K. L. Poland, Revision F T1 - Basic Transmission Theory
4.0 Digital Signal Transmission: Advantages and Problems
A digital signal transmission network can overcome noise corruption problems that plague analog voice transmission.
original signal
Digital Digital Transmitter Receiver
corrupted signal
Figure 10: A Digital Signal Network
Imagine a simple digital signal transmission network, as show in Figure 10. The digital signal consists of a string of pulses or absence of pulses. This digital signal is discretely variable over time. That is, ideally, the signal is either a pulse, or not a pulse, at any given instant of time. There are no in-between states for this digital signal. This signal is not continuously variable as is an analog signal. If this digital signal is sent over a telephone line, it suffers the same distortion, attenuation and degradation as did the analog signal. However, with a digital signal, these signal corruptions can be corrected.
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Digital Digital Transmitter Receiver
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0
Figure 11: Digital Repeater in Circuit Instead of using amplifiers to enhance the circuit’s long distance performance, repeaters are added to the transmission line. The repeater does not amplify the corrupted signal, as does the line amplifier. It recreates the digital signal. This ability to recreate the original signal is a key attribute that distinguishes digital signal transmission from analog signal transmission. This attribute provides the ability to transmit voice over great distances without the signal suffering from degradation due to the transmission. Figure 11 shows how the repeater takes a moderately-corrupted signal and from it recreates the original signal. This process is repeated again by the receiver.
detection threshold
corrupted signal sample point
reconstructed pulses
Figure 12: Digital Signal Regeneration
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The repeater uses a threshold (dotted horizontal line in Figure 12 and Figure 13) to determine the location of the pulses. If the signal rises above the threshold level, that moment is judged to be the start of a possible pulse. If the repeater sees a pulse at its sample point (measures the signal voltage to be greater in amplitude than the threshold level), then it creates an entirely new pulse to transmit. This is called regeneration. The original digital signal is faithfully recreated. Noise corruption in the signal is eliminated. Errors can still occur if the digital signal becomes too corrupted for repeaters to correct. Figure 13 compares a corrupted digital signal (black line) and the output of a repeater (gray line) that regenerates the corrupted signal.
Error of omission Error of commission
Figure 13: Digital signal Error Types
Errors of omission occur if a pulse is not detected. Figure 13 contains a pulse that is attenuated severely enough that the repeater does not consider it to be a pulse. As a result, the regenerated signal has an error of omission. Errors of commission occur if a noise spike is perceived as a pulse. Figure 13 also shows a noise spike that is large enough to fool the regenerator. The regenerator sees the noise spike as a pulse, and as a result, generates an pulse that was not part of the original signal. Creating an additional pulse in the regenerated signal in this manner is known as an error of commission. To prevent these errors, a digital transmission line must be engineered so that the signal does not become too distorted before it is regenerated. This is done by carefully spacing the repeaters along the span.
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5.0 Voice Encoding
Figure 14: An Analog Voice Signal
The digital signal has excellent transmission characteristics, but so far it does not provide a means for voice transmission. If a voice signal can be converted to a digital format, and its digital equiv- alent can be converted back into an analog voice signal, then the advantages of digital transmission can be used for telephone networks. This chapter explains the technique that is used to convert an analog voice signal (shown again in Figure 14) into a digital signal in the public telephone network.
Figure 15: Voice Signal Sampled Periodically create a PAM Signal
At periodic intervals the signal’s amplitude is preserved in slices. This is known as sampling. The resultant series of voltage “spikes” is called a Pulse Amplitude Modulated (PAM) signal.
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Positive
Negative 00010111 10000111 10110111 11011000 10010101 10000011 00010111 00100110 01001100 00110110 10010111 11010111 10110101 10010110 00011000 00110101 01000011 00010111 00000101 10010101
Figure 16: Digitizing the PAM Signal
The height of each PAM sample is measured and given a number that represents its amplitude. If the number that represents the signal amplitude has 8 bits of resolution, the PAM signal is digitized into bytes. A coder,orvocoder, performs this analog-to-digital function. This process is called encoding. Notice the original continuously-variable voice signal in Figure 14 is now represented by a series of 1s and 0s grouped into 8-bit words. This numerical encoding of a voice waveform is called Pulse Code Modulation,orPCM. Often, these words are simply referred to as PCM samples. The original analog voice signal is now in a digital format. The voice signal can now be transmitted across a digital transmission span.
6.0 Voice Reconstruction
To be useful, the voice digitalizing process must be reversible. That is, given PCM samples, it must be possible to create an intelligible voice signal from them.
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Figure 17: PCM words to Stepped Discrete Signal Figure 17 shows a stepped, discrete signal generated by converting the PCM words back to the voltage levels they represent. A digital-to-analog (D/A) converter reads the PCM sample, and creates a voltage that is represented by that PCM sample. The D/A converter keeps that voltage steady until it converts the next PCM sample it receives, and then creates a new, corresponding output voltage.
Figure 18: Approximation of Original Signal Recovered
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If the stepped signal is passed through a low-pass filter, high-frequency components associated with the sharp corners of the steps are smoothed out. The recovered signal is a close approximation of the original voice signal is produced (Figure 18). This recovered signal is not an exact duplicate of the original voice signal. Some error is inherent in the PCM process. However, with 8-bit PCM, the errors are minor enough that most listeners on a typical telephone cannot distinguish the reconstructed signal from the original signal. The lack of noise and ability to overcome effects of accumulative corruption in a PCM-encoded voice signal transmitted over great distances more than makes up for PCM’s minor inherent distortions. The increase in voice quality for a long- distance phone call, due to digital transmission, compared to analog transmission, can be astonishing. The PCM-to-analog function depicted in Figure 17 and Figure 18 is performed by a decoder.
6.1 The CODEC The Coder and Decoder can be combined into one device: the CODEC. A modern digital telephone contains a CODEC. T1 also makes use of the CODEC function.
CODEC PCM analog voice signal
Decoder 10000111 Coder
Figure 19: The CODEC function
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desired signal to encode
undesired signal is recovered
Figure 20: Aliasing due to insufficient sampling rate
6.2 Aliasing Too infrequent sampling does not encode sufficient information to properly reconstruct the voice signal. Figure 20 (top drawing) shows PAM samples created from infrequent sampling during the encoding process. When the reconstructed step signal is used to recover the original encoded signal, an undesired waveform is created (bottom drawing). The anticipated signal is not recovered. Ambiguity is caused because insufficient information to reconstruct the desired signal is encoded in these too-infrequent PAM samples. PCM derived from too-slow a sampling rate can create the wrong waveform. This is called aliasing.
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6.3 Nyquist and Proper Sampling Rate A Bell Laboratory mathematician named Harry Nyquist discovered in 1933 that a waveform must be sampled at a rate greater than twice its bandwidth if it is to be successfully recovered without aliasing. This is known as Nyquist’s sampling theorem. Nyquist’s sampling theorem must be obeyed to avoid aliasing problems.
desired signal to encode
Figure 21: Proper sampling rate avoids aliasing
Figure 21 shows the same voice signal as shown in the top half of Figure 20. In Figure 21, the PAM sampling rate is sufficiently high to obey Nyquist’s sampling theorem. If these PAM samples were processed into PCM, and the PCM processed into a stepped signal, the original signal could be recovered from that stepped signal. This successful recovery is shown in Figure 22. In this case the PAM samples contain enough information to avoid aliasing problems.
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desired signal recovered
Figure 22: Voice recovery from stepped signal of sufficient sampling rate
Bell scientists also discovered that while human voice ranges from 50 Hz to 10,000 Hz, 99% of voice information is in the bandwidth of 300 Hz to 3,400 Hz. This was adopted as the standard frequency bandwidth for the analog telephone network. According to Nyquist, to faithfully recreate a voice signal within this bandwidth, it must be sampled at a rate greater than [2 x (3400 -300)] Hz, or 6,200 times a second. In reality, problems with codecs force actual sampling rates to be about 2.4 times the audio bandwidth. Therefore, a sampling rate of 8,000 times a second was selected as the standard for PCM. This allows for accurate, unambiguous voice signal reconstruction without aliasing. From these requirements, the universal bit rate of 64 kb/s used to transmit encoded voice is derived. At 8 bits per PCM sample, multiplied by 8,000 PCM samples per second, the bit rate for a digital voice channel is 64 kb/s.
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