**Subject :**Wireless Communication

## Quantization

**Introduction: **

Quantizer is device which removes the irrelevancy of the speech signal and this process is irreversible and Quantization is the process in which we map the continuous range of amplitudes of a signal into a finite set of discrete amplitudes. This Process introduces the distortion in signal.

**Quantization Techniques:**

- Uniform quantization
- Non Uniform quantization
- Adaptive quantization
- Vector quantization

**Uniform quantization**

- Amplitude quantization is an important step in any speech coding process, and it determines to a great extent the overall distortion as well as the bit rate necessary to represent the speech waveform
- A quantizer that uses n bits can have M = 2" discrete amplitude levels.
- Distortion is directly proportional to the square of the step size,and inversely proportional to the number of levels for given amplitude range.
- Frequently used measures of distortion is the mean square error distortion which is defined as:

x (t) =original speech signal, f_{Q}(t)=quantized speech signal.

- The distortion introduced by a quantizer is often modeled as additive quantization noise, and the performance of a quantizer is measured as the output signal-to-quantization noise ratio (SQNR).SQNR is given as

α = 4.77 for peak SQNR ,α = 0 for the average SQNR.

- The above equation indicates that with every additional bit used for encoding, the output SQNR improves by 6 dB.

**Non Uniform Quantization****:**

- Non Uniform quantizers distribute the quantization levels in accordance with the pdf of the input waveform
- For aninput signal with a pdfp(x),the mean square distortion is given by

f_{Q}(x) =output of the Quantizer

- A simple and robust implementation of a non-uniform quantizer used in commercial telephony is the logarithmic quantizer
- Nonuniform quantization is obtained by first passing the analog speech signal through a compression (logarithmic) amplifier, and then passing the compressed speech into a standard uniform quantizer