Noise shaping

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The term noise shaping (engl. Noise shaping ) refers to a process in which the quantization noise of a digital signal in certain frequency ranges is more concentrated and thus a shift in the noise energy in the frequency spectrum occurs. The noise energy itself is not weakened - rather, the process “pushes” the noise into frequency ranges that are irrelevant for further signal processing. These frequency ranges can then be attenuated, for example by means of filters , and thus the noise can be suppressed.

General

The noise shaping is applied not only to the quantization noise mentioned above, but also to the so-called rounding noise. Digital filters consist of arithmetic units that have only a limited, finite resolution in the number representation. As a result, the calculations inevitably round off the calculated results, which, like the quantization noise, can become noticeable as a disturbance in the signal. Noise shaping methods are also used to minimize this rounding noise.

Noise Shaping.jpg

functionality

The spectral shaping of the quantization noise works in principle that this so-called error signal is detected at the source at which a small signal deviation occurs due to the quantization ( AD converter ) or rounding ( digital filter ) and usually via a filter to the input of the Quantization level is returned inverted. The quantization noise, not the useful signal , is thus fed back negatively . If, for example, a sample value has a rounding error of −1/4 bits in the representation, this error value is added to the input signal for the next sample value with an inverted sign . In this case the feedback filter is only a time delay of one sample, the simplest way of noise shaping.

So that even fractions of a quantization step, such as B. 1/4 bit, can be detected as an error, the arithmetic unit must have a correspondingly greater accuracy (word length) than the remaining signal paths. For this reason, among other things, the accumulators in signal processors commonly used today usually have the option of an extended number representation and thus offer the possibility of minimizing the rounding noise in digital filters by means of noise shaping. In hardware-based digital filters, implemented for example in FPGAs , corresponding additional signal paths must be made available for this.

By appropriate selection of the filter for the error signal in the feedback branch and corresponding time delays, the quantization noise can thus be spectrally shifted and thus shaped. There are various complex higher-order feedback filters for practical implementations.

Noise shaping in audio technology

In digital audio technology , the noise shaping is also filtered according to psychoacoustic specifications in order to make the overall impression “quieter” and less intrusive. In audio technology, for example, the noise energy can be shifted to frequency ranges in which the human ear is less sensitive. This is, for example, the range from 16 kHz to 20 kHz, which older listeners can only perceive poorly or not at all, and in which, in the case of music, there are usually no more important signal components.

The filters in the audio sector correspond to various specifications, often developed by companies, which are mostly based on the inverse hearing curve of the human ear (see Fletcher-Munson curves ), examples are the POW-R algorithm of the POW-R Consortium LLC and the Sony's super bit mapping algorithm .

In audio technology, noise shaping is mostly used in conjunction with dither - this optimizes the signal-to-noise ratio .

The filtering takes place via a limited loop loop, in most cases an FIR filter , and is calculated using the “ least squares method ”.

Noise shaping can be used independently of the material in question, or it can be done adaptively (depending on the material). With adaptive noise shaping, which is carried out by constantly changing filter coefficients depending on the material present, better results can be achieved (ie an improvement in the signal-to-noise ratio). However, such a filter is no longer zero phase.

Noise shaping is used mainly in combination with oversampling ( oversampling instead), whereby both terms falsely mostly as synonymous needed. Noise shaping is essential, especially with the delta-sigma converter , since the quantization error is relatively large in these systems . With a correspondingly high oversampling, the quantization noise can even be partially shifted into frequency ranges that can then be completely separated from the useful signal with a digital filter.

A method that lies between dithering and noise shaping is the UV22-HR algorithm from Apogee Electronics. The added dither is spectrally shaped before it is added and added in the upper frequency range (close to the Nyquist frequency ).

literature

  • Jerrold Goodwin: Criteria for Synthesizing Narrowband Digital Dither at Nyquist . In AES Session paper. # F-1-1. Audio Engineering Society , New York NY 1990
  • Ken C. Pohlmann: Principles of Digital Audio . 4th edition. McGraw-Hill, New York NY and others 2000, ISBN 0-07-134819-0 ( McGraw-Hill video / audio professional )
  • Werner Verhelst, Dreten Koning: Least Squares Theory and Design of Optimal Noise Shaping Filters . In Virtual synthetic and entertainment audio . Proceedings of the AES 22nd international conference, 2002 June 15 - 17, Espoo, Finland. Audio Engineering Society, New York NY 2002, ISBN 0-937803-48-0 , pp. 216–222, online (PDF; 138 kB)
  • John Watkinson: The Art of Digital Audio . 3. Edition. Focal Press, Oxford et al. 2001, ISBN 0-240-51587-0

Individual evidence

  1. ↑ Eberhard Sengpiel: Fletcher-Munson is not Robinson-Dadson (PDF; 299 kB)

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