CN105573407B - A kind of digital frequency synthesizer and ROM compression methods based on residue number system - Google Patents
A kind of digital frequency synthesizer and ROM compression methods based on residue number system Download PDFInfo
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- CN105573407B CN105573407B CN201510953852.7A CN201510953852A CN105573407B CN 105573407 B CN105573407 B CN 105573407B CN 201510953852 A CN201510953852 A CN 201510953852A CN 105573407 B CN105573407 B CN 105573407B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F1/00—Details not covered by groups G06F3/00 - G06F13/00 and G06F21/00
- G06F1/02—Digital function generators
- G06F1/03—Digital function generators working, at least partly, by table look-up
- G06F1/035—Reduction of table size
- G06F1/0353—Reduction of table size by using symmetrical properties of the function, e.g. using most significant bits for quadrant control
Abstract
The invention discloses a kind of ROM compression methods of the digital frequency synthesizer based on residue number system, and treat stored waveform using Chinese remainder theorem carries out remainder within a cosine period, obtains remainder value；It is worth to quantized value according to the remainder, wherein the quantized value that waveform to be stored is stored in ROM, using the remainder value as lookup table address；The number of the quantized value is compressed using the symmetry of cosine function, the quantized value compressed.A kind of ROM compression methods of digital frequency synthesizer based on residue number system of the present invention complete the storage of quantized value first with Chinese remainder theorem, using remainder value as the address of look-up table, 1/2 compression is carried out to quantized value using the symmetry of cosine waveform herein, reduces the space needed for storage；Simultaneously because the bit wide of remainder value is relatively low, read-write efficiency is high, to improve operational efficiency.
Description
Technical field
The present invention relates to frequency synthesis technique, more particularly to a kind of digital frequency synthesizer and ROM based on residue number system
Compression method.
Background technology
Direct Digital Frequency Synthesizers (DDS) have wider relative bandwidth, fast frequency agile, high frequency resolution,
Output phase is continuous, exportable wideband orthogonal signal, programmable and total digitalization is convenient for the superior functions such as integrated.However the poles DDS
The larger frequency control word bit wide of small frequency resolution requirements and corresponding ROM (Read Only Memory) are deep
Degree only takes the high-order output of phase accumulator to be used as look-up table address signal in practical implementations, and which results in the phases of DDS to cut
Short error and the spuious main sources of DDS.Secondly, the limited bit wides of ROM result in the amplitude quantizing mistake of DDS output waveforms
Difference.In addition to this, DAC (Digital to Analog Converter) transformed error also can further deteriorate the performance of DDS.
For the excessive problem of ROM hardware consumptions, Chren proposes two kinds of Direct Digital Frequency Synthesizers based on residue number system, this
The symmetry that waveform is utilized in two kinds of DDS only stores 1/4 waveform.But in order to store 1/4 in his such DDS for proposing
Waveform and increased logic control element is vicious, do not provide yet correction as a result, its speed of service is slow, performance is relatively low.
Therefore waveform can either be compressed by being badly in need of one kind, and not increase the DDS of additional control unit.
Invention content
In order to overcome the above-mentioned deficiency of the prior art, additional control is not increased the invention reside in a kind of compression degree height of offer and
Unit processed, the speed of service fast a kind of digital frequency synthesizer and ROM compression methods based on residue number system.
In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is：
A kind of ROM compression methods of the digital frequency synthesizer based on residue number system, include the following steps：
Stored waveform is treated using Chinese remainder theorem and carries out remainder within a cosine period, obtains remainder value；
It is worth to quantized value according to the remainder, wherein the quantized value of waveform to be stored is stored in ROM, it will
The remainder value is as lookup table address；
The number of the quantized value is compressed using the symmetry of cosine function, the quantized value compressed.
Further, described to treat stored waveform using Chinese remainder theorem and carry out remainder packet within a cosine period
It includes：
The a cycle of waveform to be stored is expressed as：
Cos (2 π Φ/M), Φ=[0, M], it is { m to enable remainder base1,m2,...,mL, wherein
According to Chinese remainder theoremWhereinMi=M/mi,
For MiTo miMould it is reciprocal, meetIt can obtain：
Then,
Wherein, ΦiFor remainder value,For quantized value, i, L are positive integer, rxM is one normal
Number.
Further, the symmetry using cosine function, which to the quantized value compress, includes,
Using formula cos θ=cos (- θ), 1/2 compression is carried out to the quantized value, for function
It is stored in ROMMi/ 2 quantized values.
Further, formula is utilizedWith the quantized value approximation of cosine function obtain it is corresponding just
The quantized value of string function, and the quantized value of the SIN function is modified.
Further, described to obtain the quantized value of corresponding SIN function with the quantized value approximation of cosine function, and to institute
State SIN function quantized value be modified including,
It is Φ in addressi、Φi+XiAnd Φi+2XiMiddle storage cosine function quantized value is respectively cos θ1、cosθ2With cos θ3,
Wherein XiFor approximation parameters, sin Δs are utilizedi≈Δi,cosΔi≈ 1 corrects error, obtains, sin θ1≈cosθ2+Δi·cosθ3,
Wherein ΔiFor angle correction error；
It is Φ when needing approximate sine function addressi+XiWhen, then
Work as miFor 4 multiple when, the quantized value of the approximate SIN function does not have error, at this time sin θ1=cos θ2, no
It needs to correct；
Work as miIt is 2 multiple, but is not 4 multiple, i.e. miWhen=4k+2, k is integer, is obtained at this time
Work as miWhen being odd number, obtain
Present invention simultaneously provides a kind of digital frequency synthesizer based on residue number system, including the first address conversioning unit,
Look-up table unit,
First address conversioning unit connects the look-up table unit, and the remainderization value for receiving phase controlled quentity controlled variable is defeated
Enter, the remainder value is converted to and matched first address value of the look-up table unit；
The look-up table unit is used for according to first address value, table look-up to obtain corresponding first quantized value carry out it is defeated
Go out；
The look-up table unit is stored with the remainder value and cosine letter of the cosine function obtained using Chinese remainder theorem
The waveform quantization value of number half period.
Further, further include Approximate Address computing unit, the second address conversioning unit,
The Approximate Address computing unit connects second address conversioning unit, for receive the remainder value with it is close
It like parameter and calculates, the result being calculated is exported；
Second address conversioning unit connects the look-up table unit, is respectively used to the Approximate Address computing unit
The result of output is converted to and matched second address value of the look-up table unit；
The look-up table unit is additionally operable to according to second address value, table look-up to obtain corresponding second quantized value carry out it is defeated
Go out；
The remainder base for the cosine function that the approximation parameters are obtained according to Chinese remainder theorem determines.
Further, further include modified address computing unit, third address conversioning unit, amending unit,
The modified address computing unit is separately connected the Approximate Address computing unit, the third address conversion list
Member, for receiving the result of Approximate Address computing unit output and the approximation parameters and calculating, the knot that will be calculated
Fruit exports；
The third address conversioning unit connects the look-up table unit, for exporting the modified address computing unit
Result be converted to and the matched third address value of the look-up table unit；
The look-up table unit is additionally operable to according to the third address value, table look-up to obtain corresponding third quantized value carry out it is defeated
Go out.
The amending unit connection and locating table is used for according to the third quantized value and correction factor, to second amount
Change value is modified.
Further, the correction factor is determined according to the remainder base.
Compared with prior art, beneficial effects of the present invention
1, a kind of ROM compression methods of digital frequency synthesizer based on residue number system of the invention are surplus first with China
Remaining theorem completes the storage of quantized value, using remainder value as the address of look-up table, utilizes the symmetry pair of cosine waveform herein
Quantized value carries out 1/2 compression, reduces the space needed for storage；Simultaneously because the bit wide of remainder value is relatively low, read-write efficiency is high,
To improve operational efficiency.
2, a kind of ROM compression methods of digital frequency synthesizer based on residue number system of the invention are by using cosine letter
Several quantized values goes approximation to obtain the quantized value of SIN function, does not need extra storage SIN function quantized value, further to press
Contracted 1/2 memory space.
Description of the drawings
It is a kind of digital frequency synthesizer based on residue number system of the specific embodiment of the present invention shown in Fig. 1
ROM compression method flow charts.
It is a kind of digital frequency synthesizer module based on residue number system of the specific embodiment of the present invention shown in Fig. 2
Block diagram.
It is a kind of digital frequency synthesizer module based on residue number system of the specific embodiment of the present invention shown in Fig. 3
Block diagram.
It is a kind of digital frequency synthesizer module based on residue number system of the specific embodiment of the present invention shown in Fig. 4
Block diagram.
It is a kind of digital frequency synthesizer structure based on residue number system of the specific embodiment of the present invention shown in Fig. 5
Figure.
Specific implementation mode
The present invention is described in further detail With reference to embodiment.But this should not be interpreted as to the present invention
The range of above-mentioned theme is only limitted to embodiment below, all models that the present invention is belonged to based on the technology that the content of present invention is realized
It encloses.
Embodiment 1：
It is a kind of digital frequency synthesizer based on residue number system of the specific embodiment of the present invention shown in Fig. 1
ROM compression method flow charts, including：
Stored waveform is treated using Chinese remainder theorem and carries out remainder within a cosine period, obtains remainder value；
It is worth to quantized value according to the remainder, wherein the quantized value of waveform to be stored is stored in ROM, it will
The remainder value is as lookup table address；
The number of the quantized value is compressed using the symmetry of cosine function, the quantized value compressed.
It is described using Chinese remainder theorem treat stored waveform and carry out remainder within a cosine period include：
If a cycle of waveform to be stored is expressed as：
Cos (2 π Φ/M), Φ=[0, M], it is { m to enable remainder base1,m2,...,mL, wherein
By Chinese remainder theoremWherein
For MiTo miMould it is reciprocal, meetIt can obtain：
Then,
At this point, can be stored in ROMWithQuantized value, and phase
The remainder value Φ of accumulatoriThe then address as each look-up table, due to ΦiBit wide is relatively low, so as to improve its operation speed
Degree.
The symmetry using cosine function carries out compression to the quantized value,
Using formula cos θ=cos (- θ), 1/2 compression is carried out to the quantized value, specifically, right
For only storeQuantized value, then forShi Ze
Have：
M in above formulai-ΦiValue range just in the quantized value stored, then only need to be by mi-ΦiAs address
Quantized value being can be obtained, in order to deposit a value facility of Rule of judgment also meeting in the case of certain remainder bases more.
A kind of ROM compression methods of digital frequency synthesizer based on residue number system of the present invention are first with Chinese Remainder
Theorem completes the storage of quantized value, using remainder value as the address of look-up table, utilizes the symmetry of cosine waveform to amount herein
Change value carries out 1/2 compression, reduces the space needed for storage；Simultaneously because the bit wide of remainder value is relatively low, read-write efficiency is high, from
And improve operational efficiency.
Further, formula is utilizedWith the quantized value approximation of cosine function obtain it is corresponding just
The quantized value of string function, and the quantized value of the SIN function is modified.
Further, described to obtain the quantized value of corresponding SIN function with the quantized value approximation of cosine function, and to institute
State SIN function quantized value be modified including,
Assuming that the address of known cos θ is ΦiWhen, thenAssuming that more than the storage
It is Φ that the ROM of string function quantized value, which goes to the address of approximate sin θ,i+Xi.Work as Φi+Xi≥miWhen, it is contemplated that the quantized value of storage is week
Phase property, enable the address be, Φ is used belowi+XiIt is illustrated as address value, then
In conjunction withIt arranges
The value of specific X is according to remainder base miValue is different and different, there is following three kinds of situations：
(1)miIt is 4 multiple
In such casesSo
As can be seen that going there is no error when near sinusoidal function quantized value with the quantized value of cosine function at this time, do not need
It corrects.
(2)miIt is 2 multiple, but is not 4 multiple, i.e. mi=4k+2, k are integer, then 3miTimes that -2=12k+4 is 4
Number, in such casesSo
In such cases, approximate angle hasError.Work as miWhen larger, ΔiValue it is smaller, this error
Sin Δs can be utilizedi≈Δi,cosΔi≈ 1 is corrected.Remember address Φi、Φi+XiAnd Φi+2XiThe cos quantized values stored are
cosθ1、cosθ2With cos θ3, the sin θ known to approximation above1=cos (θ2-Δi)、sinθ2=cos (θ3-Δi), then
It can then complete to correct using above formula.
(3)miIt is odd number
Then 3miFor odd number, 3miIt is 4 multiple there are one ± 1, at this time(± selection make 3mi±1
Multiple for 4),
In such cases, approximate angle hasError.Specific modification method with it is upper identical, herein not
It repeats again.
Specifically, referring to table 1.
Table 1
A kind of ROM compression methods of digital frequency synthesizer based on residue number system of the present invention are by using cosine function
Quantized value go it is approximate obtain the quantized value of SIN function, do not need extra storage SIN function quantized value, it is further to compress
1/2 memory space, while the SIN function quantized value of pairing approximation is modified, keep result more accurate.
Embodiment 2：
Present invention simultaneously provides a kind of digital frequency synthesizers based on residue number system, specifically, referring to Fig. 2, including the
One address conversioning unit 1, look-up table unit 2,
First address conversioning unit 1 connects the look-up table unit 2, is used for the remainder value of receiving phase controlled quentity controlled variable
Input, the remainder value is converted to and matched first address value of the look-up table unit；
The look-up table unit 2 is used for according to first address value, table look-up to obtain corresponding first quantized value carry out it is defeated
Go out；
The look-up table unit 2 is stored with the remainder value and cosine letter of the cosine function obtained using Chinese remainder theorem
The waveform quantization value of number half period.
Embodiment 3：
It is a kind of digital frequency synthesizer module frame chart based on residue number system of the present invention, the present embodiment packet shown in Fig. 3
The content in embodiment 2 is included, further includes Approximate Address computing unit 3, the second address conversioning unit 4,
The Approximate Address computing unit 3 connects second address conversioning unit 4, for receive the remainder value with
Approximation parameters simultaneously calculate, and the result being calculated is exported；
Second address conversioning unit 4 connects the look-up table unit 2, is respectively used to calculate the Approximate Address single
The result of member output is converted to and matched second address value of the look-up table unit；
The look-up table unit 2 is additionally operable to, according to second address value, table look-up to obtain corresponding second quantized value progress
Output；
The remainder base for the cosine function that the approximation parameters are obtained according to Chinese remainder theorem determines.
The calculation formula of the approximation parameters is obtained according to trigonometric function, and specific evaluation is true according to remainder base
It is fixed.
Embodiment 4：
It is a kind of digital frequency synthesizer module frame chart based on residue number system of the present invention, the present embodiment packet shown in Fig. 4
The content in embodiment 2 or 3 is included, further includes modified address computing unit 5, third address conversioning unit 6, amending unit 7,
The modified address computing unit 5 is separately connected the Approximate Address computing unit 3, the third address conversion list
Member 6, for receiving result that the Approximate Address computing unit 3 exports and the approximation parameters and calculating, by what is be calculated
As a result it exports；
The third address conversioning unit 6 connects the look-up table unit 2, for the modified address computing unit is defeated
The result gone out is converted to and the matched third address value of the look-up table unit；
The look-up table unit 2 is additionally operable to, according to the third address value, table look-up to obtain corresponding third quantized value progress
Output.
7 connection and locating table 2 of the amending unit is used for according to the third quantized value and correction factor, to described second
Quantized value is modified.
Further, the correction factor is determined according to the remainder base.
In a specific embodiment, referring to Fig. 5, first by the remainder base m in each remainder channeliIt calculates opposite
The approximation parameters X answeredi, specific value can be found in table 1, and phase value is to miΦ is then obtained after remainderi, it is respectively fed to unit 1, unit
3, the Φ after adder calculatesi+XiAnd Φi+2XiIt is respectively fed to unit 4, unit 6.
Following judgement is done in unit 1, specifically judges whether input value is more thanIf it is determined that result be then
Input value is negated along with miTo export result；If it is determined that result be otherwise directly by input value be sent into unit 2.Unit
1,4,6 function is completely the same, does not repeat herein.
Unit 2 is look-up table, when address is add, the value of storageLook-up table it is defeated
It is address to enter value, exports the storage value for appropriate address.After the output valve of unit 1,4,6 inputs 401 modules, three are respectively obtained
Cosine value is denoted as cos θ1、cosθ2With cos θ3.Wherein cos θ1For required cosine value.Needing modified, cos θ2
With cos θ3It is admitted to unit 7.
Unit 7 is by input value cos θ3It is multiplied by corrected parameter Δi(ΔiOccurrence can refer to table 1), then by result and cos θ2
Addition then obtains final result, that is, required sine value.The case where if it is that need not correct, then cos θ2Directly it is institute
The sine value asked, it is understood that be corrected parameter ΔiIt is 0.
The specific implementation mode of the present invention is described in detail above in conjunction with attached drawing, but the present invention is not restricted to
Embodiment is stated, in the spirit and scope for not departing from claims hereof, those skilled in the art can make
Go out various modifications or remodeling.
Claims (4)
1. a kind of ROM compression methods of the digital frequency synthesizer based on residue number system, which is characterized in that include the following steps：
Stored waveform is treated using Chinese remainder theorem and carries out remainder within a cosine period, obtains remainder value；
It is worth to quantized value according to the remainder, wherein the quantized value of waveform to be stored is stored in ROM, it will be described
Remainder value is as lookup table address；
The number of the quantized value is compressed using the symmetry of cosine function, the quantized value compressed；
It is described using Chinese remainder theorem treat stored waveform and carry out remainder within a cosine period include：
The a cycle of waveform to be stored is expressed as：
Cos (2 π Φ/M), Φ=[0, M], it is { m to enable remainder base1,m2,...,mL, wherein
According to Chinese remainder theoremWhereinMi=M/mi,For Mi
To miMould it is reciprocal, meetIt can obtain：
Then,
Wherein, ΦiFor remainder value,For quantized value, i, L are positive integer, rxM is a constant；
The symmetry using cosine function carries out compression to the quantized value,
Using formula cos θ=cos (- θ), 1/2 compression is carried out to the quantized value, for function
It is stored in ROMMi/ 2 quantized values；
Utilize formulaThe quantization of corresponding SIN function is obtained with the quantized value approximation of cosine function
Value, and the quantized value of the SIN function is modified；
It is described to obtain the quantized value of corresponding SIN function with the quantized value approximation of cosine function, and to the amount of the SIN function
Change value be modified including,
It is Φ in addressi、Φi+XiAnd Φi+2XiMiddle storage cosine function quantized value is respectively cos θ1、cosθ2With cos θ3, wherein
XiFor approximation parameters, sin Δs are utilizedi≈Δi,cosΔi≈ 1 corrects error, obtains sin θ1≈cosθ2+Δi·cosθ3, wherein
ΔiFor angle correction error；
It is Φ when needing approximate sine function addressi+XiWhen, then
Work as miFor 4 multiple when, the quantized value of the approximate SIN function does not have error, at this time sin θ1=cos θ2, do not need
It corrects；
Work as miIt is 2 multiple, but is not 4 multiple, i.e. miWhen=4k+2, k is integer, is obtained at this time
Work as miWhen being odd number, obtain
2. a kind of digital frequency synthesizer based on residue number system, which is characterized in that including the first address conversioning unit, look-up table
Unit,
First address conversioning unit connects the look-up table unit, and the remainder value for receiving phase controlled quentity controlled variable inputs,
The remainder value is converted to and matched first address value of the look-up table unit；
The look-up table unit is used for according to first address value, is tabled look-up to obtain corresponding first quantized value and is exported；
The look-up table unit is stored with the remainder value and cosine function half of the cosine function obtained using Chinese remainder theorem
The waveform quantization value in a period；
The digital frequency synthesizer, further includes Approximate Address computing unit, the second address conversioning unit,
The Approximate Address computing unit connects second address conversioning unit, for receiving the remainder value and approximate ginseng
It counts and calculates, the result being calculated is exported；
Second address conversioning unit connects the look-up table unit, is respectively used to export the Approximate Address computing unit
Result be converted to and matched second address value of the look-up table unit；
The look-up table unit is additionally operable to according to second address value, is tabled look-up to obtain corresponding second quantized value and is exported；
The remainder base for the cosine function that the approximation parameters are obtained according to Chinese remainder theorem determines.
3. a kind of digital frequency synthesizer based on residue number system according to claim 2, which is characterized in that further include repairing
Positive address calculation, third address conversioning unit, amending unit,
The modified address computing unit is separately connected the Approximate Address computing unit, the third address conversioning unit, uses
It is in receiving the result of Approximate Address computing unit output and the approximation parameters and calculate, the result being calculated is defeated
Go out；
The third address conversioning unit connects the look-up table unit, the knot for exporting the modified address computing unit
Fruit is converted to and the matched third address value of the look-up table unit；
The look-up table unit is additionally operable to according to the third address value, is tabled look-up to obtain corresponding third quantized value and is exported；
The amending unit connection and locating table is used for according to the third quantized value and correction factor, to second quantized value
It is modified.
4. a kind of digital frequency synthesizer based on residue number system according to claim 3, which is characterized in that the amendment
Coefficient is determined according to the remainder base.
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| CN1316150A (en) * | 1998-08-03 | 2001-10-03 | 艾利森电话股份有限公司 | System and method for lookup table by NCO |
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| US7482965B1 (en) * | 2004-12-17 | 2009-01-27 | Mayo Foundation For Medical Education And Research | Digital chirp waveform generator and method |
-
2015
- 2015-12-18 CN CN201510953852.7A patent/CN105573407B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1316150A (en) * | 1998-08-03 | 2001-10-03 | 艾利森电话股份有限公司 | System and method for lookup table by NCO |
| US7482965B1 (en) * | 2004-12-17 | 2009-01-27 | Mayo Foundation For Medical Education And Research | Digital chirp waveform generator and method |
| CN101163125A (en) * | 2006-10-13 | 2008-04-16 | 深圳市好易通科技有限公司 | CPFSK signal modulation device |
Non-Patent Citations (1)
| Title |
|---|
| 《RNS-based enhancements for direct digital frequency synthesis》;Chren W A.;《IEEE Transactions on Circuits & Systems II Analog & Digital Signal Processing》;19950831;第42卷(第8期);第516-524页 * |
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