Quantization (signal processing)

The quantization is in digital signal processing, a figure that is used in the digitization of analog signals and the source coding of images and video.

An electronic component or a function that quantizes a value or a signal that is the quantizer. The resulting error is called quantization error.

Generally

In practical use, a physical quantity in a measurement according to a measuring principle for the further processing is often converted into an electrical signal and then quantitatively determined in the quantization. Previously, the quantization in the field of measurement technology by reading the meter with a moderate number Awareness - Make the seen from a scale pointer position. By writing down the measurements of a storage in tables and numerical processing accessible ( eg calculation of the monthly average temperature from hourly individual measurements) were. Today, such calculations are practically only in computers instead, and the measured quantity is quantized in terms of equipment to an analog- to-digital converter. They embark on various types of measurement errors on such linearity and Quantisierungsabweichungen; the latter can continue to cause quantization noise.

Expiration

Means for quantizing an analog signal that must first be converted into a discrete-time, value- continuous signal. The signal can be theoretically represented by the multiplication with a Dirac comb. In practice, this sample-and- hold circuits may be used.

To Wertediskretisierung the measuring range of the input variable is divided adjacent intervals in a finite number assigned to each one quantization. The discrete-time signal is now being implemented on the quantization of the individual stages. The boundaries of the quantization are formulated in the framework of Quantisierungstheorems.

Often, the quantized signal is then coded, that is, each quantization level is associated with a unique number. This process is in contrast to the actual quantization reversible. In the reconstruction of the so- encoded values ​​are mapped back into values ​​from the measurement range of the original signal.

The now time and discrete-value signal is called digital signal.

Properties

As a quantizer maps the input signals individually, can be read from the quantization.

The resolution of the quantizer can be described by

• The number of quantization levels,
• The word length, in the sense of number of bits that is at least necessary to represent the quantized values ​​or
• On a linear quantization, the size of the intervals.

The time interval between two successive sampling points is determined by the sampling rate.

As is shown in the quantization of a large amount of input values ​​to a smaller amount, it is not linear and is not reversible, as the various input values ​​can be mapped to the same output value.

With non-linear quantization can improve the dynamic range for non- linear perceived signals (eg audio signals ), particularly at low resolutions.

Quantization is next to the scanning, a step of digitizing (A / D ) conversion of analog signals. The most common and simplest type is the scalar quantization. In each scalar input value is mapped to a scalar output value.

Method

The input value is rounded off or down to the nearest quantization level. Often is imaged on the stage with the smallest distance and therefore has the lowest sum of the quantization error. The quantization function is then:

The step size is at a uniform quantization is a real constant with any value greater than 0 and specifies the length of the interval.

For the illustration on integer intervals, the step size is set to the value 1. If the increment is sufficiently small in relation to the measuring range, the mean square error (MSE) according to the quantization:

Which in this case is equal to the variance. In this context, the root mean square deviation is referred to as a quantization error.

Alternatively, the input value can also be rounded up or down, but then increases the average error.

Lossy compression

In lossy compression method the loss of information from the quantization of the input data is due. An attempt is "unimportant " to remove information by the signal is encoded with a partially reduced resolution.

Popular representatives of such compression techniques are MP3, JPEG and MPEG.