0.8 Signal processing in processing: miscellanea  (Page 2/5)

Economic sound representations

In case of audio signals, the use of dithering aims at reducing the perceptual effect of the error produced by the changes in the quantization resolution, that one typically performs when recording and processing audio signals. For example, when recoding music, more than 16-bits of quantization are usually employed. Furthermore, mathematical operations applied to the signal (as, for instance, simple dynamical variations) require an increasing of the bit depth that is of the number of bits. As soon as one reaches the final product, the audio CD, the number of quantization bits has to be reduced to 16. In each of these consecutives processes of re-quantization one introduces an error, that adds up. In case of a reduction of the numberof bits, it is possible to truncate the values (that is the digits after the decimal point are neglected and set to zero) or round them (that is the decimal number is approximated to the closest integer). In both cases one introduces an error. In particular, when one considers signals with a well defined pitch (as in the case of musical signals), the error becomes periodic-like. From the example of the voice dithering of Wikipedia, the reason of this additional pseudo-periodic noise (i.e. harmonic-like) becomes clear. This distortion corresponds to a buzz-like sound that "follows" the pitch of the quantized sound. The whole result is quite annoying from a perceptual point of view.

In case of audio signals, thus, dithering has the function of transforming thisbuzz-like sound in a background noise similar to a rustling, less annoying from a listening point of view. In [link] an example of some periods of the waveform of a clarinet quantized with 16bits is reported. The result of a reduction of the number of bits to 8 is represented in [link] . It is clearly visible how the reduction of the quantization levels produces series of lines with constant amplitude. The application of dithering generates a further transformation that, how one can see in [link] "breaks" the constant lines by means of the introduction of white noise. The [link] , [link] and [link] represent the Fourier transforms of the sounds of [link] , [link] and [link] , respectively. In the frequecy representation, it is also visible how the change to aquantization at 8 bits introduces improper harmonics ( [link] ) not present in the sound at 16 bit ( [link] ). These harmonics are canceled by the effect of dithering ( [link] ).

There exist also methods that exploit perceptual factors as the fact that our ear is more sensitive in the central region of the audio band and less sensitive in the higher region. This allows one to make the effect of a re-quantization less audible. This is the case of the noise shaping techniques. This method consists in "modeling" the quantization noise. [link] represents the sound of a clarinet re-quantized with 8 bits. A dithering and a noise-shaping were applied to the sound. The result, apparently destructive from the point of view of the waveform, corresponds to a sound, whosespectrum is closer to that of the original sound at 16 bits, excepted for a considerable increasing of energy in the very high frequency region ( [link] ). This high frequency noise produces this "ruffled" waveform, i.e. high energy fast amplitude variations. This noise is anyway not audible. Thus, at a listening test, the final result is better than the previous one.