Radio Frequency by Steve Winder and Joe Carr - HTML preview

14.2 Pulse code modulation

To overcome the susceptibility of PAM signals to corruption of the amplitude waveform by noise and interference, the waveform is processed further to produce pulse code modulation (PCM) before transmission.

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In this process the magnitude of the PAM samples with respect to a fixed reference is quantized and converted to a digital (data) signal. Quantizing rounds off the instantaneous sample pulse amplitude to the nearest one of a number of adjacent voltage levels. Figure 14.2 illustrates the process for an eight-level system. In the figure the amplitude at t₀ is 2, between 4 and 5 at t₁, between 5 and 6 at t₂, etc. After quantization the values would be 2 at t₀,5at t₁,5at t₂andsoon. The difference between the amplitude levels and the rounded-off values is the quantization noise or distortion.

₇ 111
₆ 110
₅ 101
₄ 100
₃ 011
₂ 010
₁ 001

0
000 t t t t t t t t t t
_{^{0 1 2 3 4 5 6 7 8 9}}T
( T = clock period) Figure 14.2 Eight-level pulse code modulation

 

The binary pulse train – leaving a one-bit synchronizing space between each number – for this example would be as in Figure 14.3.

 

t st₁ st₂ st₃s
0
s= Synchronization space Figure 14.3 Binary pulse train (from Figure 14.2)

The number of quantizing levels is 2ⁿ and the highest denary number represented is (2ⁿ − 1) where n is the number of bits used to represent each sample. If each train of pulses is accompanied by one synchronizing bit, the number of bits per sample is (n+ 1).Ifthe sampling rate is f_c, the transmitted bit rate is (n+ 1)f_c. For example, an eight-bit word – including the synch. bit – is commonly used to represent a sample, so, with a clock frequency of 8 kHz:

number of quantizing levels = 2⁷ = 128 sampling rate,f_c =8kHz
therefore transmitted bit rate = (n+ 1)f_c = 64 kb/s

The maximum frequency of the pulses will be when transmitting alternate 1s and 0s, and the occupied bandwidth,¹ × bit rate, 32 kb/s.₂

Quantization as described above is linear, i.e. the spacing of the quantization levels is the same over the range of pulse amplitudes. This produces a poor signal-to-noise ratio for low-level signals which is improved by the use of more closely-spaced levels at small signal amplitudes than at large amplitudes. Where non-linear quantization is used the most significant bit of the sample character identifies the polarity of the signal.

If linear quantization is used then about 12 bits per sample are needed to give a good voice quality, which requires a bit rate of about 96 kbits/s. For coding speech using non-linear quantization 8 bits per sample is sufficient, which requires a bit rate of 64 kbits/s. Two slightly different non-linear PCM codecs were standardized in the 1960s. In America u-law coding is the standard, but in Europe A-law coding is used.