Digital watermark decoding method

DETAILED DESCRIPTION In the following discussion of an illustrative embodiment, the words "signal" and "image" are used interchangeably to refer to both one, two, and even beyond two dimensions of digital signal.
Examples will routinely switch back and forth between a one dimensional audio-type digital signal and a two dimensional image-type digital signal.
In order to fully describe the details of an illustrative embodiment, it is necessary first to describe the basic properties of a digital signal.
FIG.
1 shows a classic representation of a one dimensional digital signal.
The x-axis defines the index numbers of sequence of digital "samples," and the y-axis is the instantaneous value of the signal at that sample, being constrained to exist only at a finite number of levels defined as the "binary depth" of a digital sample.
The example depicted in FIG.
1 has the value of 2 to the fourth power, or "4 bits," giving 16 allowed states of the sample value.
For audio information such as sound waves, it is commonly accepted that the digitization process discretizes a continuous phenomena both in the time domain and in the signal level domain.
As such, the process of digitization itself introduces a fundamental error source, in that it cannot record detail smaller than the discretization interval in either domain.
The industry has referred to this, among other ways, as "aliasing" in the time domain, and "quantization noise" in the signal level domain.
Thus, there will always be a basic error floor of a digital signal.
Pure quantization noise, measured in a root mean square sense, is theoretically known to have the value of one over the square root of twelve, or about 0.
29 DN, where DN stands for `Digital Number` or the finest unit increment of the signal level.
For example, a perfect 12-bit digitizer will have 4096 allowed DN with an innate root mean square noise floor of .
sup.
- 0.
29 DN.
All known physical measurement processes add additional noise to the transformation of a continuous signal into the digital form