Sampling and Quantization - Digital Speech: Coding for Low Bit Rate Communication Systems - page 30

Table 3.1 Max quantizer input and output levels for 1, 2, 3, 4, and 5 bit quantizers
Max quantizer thresholds

1bit 2bit 3bit 4bit 5bit

i/p o/p i/p o/p i/p o/p i/p o/p i/p o/p

0.0000 0.7980 0.0000 0.4528 0.0000 0.2451 0.0000 0.1284 0.0000 0.0659

0.9816 1.5100 0.5006 0.7560 0.2582 0.3881 0.1320 0.1981

1.0500 1.3440 0.5224 0.6568 0.2648 0.3314

1.7480 2.1520 0.7996 0.9424 0.3991 0.4668

1.0990 1.2560 0.5359 0.6050

1.4370 1.6180 0.6761 0.7473

1.8440 2.0690 0.8210 0.8947

2.4010 2.7330 0.9718 1.0490

1.1300 1.2120

1.2990 1.3870

1.4820 1.5770

1.6820 1.7880

1.9080 2.0290

2.1740 2.3190

2.5050 2.6920

2.9770 3.2630

variance, σ x , of the input signal but made no assumption of fine quantization.
The quantizer input-output threshold values for 1-5 bit Max quantizers are
tabulated in Table 3.1 [4]. The quantizers in Table 3.1 are for a unit variance
signal with a normal probability density function. Each quantizer has the
same threshold values in the corresponding negative side of the quantizer.
Nonuniform quantization is advantageous in speech coding, both in coarse
and fine quantization cases, for two reasons. Firstly, a nonuniform quantizer
matches the speech probability density function better and hence produces
higher signal to noise ratio than a uniform quantizer. Secondly, lower ampli-
tudes, which contribute more to the intelligibility of speech, are quantized
more accurately in a nonuniform quantizer.
In speech coding, Max's quantizer [4] is widely used to normalize the
input samples to unit variance, which guarantees the input dynamic range. In
many other cases, specific nonuniform quantizers are designed by optimizing
the quantizer intervals using a large number of samples of the signal to be
quantized. Although, these specific quantizers are not generally applicable,
they give the best performance for a given signal with a given probability
density function and variance. In cases where the variance of the signal has
a large dynamic range, the variance of the signal is transmitted separately at