Claims
- 1. A compact Haar transform apparatus, for executing a spectral transformation corresponding to a sequence of n-bit samples, the compact Haar transform apparatus comprising:
sum-and-truncate logic, configured to generate a plurality of intermediate terms, wherein at most n bits are required to represent each of said plurality of intermediate terms; a plurality of coefficient generators, coupled to said sum-and-truncate logic, configured to generate a plurality of spectral coefficients, wherein at most n+1 bits are required to represent each of said plurality of spectral coefficients.
- 2. The compact Haar transform apparatus as recited in claim 1, wherein pairs of the n-bit samples are summed to produce a first rank of said plurality of intermediate terms.
- 3. The compact Haar transform apparatus as recited in claim 2, wherein pairs of said first rank of said plurality of intermediate terms are summed to produce a second rank of said plurality of intermediate terms.
- 4. The compact Haar transform apparatus as recited in claim 3, wherein a first rank of said plurality of the spectral coefficients is derived by taking differences between pairs of the n-bit samples.
- 5. The compact Haar transform apparatus as recited in claim 4, wherein a second rank of said plurality of the spectral coefficients is derived by taking differences between pairs of said first rank of said plurality of intermediate terms.
- 6. The compact Haar transform apparatus as recited in claim 5, wherein said sum-and-truncate logic truncates the least significant bit of a generated n+1-bit sum to form an n-bit intermediate term.
- 7. The compact Haar transform apparatus as recited in claim 6, wherein said n-bit intermediate term corresponds to one of said plurality of spectral coefficients, said one of said plurality of spectral coefficients indicating whether said generated n+1-bit sum was even or odd.
- 8. The compact Haar transform apparatus as recited in claim 7, wherein said n+1-bit sum is restored by adding the least significant bit of said one of said plurality of spectral coefficients to said n-bit intermediate term.
- 9. The compact Haar transform apparatus as recited in claim 8, wherein said sum-and-truncate logic comprises a plurality of n+1-bit adders.
- 10. The compact Haar transform apparatus as recited in claim 9, wherein said plurality of coefficient generators comprises a plurality of n+1-bit subtractors.
- 11. The compact Haar transform apparatus as recited in claim 10, further comprising:
inverse transform logic, coupled to said plurality of spectral coefficient generators, configured to reproduce the sequence of n-bit samples, wherein each of the n-bit samples is derived from particular spectral coefficients, said particular spectral coefficients being selected based upon an n-bit sample index.
- 12. The compact Haar transform apparatus as recited in claim 11, wherein said inverse transform logic comprises:
a rank decoder, configured to receive said n-bit sample index, and to provide one of said particular spectral coefficients, said one of said particular specific spectral coefficients corresponding to a rank of the spectral transformation; a coefficient negator, coupled to said rank decoder, configured to negate said one of said particular spectral coefficients based upon the state of a bit of said n-bit sample index; and LSB restoral logic, coupled to said rank decoder, configured to add a least significant bit of said one of said particular spectral coefficients into an n-bit sample computation.
- 13. An apparatus for executing a compact Haar transform, comprising:
an index signal, for indicating a specific n-bit sample, said specific n-bit sample being one of a sequence of n-bit samples corresponding to the compact Haar transform; and inverse transform logic, coupled to said index signal, for computing said specific n-bit sample, wherein said specific n-bit sample is derived from selected spectral coefficients, and wherein at most n+1 bits are required to represent each of said selected spectral coefficients.
- 14. The apparatus as recited in claim 13, wherein said inverse transform logic comprises:
a rank decoder, for decoding said index signal to provide one of said selected spectral coefficients, said one of said selected spectral coefficients corresponding to a compact Haar spectral rank.
- 15. The apparatus as recited in claim 14, wherein said inverse transform logic further comprises:
coefficient negation logic, coupled to said rank decoder, for negating said one of said selected spectral coefficients based upon the state of a bit of said index signal, wherein the state of said bit of said index signal indicates whether a Haar basis function corresponding to said one of said selected spectral coefficients is positive or negative; and LSB restoral logic, coupled to said rank decoder, for adding a least significant bit of said one of said selected spectral coefficients into an n-bit sample computation, said n-bit sample computation being required to compute said n-bit sample.
- 16. The apparatus as recited in claim 15, wherein said rank decoder comprises a read-only memory (ROM).
- 17. The apparatus as recited in claim 16, wherein said ROM comprises memory locations, each of said memory location having a width in bits that corresponds to the number of bits required to represent an associated spectral coefficient.
- 18. The apparatus as recited in claim 15, further comprising:
forward transform logic, for generating said selected spectral coefficients from said sequence of n-bit samples.
- 19. The apparatus as recited in claim 18, wherein said forward transform logic comprises:
a plurality of coefficient generators, for computing said selected spectral coefficients. sum-and-truncate logic, coupled to said coefficient generators, for computing intermediate terms, wherein at most n bits are required to represent each of said intermediate terms.
- 20. The apparatus as recited in claim 19, wherein said sum-and-truncate logic truncates the least significant bit of a particular n+1-bit intermediate sum to form a particular n-bit intermediate term.
- 21. The apparatus as recited in claim 20, wherein said particular n-bit intermediate term corresponds to a particular spectral coefficient, said particular spectral coefficient indicating whether said particular n+1-bit intermediate sum is even or odd.
- 22. The apparatus as recited in claim 21, wherein said n+1-bit intermediate sum is restored in an inverse transformation by said LSB restoral logic.
- 23. The apparatus as recited in claim 22, wherein said sum-and-truncate logic comprises an n+1-bit adder.
- 24. The apparatus as recited in claim 23, wherein said plurality of coefficient generators comprises a plurality of n+1-bit subtractors.
- 25. A computer program product for use in describing a compact Haar transform circuit, the computer program product comprising:
a storage medium, having computer readable instructions embodied thereon, for causing a computer upon which said computer readable instructions are executed to describe the compact Haar transform circuit, said computer readable instructions comprising:
first instructions, for causing said computer to describe forward Haar transform logic, said forward Haar transform logic being configured to compute spectral coefficients that correspond to a sequence of n-bit data samples, wherein at most n+1 bits are required to represent each of said spectral coefficients.
- 26. The computer program product as recited in claim 25, wherein said forward Haar transform logic comprises:
sum-and-truncate logic, for computing intermediate terms, wherein at most n bits are required to represent each of said intermediate terms. a plurality of coefficient generators, coupled to said sum-and-truncate logic, for generating said spectral coefficients.
- 27. The computer program product as recited in claim 26, wherein said sum-and-truncate logic truncates the least significant bit of a generated n+1-bit sum to form an n-bit intermediate term.
- 28. The computer program product as recited in claim 27, wherein said n-bit intermediate term corresponds to one of said spectral coefficients, said one of said spectral coefficients indicating whether said generated n+1-bit sum is even or odd.
- 29. A computer program product for use in designing, simulating, fabricating, or testing a compact Haar transform circuit, the computer program product comprising:
a storage medium, having computer readable instructions embodied thereon, for causing a computer upon which said computer readable instructions are executed to describe the compact Haar transform circuit, said computer readable instructions comprising:
first instructions, for causing said computer to describe inverse Haar transform logic, said inverse Haar transform logic being configured to compute n-bit samples, wherein each of said n-bit samples is derived from spectral coefficients, and wherein at most n+1 bits are required to represent each of said spectral coefficients.
- 30. A computer program product as recited in claim 29, wherein said inverse transform logic comprises:
a rank decoder, for receiving an index signal from a source thereof, and for providing one of said spectral coefficients, said one of said specific spectral coefficients corresponding to a rank of a compact Haar spectrum; a coefficient negator, coupled to said rank decoder, for negating said one of said spectral coefficients based upon the state of a bit of said index signal; and LSB restoral logic, coupled to said rank decoder, for adding a least significant bit of said one of said spectral coefficients into an n-bit sample computation, said n-bit sample computation being required to generate a particular n-bit sample.
- 31. A method for executing a forward compact Haar transform, comprising:
a) providing a sequence of M n-bit data samples; and b) generating corresponding n-bit intermediate spectral terms.
- 32. The method as recited in claim 31, wherein said generating comprises:
i) summing pairs of the n-bit data samples to form n+1-bit intermediate sums corresponding to a first rank of a compact Haar spectrum; and ii) truncating the least significant bits of each of the n+1-bit intermediate sums corresponding to the first rank of the compact Haar spectrum to form n-bit intermediate spectral terms corresponding to the first rank of the compact Haar spectrum.
- 33. The method as recited in claim 32, wherein said generating further comprises:
iii) summing pairs of the form n-bit intermediate spectral terms corresponding to the first rank of the compact Haar spectrum to form n+1-bit intermediate sums corresponding to a next rank of the compact Haar spectrum; and iv) truncating the least significant bits of each of the n+1-bit intermediate sums corresponding to the next rank of the compact Haar spectrum to form n-bit intermediate spectral terms corresponding to the next rank of the compact Haar spectrum.
- 34. A method for executing a forward compact Haar transform of a sequence of n-bit data samples, comprising:
a) generating n-bit intermediate spectral terms; and b) computing n+1-bit spectral coefficients.
- 35. The method as recited in claim 34, wherein said generating comprises:
i) summing pairs of the n-bit data samples to form n+1-bit intermediate sums corresponding to a first rank of a compact Haar spectrum; and ii) truncating the least significant bits of each of the n+1-bit intermediate sums corresponding to the first rank of the compact Haar spectrum to form n-bit intermediate spectral terms corresponding to the first rank of the compact Haar spectrum.
- 36. The method as recited in claim 35, wherein said generating further comprises:
iii) summing pairs of the form n-bit intermediate spectral terms corresponding to the first rank of the compact Haar spectrum to form n+1-bit intermediate sums corresponding to a next rank of the compact Haar spectrum; and iv) truncating the least significant bits of each of the n+1-bit intermediate sums corresponding to the next rank of the compact Haar spectrum to form n-bit intermediate spectral terms corresponding to the next rank of the compact Haar spectrum.
- 37. The method as recited in claim 36, wherein said computing comprises:
i) taking the difference between pairs of the n-bit data samples to form n+1-bit spectral coefficients corresponding to the first rank of the compact Haar spectrum; ii) taking the difference between pairs of n-bit intermediate spectral terms corresponding to the first rank of the compact Haar spectrum to form n+1-bit spectral coefficients corresponding to the next rank of the compact Haar spectrum.
- 38. A method for executing an inverse compact Haar transform, comprising:
a) decoding an index to select n+1-bit spectral coefficients, the n+1-bit spectral coefficients being required to compute a specific n-bit data sample; b) negating those n+1-bit spectral coefficients whose corresponding Haar basis function is negative for the index in a); c) computing a sum of the negated n+1-bit spectral coefficients with the n+1-bit spectral coefficients selected in a) which are not negated by b); and d) adding the least significant bits of all of the n+1-bit spectral coefficients selected in a) to the sum computed in c).
- 39. The method as recited in claim 38, further comprising:
e) dividing the result of d) by 2 to generate the specific n-bit data sample.
- 40. The method as recited in claim 39, further comprising:
f) altering the value of the index to indicate a next n-bit data sample; and g) repeating a) through f) until all n-bit data samples within an original sequence are computed.
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is related to co-pending U.S. patent application Ser. No. ------ entitled Apparatus and Method for Direct Digital Frequency Synthesis, Docket Number SLD:002, which is hereby incorporated by reference in its entirety for all purposes.
Continuations (1)
|
Number |
Date |
Country |
Parent |
09390899 |
Sep 1999 |
US |
Child |
10340656 |
Jan 2003 |
US |