Waveform Encoding - Digital Communication: Principles and System Modelling - page 34

(i) For uniform quantization, the step size, S can be determined easily
as

× ×

2 V

256 =

2 40

256

= =

S 312.5mV

(ii) To apply μ - law for non-uniform quantization, for μ = 255

The smallest height h would be increased in GP as

h + 2 h + 4 h + 8 h + 16 h + 32 h + 64 h + 128 h = 2V

⇒ 255 h = 2V

⇒ = =

h 0.0078 V 7.8mV

⇒ 128 h = 1.0039 V

Therefore the maximum and minimum step size employing μ - law for non-

uniform quantization, for μ = 255 are 1.0039 V and 7.8 mV respectively.

2.3 Differential Pulse Code Modulation (DPCM)

In analog messages we can make a good guess about a sampled value from the
knowledge of the past sampled values. In other words, the sampled values are
not independent, and generally there is a great deal of redundancy in the Nyquist
samples. Proper exploitation of this redundancy leads to encoding a signal with
lesser number of bits. Consider a sampling scheme where instead of transmitting
the sampled values, we transmit the difference between the successive samples. By
employing the technique of transmitting the quantized difference values of the suc-
cessive samples we can efficiently use the bandwidth provided by the transmitting
channel.

2.3.1 Cumulative Error in PCM

In general PCM system, a quantization error e q i is added to the quantized output
while quantizing the ith sample. Now just take a look on how the quantization error
affects the DPCM output.
Here Z i is the sampled value at ith instant and Z i is the predicted sample (considered
as delayed sample) at ith instant.
Now, from the Fig. 2.20 ,

Z i − Z i

d i =

= Z i − Z i − 1

(2.25)

Or recovered sample at the receiver is Z i = d i +

Z i − 1

1. So, Z 1 = d 1 + For the 1st sample, i = Z 0