Non-uniform quantization

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Instruction Manual (German)

non uniform quantization.
Non-uniform quantization

The lesson learned from the uniform quantization experiment is that uniform quantization produces poor quality for small sounds. In this approach, non-uniform quantization should overcome this shortcomming. Logarithmic compressing and expanding (companding) improves the Signal-to-quantization-noise ratio for signals with a large dynamic range like speech. Logarithmic curves like the European A-law are troublesome to implement but can be approximated using piecewise linear segments. In this online simulation app, 13 straight line segments are used - 13-Segment-Kennlinie.

Figure out these questions using the online simulation:

Listen to signals using the audio play measure (right click on wire):

External links

Companding: Logarithmic Laws, Implementation, and Consequences

https://en.wikipedia.org/wiki/Companding

Click on source symbol

m(t)

Select and adjust input signal

signal generator

Click on Quantizer

quantizer

Vary the bit per sample resolution

quantizer properties

Right click on wire

v(t)
v(t) select

Open any measure for a signal

quantized signal
source signal
compressed sine
6bit quantized compressed sine
A sine signal is processed by the compressor to amplify the parts with small amplitudes.
The same signal after a 6-bit quantization.
expanded sine
probability density total error
Finally the expanded signal. You can see a much finer resolution at low signal levels.
Probability density of the total error.
comparison uniform
comparison nonuniform
For comparison here is again a uniform quantized signal.
And here is the same signal processed through a non uniform quantization.
quant diagram
Signal-to-quantization-noise ratios of uniform and non-uniform quantization.