Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
1999-06-11
2001-12-11
Mai, Tan V. (Department: 2121)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
C708S276000
Reexamination Certificate
active
06330578
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and apparatus for digitally representing a waveform. More particularly, aspects of the invention are directed to digitally representing a waveform as phase-interleaved first and second sets of samples, the ordinates of adjacent samples differing differentially. The invention has particular application in numerically controlled oscillators.
2. Background
Numerically controlled oscillators (NCOs) are components in digital communication systems, including digital transceivers. Incorporated into a digital mixer, an NCO provides digitally controlled frequency synthesis and frequency tuning.
At its heart, an NCO includes a read only memory (ROM) lookup table that stores a waveform's peak values (ordinates) at discrete phase intervals (abscissa). When the lookup table is addressed in a predetermined sequence at a predetermined clock-rate, the lookup table outputs a sequence of peak values that discretely reconstruct the waveform at a predetermined frequency. Effectively, the lookup table maps waveform phase into amplitude at discrete intervals.
The precision of the waveform representation increases with finer phase resolution and finer amplitude quantization. However, precision comes at a cost. Finer phase resolution requires that the size of the lookup table, and hence the ROM, be increased to store more ordinates. Similarly, finer amplitude quantization requires that the size of the lookup table, and hence the ROM, be increased to store ordinates encoded with more bits.
An important design criterion is to minimize the size of the ROM lookup table, while maintaining adequate precision in representing a waveform.
SUMMARY OF THE INVENTION
Aspects of the present invention are directed toward providing a compact yet precise digital representation of a waveform, suitable for efficient storage in a lookup table, including a read only memory.
Embodiments of the present invention take advantage of a number of techniques to achieve compact waveform representation. Correlation between adjacent ordinates is exploited through differential pulse coding. A difference function is exploited to define each ordinate as the concatenation of a value stored in a lookup table cell plus the address of that lookup table cell. Waveform symmetry is exploited to avoid storing ordinates that can instead be calculated as symmetrical mappings of previously stored ordinates.
Thus, according to one embodiment of the invention, there is provided a method for digitally representing a waveform segment defined by discrete ordered pairs of abscissae and ordinates, the ordered pairs being divided into an odd set and an even set, the method including: for each even abscissa, generating a difference code representing a difference between an even ordinate paired with the even abscissa and the even abscissa, whereby the even ordinate paired with the even abscissa is represented as the sum of the even abscissa and the corresponding difference code; and for each odd abscissa, generating a differential code representing a differential between an odd ordinate paired with the odd abscissa and an even ordinate corresponding to the odd abscissa, whereby the odd ordinate paired with the odd abscissa is represented as the sum of the corresponding even ordinate and the corresponding differential code.
Desirably, the even ordinate corresponding to the odd abscissa is paired with an even abscissa that is proximate to, or less than and adjacent to, or even immediately preceding the odd abscissa.
Generating a difference code preferably includes: bit-shifting the even abscissa to generate a bit-shifted even abscissa; and generating a difference code representing a difference between an even ordinate paired with the even abscissa and the bit-shifted even abscissa.
Advantageously, the method might further include: storing each difference code in a respective even memory cell addressable by the respective even abscissa; and storing each differential code in a respective odd memory cell addressable by the respective odd abscissa. The method might still further include concatenating into a combined memory cell an odd memory cell addressable by an odd abscissa and an even memory cell addressable by an even abscissa, the odd abscissa corresponding to and the even abscissa being paired with the same even ordinate.
The method might extend to digitally representing a second waveform segment that is symmetrical to the waveform segment, the method including: symmetrically mapping discrete ordered pairs that define the waveform segment into the second waveform segment.
Desirably, the method includes: ordinally selecting each abscissa; for each even selected abscissa, generating an ordinate as the sum of the selected abscissa plus the corresponding difference code; and for each odd selected abscissa, generating an ordinate as the sum of the selected abscissa plus the corresponding ordinate plus the corresponding differential code.
According to another aspect of the invention, there is provided an apparatus for digitally representing a waveform segment defined by discrete ordered pairs of abscissae and ordinates, the ordered pairs being grouped into an odd set and an even set, including: an even signal generator for generating for each even abscissa a difference code representing a difference between an even ordinate paired with the even abscissa and the even abscissa, whereby the even ordinate paired with the even abscissa is represented as the sum of the even abscissa and the corresponding difference code; and an odd signal generator for generating for each odd abscissa a differential code representing a differential between an odd ordinate paired with the odd abscissa and an even ordinate corresponding to the odd abscissa, whereby the odd ordinate paired with the odd abscissa is represented as the sum of the corresponding even ordinate and the corresponding differential code.
According to another aspect of the invention, there is provided an apparatus for digitally representing a waveform segment defined by discrete ordered pairs of abscissae and ordinates, the ordered pairs being grouped into an odd set and an even set, comprising: a module for generating for each even abscissa a difference code representing a difference between an even ordinate paired with the even abscissa and the even abscissa, whereby the even ordinate paired with the even abscissa is represented as the sum of the even abscissa and the corresponding difference code; and a module for generating for each odd abscissa a differential code representing a differential between an odd ordinate paired with the odd abscissa and an even ordinate corresponding to the odd abscissa, whereby the odd ordinate paired with the odd abscissa is represented as the sum of the corresponding even ordinate and the corresponding differential code.
According to yet another embodiment of the invention, there is provided a storage medium for storing a digital representation of a waveform segment defined by discrete ordered pairs of abscissae and ordinates, the ordered pairs being grouped into an odd set and an even set, comprising: for each even abscissa, a difference code representing a difference between an even ordinate paired with the even abscissa and the even abscissa, whereby the even ordinate paired with the even abscissa is represented as the sum of the even abscissa and the corresponding difference code; and for each odd abscissa, a differential code representing a differential between an odd ordinate paired with the odd abscissa and an even ordinate corresponding to the odd abscissa, whereby the odd ordinate paired with the odd abscissa is represented as the sum of the corresponding even ordinate and the corresponding differential code.
According to still another embodiment of the invention, there is provided a signal digitally representing a waveform segment defined by discrete ordered pairs of abscissae and ordinates, the ordered pairs being grouped into an odd set and an even set, the signal i
Morris Bradley John
Savin Cristian Emanuel
Mai Tan V.
Nortel Networks Limited
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