Quantization



next up previous
Next: Finding the Frequency Up: Lab 06: Quantization and Previous: Introduction

Quantization

If the amplitude of a signal takes on values over an interval from to , quantization of this signal into levels can be thought of as breaking the interval into bins. All values that lie in a given bin are rounded to the reconstruction value associated with that bin; reconstruction values are usually chosen to be the value of the center of each bin. Once the bins and reconstruction values have been determined, each sample of the signal is then quantized by figuring out the bin into which it falls, and then changing the sample value to the associated reconstruction value. This process is illustrated in Figure 1.

  
Figure 1: A signal is quantized into four levels. First the range from to is divided into four bins, with the four reconstruction values as the centers of each of the bins. Then the signal amplitudes are rounded to the reconstruction level of the bin into which they fall. Dotted lines indicate the bins. Note that the amplitudes that fall on the edge of a bin are arbitrarily declared to lie in the highest bin.

If bits are used to represent the reconstruction values, then there are possible reconstruction values.

If we do not care about the actual reconstruction values, but only wish to break the signal amplitudes into possible levels, then one way to quantize is to:

(a) Normalize the signal to fall into the range 0 to 1.
(b) Multiply the normalized signal by .
(c) Round the sample values down to the nearest integer.
(d) Divide by .

This will give you possible values for the signal in a range from 0 to 1.

Quantization can be thought of as taking your original signal and adding noise to it. The noise reflects the error introduced by quantization.



next up previous
Next: Finding the Frequency Up: Lab 06: Quantization and Previous: Introduction



Kenneth Chiang