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Concept
Noise shaping
Summary
Noise shaping is a technique typically used in digital audio, , and video processing, usually in combination with dithering, as part of the process of quantization or bit-depth reduction of a digital signal. Its purpose is to increase the apparent signal-to-noise ratio of the resultant signal. It does this by altering the spectral shape of the error that is introduced by dithering and quantization; such that the noise power is at a lower level in frequency bands at which noise is considered to be less desirable and at a correspondingly higher level in bands where it is considered to be more desirable. A popular noise shaping algorithm used in image processing is known as ‘Floyd Steinberg dithering’; and many noise shaping algorithms used in audio processing are based on an ‘Absolute threshold of hearing’ model.
Noise shaping works by putting the quantization error in a feedback loop. Any feedback loop functions as a filter, so by creating a feedback loop for the error itself, the error can be filtered as desired.
For example, consider the feedback system:
where y[n] is the output sample value that is to be quantized, x[n] is the input sample value, n is the sample number, and e[n] is the quantization error introduced at sample n:
In this model, when any sample's bit depth is reduced, the quantization error between the quantized value and the original value is measured and stored. That "error value" is then re-added into the next sample prior to its quantization. The effect is that the quantization error is low-pass filtered by a 2-sample boxcar filter (also known as a simple moving average filter). As a result, compared to before, the quantization error has lower power at higher frequencies and higher power at lower frequencies.
Note that we can adjust the cutoff frequency of the filter by modifying the proportion, b, of the error from the previous sample that is fed back:
More generally, any FIR filter or IIR filter can be used to create a more complex frequency response curve. Such filters can be designed using the weighted least squares method.
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Ontological neighbourhood
Related concepts (11)
Audio bit depth
In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample. In basic implementations, variations in bit depth primarily affect the noise level from quantization error—thus the signal-to-noise ratio (SNR) and dynamic range.
Audio system measurements
Audio system measurements are a means of quantifying system performance. These measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment. Maintenance engineers make them to ensure equipment is still working to specification, or to ensure that the cumulative defects of an audio path are within limits considered acceptable. Audio system measurements often accommodate psychoacoustic principles to measure the system in a way that relates to human hearing.
Pulse-code modulation
Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the amplitude of the analog signal is sampled at uniform intervals, and each sample is quantized to the nearest value within a range of digital steps. Linear pulse-code modulation (LPCM) is a specific type of PCM in which the quantization levels are linearly uniform.