Adds dither to the input data in preparation for (re-)quantisation. Supports a variety of standard dithering methods including noise-shaping with a user-specified custom FIR shaping filter.

Implements exactly the same dither methods as provided in the wavout function. However, no quantization is performed after adding the dither, thereby leaving the user with the flexibility in the choice of quantization method (by contrast, the wavout function always applies PCM quantization directly after the dither, then writes the results to a WAV file).

y=audiodither(x,bits);

matrix of input data. For example, if x is read from a WAV file using wavin, then the dimensions will be (Number of samples * Number of Channels). It is assumed that the input data is within the floating-point range -1:+1 (i.e. for correct computation of dither amplitude).

a structure containing the following fields:

• QuantizationBits field (i.e. bits.QuantizationBits): quantization bit-depth for determining the dither amplitude [default value of 16]
• DitherMethod field (i.e. bits.DitherMethod): numerical value indicating which type of dithering method is applied before quantisation. Possible values are:
  • 0: no dither
  • 1: rectangular PDF dither, with a peak-to-peak amplitude of 1*LSB
  • 2: [default] triangular PDF dither, with a peak-to-peak amplitude of 2*LSB
  • 3: triangular PDF with first-order high-pass noise shaping
  • 4: triangular PDF with custom FIR noise shaping filter
• DitherGain field (i.e. bits.DitherGain): gain applied to amplitude of dither [default value of 1] i.e. rectangular PDF dither has amplitude of LSB*DitherGain, and triangular PDF dither has amplitude of 2*LSB*DitherGain.
• NoiseShapeGain field: (i.e. bits.NoiseShapeGain): gain applied to the feedback path in the case where where noise shaping is activated (i.e. for DitherMethod values greater than 2) [default value of 1]
• NoiseShapeFIR field: (i.e. bits.NoiseShapeFIR): vector of coefficients for custom noise shaping filter (only valid for DitherMethod = 4). An arbitrary filter of any order may be specified. Default value is the following fifth order filter: [2.033 -2.165 1.959 -1.590 0.6149] taken from ref [1] p 851 (note: designed for 44.1 kHz).

matrix of output data with dither applied. Note: clipping is applied post-dither to prevent the data from exceeding the range -1:+1.

See the M-Pack 1 overview for a detailed discussion of the dithering and noise-shaping techniques used in this m-function.

Ref[1]: "Minimally Audible Noise Shaping", Stanley P. Lipshitz, John Vanderkooy, and Robert A. Wannamaker, J. Audio Eng. Soc., Vol. 39, No. 11, November 1991.

For a practical audible demonstration of the applications of dither, refer to the examples section of the wavout help page.

The following examples illustrate the usage of the audiodither function (and in doing so, serves to demonstrate graphically the effects of dither). All the code samples can be found in the test script xmplaudiodither.m.

For the purposes of demonstration, a low-level signal (i.e. with an amplitude comparable with the quantization step size) is preferable. Namely, consider the following sinusoidal test signal, x, with a peak-to-peak amplitude of 6 LSB (where 1 LSB corresponds to the quantization step size):

The top plot shows the undithered case. The quantization error is clearly seen to be strongly correlated with the signal in a nonlinear manner. This modulation of the quantization noise by the signal leads to highly undesirable audible distortion. The purpose of the dither is to reduce this distortion.

The second and third plots (from the top) show the beneficial effect of additive rectangular and triangular dither, respectively. The correlation between the signal and the noise has been reduced in both cases, though at the expense of added background noise. The suppression of the nonlinear modulation is generally desirable (from an auditory point of view), even at the expense of the additional noise. The choice between rectangular and triangular dither depends on the signal bandwidth and the sample rate. In most applications, triangular dither is preferable.

The fourth and fifth plots (from the top) show the effect of first-order highpass and of 5-coefficient FIR feedback noise-shaped dither, respectively. The added background noise is noticeably greater, especially for the 5-coefficient FIR noise-shaper (lowest plot, noting that the y-axis scale is greater). However, as explained in the M-Pack 1 overview, this is to be expected. The point is that even though the actual noise level is higher, the perceived noise will be lower, assuming that the noise-shaping filter is designed such as to shift the quantization noise into the region of the spectrum where the human hearing is at its least sensitive. Refer to the examples section of the wavout help page for an audio demonstration of the effectiveness of noise-shaping in a "real-world" example.