How does quantization error depends on step size?

How does quantization error depends on step size?

The quality of a Quantizer output depends upon the number of quantization levels used. The discrete amplitudes of the quantized output are called as representation levels or reconstruction levels. The spacing between the two adjacent representation levels is called a quantum or step-size.

What is a step size?

Step Size. The step size is the voltage difference between one digital level (i.e. 0001) and the next one (i.e. 0010 or 0000). For example if an ADC has a step size of 1 Volt an input of 1 volt will produce an output, in a 4 bit converter, of 0001. 0 volts is always considered 0000.

How is the step size of quantization calculated?

As already discussed, quantization is achieved by dividing the transform coefficient by a quantization step size and rounding the result (refer to Equations (2.8) and (2.10) ).

When to use a multilevel quantizer for scalability?

To achieve a wide range of scalability levels, a multilevel quantizer is used where the quantization levels are defined by the encoder. Different quantization step sizes can be specified for each level of scalability. All higher subband quantizers are uniform midrise quantizers with a dead zone twice the quantizer step size.

How to calculate the scaling factor for quantization?

For example, the popular IJPEG implementation, freely available in the public domain, allows this adjustment through the use of quality factor Q for scaling all elements of the quantization table. The scaling factor is computed as (17.1) Scale factor = { + 5000 Q for 1 ≤ Q < 50 200 − 2 * Q for 50 ≤ Q ≤ 99 1 for Q = 100.

How many values can be indexed by the quantization parameter?

There are a total of 52 possible q step [ i] values indexed by the quantization parameter (QP) which ranges in value from 0 to 51. The quantization step-size doubles over six QP values and is set to 1 for a QP value of 4.