Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
1998-08-11
2001-01-09
Malzahn, David H. (Department: 2787)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
06173301
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to a method for generating a signal amplitude behaving according to a desired function; in said method amplitude is generated digitally and variable data of the function is used as address data.
The invention also relates to a converter for generating a signal amplitude behaving according to a desired function, the converter being arranged to generate the amplitude digitally and to use variable data of the function as address data.
BACKGROUND OF THE INVENTION
In Direct Digital Synthesis (DDS), desired signal behaviour is achieved by converting digital phase data or other variable data to digital amplitude data, for instance by means of look-up tables. The digital amplitude data can then be converted to an analog amplitude by a digital-to-analog converter, or the amplitude data can be further used e.g. for signal phase or frequency processing.
A sine form signal converted from phase data represents a typical DDS conversion. The simplest way to perform the conversion is to store amplitude values of a sine function in a ROM memory (Read Only Memory) functioning as a look-up table, said values being indicated by the phase data. The use of look-up table alone will, however, lead to extensive deployment of memory which, in turn slows down the converter and the frequency of the signal obtained from the converter.
To reduce the need for memory, it is possible to approximate the function according to which the amplitude is to behave. One alternative is to use the Taylor series expansion disclosed in U.S. Pat. No. 4,905,177. From the series expansion are taken into account three first terms, which are used for making the conversion. An impairment of the method is that it requires a third, non-linear term and a multiplier for performing multiplication. Due to such shortcomings, the solution is slow.
SUMMARY OF THE INVENTION
An object of the present invention is thus to provide a solution which applies an amplitude according to a desired function in an approximative manner and which uses neither non-linear terms nor multiplication.
This is achieved with a method of the type described in the preamble, characterized by representing a desired amplitude behaviour in an approximative manner by means of a predetermined number N of piecewise straight lines, an slope and a constant term of which are stored, said straight lines being generated using a linear regression or the like and comprising a predetermined number M of variable values; dividing address data in two parts, a first part functioning as an address for the slope and the constant term of each straight line and a second part corresponding to a variable value on each piecewise straight line; converting the addresses of the second part of the address data to negative and positive variable values of the straight lines so that an address substantially in the middle of the second part of the address data becomes a variable value, which is preferably zero; selecting, by means of the first part of the address data, the slope and the constant term of each generated approximative straight line and selecting, by means of the second part, a variable value on a piecewise straight line; generating, by means of the variable value and the slope, a coefficient term of the piecewise straight line; generating a desired amplitude value by summing the coefficient term and the constant term of the piecewise straight line.
This is achieved with a method of the type described in the preamble, characterized by generating, by means of straight lines, a piecewise linear approximation of a function g(z)=f(z)−tz, where f(z) is a function according to which the amplitude is to behave, z is a variable value and t is a constant, said approximation comprising a predetermined number N of straight lines, an slope and a constant term of which are stored; said straight lines being generated by a linear regression or the like and comprising a predetermined number M of variable values; dividing address data in two parts, a first part functioning as an address for the slope and the constant term and for the first part tz of the address data, multiplied by the constant, in each straight line, and a second part corresponding to a variable value on each piecewise straight line; converting addresses of the second part of the address data to negative and positive variable values so that an address substantially in the middle of the address data becomes a variable value, which is preferably zero; selecting, by means of the first part of the address data, the slope, the constant term and the first part tz of the address data, multiplied by the constant, in each generated, approximative straight line, and selecting, by means of the second part, a variable value on the piecewise straight line; generating, by means of the variable value and the slope determined by the second part of the address data, an slope of the piecewise straight line; generating a desired amplitude value by summing the coefficient term, the constant term and the first part tz of the address data, multiplied by the constant, of the piecewise straight line.
A converter of the invention is characterized in that the converter comprises a memory for describing the behaviour of an amplitude according to a desired function on approximatively piecewise straight lines, with an slope and a constant term being stored in a memory, said straight lines being generated by a linear regression or the like and comprising a predetermined number of variable values; means for dividing the address data in two parts, a first part determining the slope and the constant term of each generated approximative straight line, and a second part corresponding to variable values of each piecewise straight line; means for converting addresses of the second part of the address data to positive and negative variable values so that an address substantially in the middle of the second part of the address data becomes a variable value, which is preferably zero, and for generating, by means of the variable value and the slope based on the second part of the address data, a coefficient term of a piecewise straight line; means for generating desired amplitude data by summing the coefficient term and the constant term of the piecewise straight line.
The converter of the invention is characterized in that the converter comprises a memory for generating, by means of straight lines, a piecewise linear approximation of a function g(z)=f(z)−tz, where f(z) is a function according to which an amplitude is to behave, z is a variable and t is a constant, the approximation comprising a predetermined number N of straight lines, with an slope and a constant term being stored in the memory, said straight lines being generated using a linear regression or the like and comprising a predetermined number M of variable values; means for generating a first part tz of the address data multiplied by the constant; means for dividing the address data in two parts, a first part determining the slope and the constant term of each generated approximative straight line, and a second part corresponding to variable values of each piecewise straight line; means for converting the addresses of the second part of the address data to positive and negative variable values so that an address substantially in the middle of the address data becomes a variable value, which is preferably zero, and for generating a coefficient term of the piecewise straight line, by using the slope and the variable value based on the second part of the address data; means for summing a first constant part and the first part tz of the address data multiplied by the constant and means for generating a desired amplitude data by summing the coefficient part and the corrected constant part of the piecewise straight line.
The method of the invention provides considerable advantages. An approximative method allows the size of the memory to be reduced, thus accelerating the operation of the inventive solution. In addition, the operation of the s
Altera Law Group LLC
Malzahn David H.
Nokia Telecommunications Oy
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