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Chapter 11

Quantization

Three lessons in Part IV, From analog to digital. Read them in order, or start anywhere: a prerequisite is a link, never a gate.

Start with 11.1
0 of 3 read1 on the essential pathabout 52 minutes

Lessons in this chapter

Two stacked panels against time in seconds, 0 to 8. Top: a ramp from −1 to 1, the input x, and its 3-bit staircase, the output x_q, over 8 faint level lines. Bottom: the error e = x_q − x, a sawtooth between dashed lines at ±Δ/2 = ±0.125. The whole ramp is drawn. Input 1.000, output 0.875, mean square of error ÷ Δ² 0.083.Two stacked panels against time in seconds, 0 to 8. Top: a ramp from −1 to 1, the input x, and its 3-bit staircase, the output x_q, over 8 faint level lines. Bottom: the error e = x_q − x, a sawtooth between dashed lines at ±Δ/2 = ±0.125. The whole ramp is drawn. Input 1.000, output 0.875, mean square of error ÷ Δ² 0.083.

Lesson 1 Essential15 minYou are hereRead

Quantization & noise

Round a signal to B bits, watch the error stay within half a step, and see why each bit adds about 6 dB of SNR.

A gradient from dark to light, 256 pixels wide: stored with 8 shades after adding a little noise: fine grain and no bands. Below, the brightness of the top row against position, 0 to 255 pixels. Shades available: 8.A gradient from dark to light, 256 pixels wide: stored with 8 shades after adding a little noise: fine grain and no bands. Below, the brightness of the top row against position, 0 to 255 pixels. Shades available: 8.

Lesson 215 minYou are hereRead

Dither

Add a little noise before rounding and see why the error stops following the signal, why triangular noise keeps the hiss steady, and what it costs.

Oversampling ratio 16: 16 slices each hold 1/16 of the error's power. The first slice is the band we keep; the rest are removed by the digital low-pass. Noise in the band −12.04 dB, total noise 0.00 dB.Oversampling ratio 16: 16 slices each hold 1/16 of the error's power. The first slice is the band we keep; the rest are removed by the digital low-pass. Noise in the band −12.04 dB, total noise 0.00 dB.

Lesson 322 minYou are hereRead

Oversampling and noise shaping

See why sampling faster gains 3.01 dB per doubling, and how feeding the error back pushes it up in frequency, where a filter removes it.

After this chapter

Where to go next.

The chapters either side, and the rest of Part IV in the library.

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