(t) may be reconstructed from

these samples by the use of a low-pass filter.

For the interested reader, a proof is provided in Lesson 4A. If voice data

are limited to frequencies below 4000 Hz, a conservative procedure for intelligibility,

8000 samples per second would be sufficient to completely characterize the

voice signal. Note, however, that these are analog samples.

This is illustrated in Figure 4.12a and b. The original signal is assumed to be

bandlimited with a bandwidth of B. Samples are taken at a rate 2B, or once every

112B seconds. These samples are represented as narrow pulses whose amplitude is

proportional to the value of the original signal. This process is known as pulse

Each additional bit used for quantizing increases SIN by 6 dB, which is a factor

of 4.

Typically, the PCM scheme is refined using a technique known as nonlinear

encoding, which means, in effect, that the quantization levels are not equally

spaced. The problem with equal spacing is that the mean absolute error for each

sample is the same, regardless of signal level. Consequently, lower amplitude values

are relatively more distorted. By using a greater number of quantizing steps for signals

of low amplitude, and a smaller number of quantizing steps for signals of large

amplitude, a marked reduction in overall signal distortion is achieved (e.g., see

Figure 4.14).

The same effect can be achieved by using uniform quantizing but companding

(compressing-expanding) the input analog signal. Companding is a process that

compresses the intensity range of a signal by imparting more gain to weak signals

than to strong signals on input. At output, the reverse operation is performed.

Figure 4.15 is a typical companding function.

Nonlinear encoding can significantly improve the PCM SIN ratio. For voice

signals, improvements of 24 to 30 dB have been achieved.

Delta Modulation (DM)

A variety of techniques have been used to improve the performance of PCM or to

reduce its complexity. One of the most popular alternatives to PCM is delta modulation

(DM).

With delta modulation, an analog input is approximated by a staircase function

that moves up or down by one quantization level (6) at each sampling interval

(Ts). An example is shown in Figure 4.16, where the staircase function is overlaid

on the original analog waveform. The important characteristic of this staircase function

is that its behavior is binary: At each sampling time, the function moves up or

down a constant amount 6. Thus, the output of the delta modulation process can be

represented as a single binary digit for each sample. In essence, a bit stream is produced

by approximating the derivative of an analog signal rather than its amplitude.

A 1 is generated if the staircase function is to go up during the next interval; a 0 is

generated otherwise.

The transition (up or down) that occurs at each sampling interval is chosen so

that the staircase function tracks the original analog waveform as closely as possible.

Figure 4.17 illustrates the logic of the process, which is essentially a feedback

mechanism. For transmission, the following occurs: At each sampling time, the analog

input is compared to the most recent value of the approximating staircase function.

If the value of the sampled waveform exceeds that of the staircase function, a

1 is generated; otherwise, a 0 is generated. Thus, the staircase is always changed in

the direction of the input signal. The output of the DM process is therefore a binary

sequence that can be used at the receiver to reconstruct the staircase function. The

staircase function can then be smoothed by some type of integration process or by

passing it through a low-pass filter to produce an analog approximation of the analog

input signal.

There are two important parameters in a DM scheme: the size of the step

assigned to each binary digit, 6, and the sampling rate. As Figure 4.16 illustrates, 6

must be chosen to produce a balance between two types of errors or noise. When

the analog waveform is changing very slowly, there will be quantizing noise, which

increases as S is increased. On the other hand, when the analog waveform is changing

rapidly enough such that the staircase can't follow, there is slope-overload noise.

This noise increases as 6 is decreased.

It should be clear that the accuracy of the scheme can be improved by increasing

the sampling rate; however, this increases the data rate of the output signal.

Consider what this means from the point of view of bandwidth requirement.

An analog voice signal occupies 4 kHz. A 56-kbps digital signal will require on the

order of at least 28 kHz! Even more severe differences are seen with higher bandwidth

signals. For example, a common PCM scheme for color television uses 10-bit

codes, which works out to 92 Mbps for a 4.6-MHz bandwidth signal. In spite of these

numbers, digital techniques continue to grow in popularity for transmitting analog

data. The principal reasons for this are

e Because repeaters are used instead of amplifiers, there is no additive noise.

As we shall see, time-division multiplexing (TDM) is used for digital signals

instead of the frequency-division multiplexing (FDM) used for analog signals.

With TDM, there is no intermodulation noise, whereas we have seen that this

is a concern for FDM.

0 The conversion to digital signaling allows the use of the more efficient digital

switching techniques.

Furthermore, techniques are being developed to provide more efficient codes.

In the case of voice, a reasonable goal appears to be in the neighborhood of 4 kbps.

With video, advantage can be taken of the fact that from frame to frame, most picture

elements will not change. Interframe coding techniques should allow the video

requirement to be reduced to about 15 Mbps, and for slowly changing scenes, such

as found in a video teleconference, down to 64 kbps or less.

As a final point, we mention that in many instances, the use of a telecommunications

system will result in both digital-to-analog and analog-to-digital processing.

The overwhelming majority of local terminations into the telecommunications

network are analog, and the network itself uses a mixture of analog and digital techniques.

As a result, digital data at a user's terminal may be converted to analog by

a modem, subsequently digitized by a codec, and perhaps suffer repeated conversions

before reaching its destination.

Because of the above, telecommunication facilities handle analog signals that

represent both voice and digital data. The characteristics of the waveforms are quite

different. Whereas voice signals tend to be skewed to the lower portion of the bandwidth

(Figure 2.10), analog encoding of digital signals has a more uniform spectral

content and therefore contains more high-frequency components. Studies have

shown that, because of the presence of these higher frequencies, PCM-related techniques

are preferable to DM-related techniques for digitizing analog signals that

represent digital data.

ANALOG DATA,ANALOG SIGNAL

Modulation has been defined as the process of combining an input signal m(t) and

a carrier at frequency fc to produce a signal s(t) whose bandwidth is (usually)

centered on fc. For digital data, the motivation for modulation should be clear:

When only analog transmission facilities are available, modulation is required to

convert the digital data to analog form. The motivation when the data are already

analog is less clear. After all, voice signals are transmitted over telephone lines at

their original spectrum (referred to as baseband transmission). There are two principal

reasons:

0 A higher frequency may be needed for effective transmission. For unguided <

transmission, it is virtually impossible to transmit baseband signals; the

required antennas would be many kilometers in diameter.

In this section, we look at the principal techniques for modulation using analog

data: amplitude modulation (AM), frequency modulation (FM), and phase

modulation (PM). As before, the three basic characteristics of a signal are used for

modulation.

Amplitude Modulation

Amplitude modulation (AM) is the simplest form of modulation, and is depicted in

Figure 4.18. Mathematically, the process can be expressed as

Example

with a bandwidth that extends from 300 to 3000 Hz being modulated on a 60-kHz

carrier. The resulting signal contains an upper sideband of 60.3 to 63 kHz, a lower

sideband of 57 to 59.7 kHz, and the 60-Hz carrier. An important relationship is

 

Another variant is double-sideband suppressed carrier (DSBSC), which filters

out the carrier frequency and sends both sidebands. This saves some power but uses

as much bandwidth as DSBTC.

The disadvantage of suppressing the carrier is that the carrier can be used for

synchronization purposes. For example, suppose that the original analog signal is an

ASK waveform encoding digital data. The receiver needs to know the starting point

of each bit time to interpret the data correctly. A constant carrier provides a clocking

mechanism by which to time the arrival of bits. A compromise approach is vestigial

sideband (VSB), which uses one sideband and a reduced-power carrier.

Angle Modulation

Frequency modulation (FM) and phase modulation (PM) are special cases of angle

modulation. The modulated signal is expressed as