Noise shaping

The term noise shaping ( engl. noise shaping ) refers to a process in which the quantization noise of a digital signal is more concentrated in certain frequency ranges, and it leads to a shift of the noise energy in the frequency spectrum. The noise energy itself is not weakened here - rather, the noise is "pushed" by the process only in frequency ranges that are for further signal processing without meaning. These frequency ranges can then be damped, for example by means of filters and thus the noise can be suppressed.

General

The noise shaping is applied not only to the above-mentioned quantization noise, but also the so-called rounding noise. Digital filters consist of arithmetic units that have only a limited, finite resolution of the numerical representation. This results in the calculations to inevitable rounding the calculated results, which can make similarly to the quantization noise as a disturbance in the signal noticeable. To minimize this noise rounding well as methods of noise shaping to apply.

Operation

Spectral shaping the quantization functions in principle in that a small signal variation occurs at the source at which the quantization ( AD converter) or rounding ( digital filters ), this so-called error signal is detected, and most of the way of a filter to the input of quantization is returned inverted. The quantization noise, not the useful signal, thereby negatively fed back. Thus, when, for example, a sample value having a rounding error of -1 / 4 bit in the representation of the error value is added in the next Abstastwert with inverted sign in addition to the input signal. In this case, the feedback filter is a delay by one sample, the easiest way of noise shaping.

So now at all fractions can be detected by a quantization step as 1/4 bit for error, the arithmetic unit in signal processing via a correspondingly greater dynamic (resolution) must have as the remaining signal paths. Partly for this reason, most of the batteries have in common today signal processors the opportunity to an expanded number representation on, and thus offer the possibility to minimize the rounding noise in digital filters using noise shaping. In hardware- based digital filters implemented in FPGAs for example, for appropriate additional signal paths must be provided.

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

Noise shaping in audio engineering

In the digital audio technology, the noise shaping is filtered by psychoacoustic requirements to make it in the overall impression " quieter " and less intrusive. Thus, the noise power can be shifted in frequency areas in audio engineering, in which the human ear is less sensitive. This is for example the range of 16 kHz to 20 kHz, which is also only poorly or not at all perceived by older listeners, and in the most part anyway are in the case of music no important signal components more.

The filters in the audio range comply with various, often developed by company policy, mostly on the inverse ear curve of the human ear are based (see Fletcher -Munson curves), are examples of the POW -R algorithm of the POW -R Consortium LLC and super bit mapping algorithm from Sony.

Noise shaping is usually applied in audio technology in conjunction with dither - thereby optimizing the Signal-/Rauschabstandes is achieved.

The filtering is performed on a limited LOOP, in most cases an FIR filter, and is calculated according to the " method of least squares ."

The noise shaping can be applied independent of the existing material, or adaptive done ( depends on material ). Through adaptive noise shaping, which is carried out by continuously changing the filter coefficients depend on the available material, can achieve better results (ie, an improvement in the signal to noise ratio ). However, such a filter is not nullphasig.

Noise Shaping takes place mainly in combination with oversampling ( oversampling ), which both terms are often mistakenly used as a synonym. Especially with the delta - sigma converter noise shaping is essential, as in these systems the quantization error is relatively large precipitates. By correspondingly high oversampling, the quantization noise may even be pushed partly in the frequency ranges which can be completely separated from the useful signal with a digital filter hereinafter.

One method that is between dithering and noise shaping, the UV22 - HR algorithm of Apogee Electronics. Here, the added dither is spectrally shaped before its incorporation and added in the upper frequency range (near the Nyquist frequency).