Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
1998-11-16
2001-09-11
Malzahn, David H. (Department: 2121)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
06289367
ABSTRACT:
CROSS-REFERENCES TO RELATED APPLICATIONS
Not Applicable.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
Not Applicable.
BACKGROUND OF THE INVENTION
The present embodiments relate to signal processing, and are more particularly directed to digital signal processing circuits, systems, and methods implementing approximations for logarithm and inverse logarithm.
Digital signal processing is prevalent in numerous types of contemporary technologies, and involves various types of devices, signals, and evaluations or operations. For example, devices involved in signal processing may include a general purpose digital signal processor (“DSP”), an application specific processor, (“ASP”), an application specific integrated circuit (“ASIC”), a microprocessor, or still others. The types of processed signals may include various types of signals, where audio signals are a relevant example for reasons detailed below. Lastly, the operations on these signals may include numerous logic and arithmetic-type operations, where such operations may occur with a general purpose arithmetic logic unit or dedicated hardware/software included within the device performing the signal processing. The present embodiments arise within these considerations, as further explored below.
Given the various device types, signals, and operations involved in signal processing, it is recognized in connection with the present embodiments that the precision involved with some types of signal processing may be less than that required in other contexts. For example, the precision expected of a mathematical calculation performed by a hand held calculator or central processing unit may be considered to define a standard that is relatively high, while the precision required of some other signal processing may be lower than this high standard. One example where lower precision in signal processing may arise is in an audio signal processor or processing system. Such a system may perform various signal processes and ultimately output an audio signal to be played by a speaker or the like. However, since the human ear is forgiving of various signal fluctuations, then likewise the signal processing involved may have a lesser standard of precision than is required of the above-mentioned examples of a hand held calculator or central processing unit. Consequently, the present embodiments have particular application for this and other instances of signal processing that require less than exact signal evaluation.
By way of further background, it is noted that some contemporary digital processing systems implement relatively costly solutions to signal processing. For example, the present embodiments provide approximations to the functions of logarithms and inverse logarithms. Thus, where the present embodiments are not used, alternative systems may require sophisticated arithmetic logic units or the like to perform these logarithmic functions. Such approaches may cause numerous problems, such as increasing device size, complexity, and consequently, device cost. Moreover, in some implementations these increases are simply unacceptable, in which case designs in their entirety may have to be discarded or, at a minimum, considerably altered given the overall system specifications.
In view of the above, there arises a need to address the drawbacks of prior systems which require complex implementations to determine logarithmic functions, and to provide efficient circuits, systems, and methods for determining an acceptable approximation for such functions.
BRIEF SUMMARY OF THE INVENTION
In one embodiment there is a digital signal system for determining an approximate logarithm of a value of x having a base b. The approximate logarithm includes an integer portion and a decimal portion. The system comprises an input for receiving a signal, and circuitry for measuring an attribute of the signal. The attribute relates at least in part the value of x. The system further comprises circuitry for identifying a bounded region within which x falls. The bounded region is one of a plurality of bounded regions, where each of the plurality of bounded regions corresponds to a different value of an integer n and is bounded on a lower side by b
n
and on a higher side by b
n+1
. Additionally, the identified bounded region identifies the integer portion of the approximate logarithm. The system further comprises circuitry for determining the decimal portion of the approximate logarithm by mapping a portion of x to a point along a curve representing an approximation of a portion of an actual logarithm value of x. Other circuits, systems, and methods are also disclosed and claimed, including but not limited to those directed to antilogs.
REFERENCES:
patent: 5365465 (1994-11-01), Larson
patent: 5642305 (1997-06-01), Pan et al.
patent: 5703801 (1997-12-01), Pan et al.
patent: 5801974 (1998-09-01), Park
patent: 5831878 (1998-11-01), Ishida
“Computation of the Base Two Logarithm of Binary Numbers,” IEEE Trans. Electron. Comput., EC-14, pp. 863-867, 1965 (M. Combet, H. Van Zonneveld, and L. Verbeek).
“New Algorithms for the Approximate Evaluation of Hardware of Binary Logarithms and Elementary Functions,” IEEE Trans. Comput., C-21, pp. 1416-1421, 1972 (D. Marino).
“A Note on Base-2 Logarithm Computations,” IEEE Proc., 61, pp. 1519-1520, 1973 (J.C. Majithia and D. Levan).
“A Class of Algorithms for Ln x, Exp x, Sin x, Cos x, Tan&Lgr;-1 x and Cot&Lgr;-1 x, ” IEEE Trans. Electron. Comput., EC-14, pp. 85-86, 1965 (W. H. Specker).
Brady III Wade James
Holmbo Dwight N.
Malzahn David H.
Telecky , Jr. Frederick J.
Texas Instruments Incorporated
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