CN100539434C - A kind of digital-analog convertion method - Google Patents

Abstract

The present invention relates to a kind of digital-analog convertion method, belong to the signal processing technology field.At first the data to input compensate filtering, and the data transfer rate behind compensation filter is identical with data transfer rate before the compensation filter, the output signal behind the compensation filter; This output signal is carried out interpolation filtering and data transfer rate rising, carry out the Delta-Sigma modulation at last, the data flow of output single-bit is carried out semi digital filtering to the data flow of single-bit, the output analog signal; Analog signal is carried out analogue low pass filtering, export last analog signal.The advantage of the inventive method is, under the condition that guarantees the data transaction precision, reduced the sequencing control complexity of interpolation filtering, thereby reduced the hardware spending of digital to analog converter, saves chip area, reduces production costs.The semi digital filtering method that adopts among the present invention when hardware is realized, does not need elements such as electric capacity, resistance, is convenient to the digital technology compatibility with main flow, has reduced design complexities.

Description

A kind of digital-analog convertion method

Technical field

The present invention relates to a kind of digital-analog convertion method, belong to the signal processing technology field.

Background technology

Existing Delta-Sigma digital to analog converter is widely used in high-quality audio-frequency signal process chip, the multimedia signal dispose chip with its high accuracy with the characteristics such as good integrated level of digital system.

The principle of Delta-Sigma digital to analog converter as shown in Figure 1.The digital signal (data rate is fs) of input compensates filtering, and the signal after the filtering carries out interpolation filtering, and data rate improves behind the interpolation filtering, and the multiple of raising is identical with the over-sampling rate of digital-to-analogue conversion (OSR).It is 1 data flow that the digital signal of over-sampling is blocked through the Delta-Sigma modulator.The signal to noise ratio of this data flow in signal band is very high, and signal cutout and the quantizing noise that produces are all moved outside the signal band.Data flow is converted to analog signal behind semi digital filtering, it is final simulation output that this simulation output is filtered into through simulation once again, thereby has finished the conversion of digital signal to analog signal.

Interpolation filtering in the above-mentioned digital-to-analogue conversion, its performance has material impact to the service behaviour of whole digital-to-analogue conversion.During interpolation filtering, the complexity the when approximation accuracy of tap coefficient has determined that the data transaction precision of filtering and hardware are realized.In various multiplier-less implementation methods, prior art is approached coefficient mostly with 2 power time sum, promptly adopt base 2 decomposition methods of coefficient, " A simple design of FIR filters with powers-of-twocoefficients " referring to Q.Zhao etc., IEEE Trans.Circuit Syst., vol.35, pp 566-570, May 1988, and B.R.Horng etc. " The design of two-channel lattice structureperfect-reconstruction filter banks using powers of two coefficients ", IEEE Trans.Circuits Syst.I, vol.40, pp.497-499, July 1993.The basic decomposition method of this list has advantages such as design is easy, and time sequence control logic is simple, but also has the problem in many realizations.

The weak point of above-mentioned basic 2 decomposition methods mainly contains the following aspects.The first, the coefficient approximation accuracy that base 2 decomposes is lower.In order to guarantee the high accuracy conversion of data, must use very long shift register to deposit small amount of data, this will increase hardware spending greatly and take more chip area.Common digital to analog converter chip overwhelming majority area is occupied by the digital interpolation filter.The second, it is very inequality that different coefficients decomposes the data format that launches by base 2, makes this method for designing lack versatility, and the hardware circuit that obtains is very irregular, is difficult to carry out the procedure design.

For fear of the problems referred to above, in recent years, people begin to adopt many basic thinkings of decomposing to improve the regular degree of data transaction precision and hardware, prior art is referring to S.Ghanekar etc. " Signal-digit based multiplier-freerealizations for multirate converters ", IEEE Trans.Signal Process., vol.43, pp.628-639, Mar.1995, and J.L.Li etc. " Multiplier-free realizations for FIRmultirate converts based on mixed-radix number representation ", IEEE Trans.SignalProcess., vol 45, pp.880-890, April 1997.This method can be saved hardware resource effectively, but it often adopts sacrifice speed to exchange the way of precision for, the sequential control circuit more complicated, and data processing usefulness is lower.Simultaneously, this method may be complicated with originally simple data processing method.

Summary of the invention

The present invention proposes a kind of digital-analog convertion method, its objective is when guaranteeing the data transaction precision, the sequencing control complexity when reducing the hardware realization as much as possible is to reduce the production cost of hardware.

The digital-analog convertion method that the present invention proposes comprises the steps:

(1) the data x (n) to input compensates filtering, and the data transfer rate behind compensation filter is identical with data transfer rate before the compensation filter, and the output signal behind the compensation filter is xc (n);

(2) above-mentioned output signal xc (n) is carried out interpolation filtering, output signal is xp (n), and the data transfer rate behind the interpolation filtering rises, and the rising multiple is identical with the over-sampling rate of described digital-to-analogue conversion;

(3) the output xp (n) to above-mentioned interpolation filtering carries out the Delta-Sigma modulation, the data flow xd (n) of output single-bit;

(4) the data flow xd (n) to above-mentioned single-bit carries out semi digital filtering, output analog signal xs;

(5) above-mentioned analog signal xs is carried out analogue low pass filtering, output analog signal y.

In the said method, the method to input data x (n) compensate filtering may further comprise the steps:

(2-1) receives the data-signal x (n) of input continuously, postpones to deposit, and obtains the delay chain of depositing of an input data signal x (n), and the length of delay chain is N, and N is an odd number;

(2-2) obtain signal C with above-mentioned first signal and last signal plus of depositing in the delay chain ₀(n), second signal and penult signal plus obtain signal C ₁(n), and the like, C obtained ₂(n), C ₃(n), C _(N-3)/2(n), Sheng Xia M signal is designated as C _(N-1)/2(n), C ₀(n)～C _(N-1)/2(n) respectively with the coefficient HC of described compensation filter ₀, HC ₁, HC ₂..., HC _(N-1)/2Multiply each other,, obtain xc (n) again with all multiplied result additions.

In the said method, the method to signal xc (n) carries out interpolation filtering may further comprise the steps:

(3-1) carries out the semi-band filtering first time to the output signal xc (n) of compensation filter, with the input of primary filtering result as the filtering second time, carries out the semi-band filtering second time, has been total to the sample rate that quadruples and has promoted;

Output signal after (3-2) promote above-mentioned sample rate is combed value filtering, and the comb value filtering is finished 32 times sample rate lifting altogether, obtains xp (n).

Wherein the output signal xc (n) of compensation filter is carried out the method for semi-band filtering, may further comprise the steps:

(4-1) receives the output signal xc (n) of compensation filter continuously, postpones to deposit, and obtains one and deposits delay chain, and the length of delay chain is Nf/2+3, and wherein Nf is the semi-band filtering exponent number, and Nf/2 is an odd number;

(4-2) are with above-mentioned first signal and last signal plus of depositing in the delay chain, obtain signal u0 (n), second signal and penult signal plus, obtain signal u1 (n), and the like, until remaining middle two signals, the signal plus postscript of middle two signal both sides is uM-2 (n), M=(Nf+6)/4 wherein, 1/2 of the signal value after leaning in two signals in the middle of getting carries out first input signal that the alternative multichannel is selected during as semi-band filtering;

(4-3) with above-mentioned signal u0 (n), u1 (n) ... sample successively maintenance, weighted sum and modulation of uM-2 (n) adds up, and obtains signal y ' (m);

(4-4) (m) are extracted above-mentioned signal y ' and the convergent-divergent that gains, second input signal that the alternative multichannel is selected during as semi-band filtering;

Two input signals that (4-5) select above-mentioned alternative multichannel carry out alternately output of periodicity, are the output signal of semi-band filtering, and the speed that replaces output is 2 times of input signal speed.

Wherein to signal u0 (n), u1 (n) ... uM-2 (n) method that keeps of sampling is: with signal u0 (n), u1 (n) ... uM-2 (n) duplicates K time respectively, obtains v0 (m), v1 (m) ... vM-2 (m), signal v0 (m), v1 (m) ... the speed of vM-2 (m) is signal u0 (n), u1 (n) ... the K of uM-2 (n) times, wherein K is the dimension that the semi-band filtering mixed base decomposes, mixed base decomposition precision P according to semi-band filtering chooses $P=-{\log }_2\left({\mathrm{Cr}}_1^{-N}{r}_2^{-(K-1)}\right)+1,$ R1 wherein, r2 is two substrates that the semi-band filtering mixed base decomposes, and C is the normalization factor that the semi-band filtering mixed base decomposes, and N is another dimension that the semi-band filtering mixed base decomposes, it is the decomposition that double band filter factor h (n) carries out that the semi-band filtering mixed base decomposes, promptly $h\left(n\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)},n=\mathrm{0,1},\·\·\·,N_f,$ Wherein

Be to decompose the coefficient that obtains by the semi-band filtering mixed base.

The method that wherein signal vi (m) (i is from 0 to M-2) is weighted summation is: after the every renewal once of signal value of vi (m) (i is from 0 to M-2), at v _i(m) will finish following operation in each signal period:

(6-1) makes above-mentioned signal v _i(m) enter N bar individual path, with the signal v on j (j from 0 to N) the bar individual path _i(m) multiply by j, numerical value is Gain factor, multiply by the periodically time-varying gain factor again

Obtain N weighted results, all signal v _i(m) it is individual that weighted results has N * (M-1); The time-varying gain factor periodically wherein

Obtain by semi-band filtering coefficient mixed base decomposition transform, promptly $d_n^i(\mathrm{\μK}+\mathrm{\η})=c_{\mathrm{\μ}+2n}^i\left(\mathrm{\η}\right),$ η=0,1 ..., K-1 and μ=0,1, wherein

By the mixed base decomposition formula $h\left(n\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)},$ N=0,1 ..., N _fObtain N, the dimension that K decomposes for the semi-band filtering mixed base, r ₁, r ₂Be two substrates that the semi-band filtering mixed base decomposes, h (n) is the semi-band filtering coefficient, and C is the normalization factor that the semi-band filtering mixed base decomposes;

(6-2) obtain signal w (m) with above-mentioned N * (M-1) individual weighted results addition;

(6-3) are modulated above-mentioned signal w (m) and are added up, and modulation factor is

Wherein＜m 〉 _KExpression m asks mould surplus to K;

When arrived when the next signal period (6-4), repeating step (6-1), (6-2), (6-3), and k increases by 1, up to k=K-1, after this k is clear 0, and accumulation result is zero clearing also.

The digital-analog convertion method that the present invention proposes, its advantage are, under the condition that guarantees the data transaction precision, reduce the sequencing control complexity of interpolation filtering, thereby used the digital to analog converter of this method design, can significantly reduce hardware spending, save chip area, reduce production costs.The semi digital filtering method that adopts among the present invention when hardware is realized, does not need elements such as electric capacity, resistance, therefore is convenient to the digital technology compatibility with main flow, has reduced the design complexities of digital to analog converter.

Description of drawings

Fig. 1 is the FB(flow block) of the inventive method.

Fig. 2 is the FB(flow block) of compensation filter in the inventive method.

Fig. 3 is the FB(flow block) of interpolation filtering in the inventive method.

Fig. 4 is the FB(flow block) of semi-band filtering in the interpolation filtering.

Fig. 5 is the FB(flow block) of comb value filtering in the interpolation filtering.

Fig. 6 is the FB(flow block) of Delta-Sigma modulation in the inventive method.

Fig. 7 is the semi digital filtering in the inventive method and the FB(flow block) of analog filtering.

Embodiment

The digital-analog convertion method that the present invention proposes, its FB(flow block) as shown in Figure 1, at first the data x (n) to input compensates filtering, the data transfer rate behind compensation filter is identical with data transfer rate before the compensation filter, the output signal behind the compensation filter is xc (n); Output signal xc (n) is carried out interpolation filtering, and output signal is xp (n), and the data transfer rate behind the interpolation filtering rises, and the rising multiple is identical with the over-sampling rate of described digital-to-analogue conversion; Output xp (n) to interpolation filtering carries out the Delta-Sigma modulation, the data flow xd (n) of output single-bit; Data flow xd (n) to single-bit carries out semi digital filtering, output analog signal xs; Analog signal xs is carried out analogue low pass filtering, output analog signal y.

In the said method, to importing the method that data x (n) compensate filtering, its FB(flow block) as shown in Figure 2, receive the data-signal x (n) of input continuously, postpone to deposit, obtain the delay chain of depositing of an input data signal x (n), the length of delay chain is N, and N is an odd number; With above-mentioned first signal and last signal plus of depositing in the delay chain, obtain signal C ₀(n), second signal and penult signal plus obtain signal C ₁(n), and the like, C obtained ₂(n), C ₃(n), C _(N-3)/2(n), Sheng Xia M signal is designated as C _(N-1)/2(n), C ₀(n)～C _(N-1)/2(n) respectively with the coefficient HC of described compensation filter ₀, HC ₁, HC ₂..., H _{C (N-1)/2}Multiply each other,, obtain xc (n) again with all multiplied result additions.

In the said method, signal xc (n) is carried out the method for interpolation filtering, its FB(flow block) as shown in Figure 3, at first the output signal xc (n) to compensation filter carries out the semi-band filtering first time, with the input of primary filtering result as the filtering second time, carry out the semi-band filtering second time, be total to the sample rate that quadruples and promoted; Output signal after the last sample rate lifting is combed value filtering, and the comb value filtering is finished 32 times sample rate lifting altogether, obtains xp (n).

Wherein the output signal xc (n) of compensation filter is carried out the method for semi-band filtering, its FB(flow block) as shown in Figure 4, receive the output signal xc (n) of compensation filter at first continuously, postpone to deposit, obtain one and deposit delay chain, the length of delay chain is Nf/2+3, and wherein Nf is the semi-band filtering exponent number, and Nf/2 is an odd number; With above-mentioned first signal and last signal plus of depositing in the delay chain, obtain signal u0 (n), second signal and penult signal plus, obtain signal u1 (n), and the like, until remaining middle two signals, the signal plus postscript of middle two signal both sides is uM-2 (n), M=(Nf+6)/4 wherein, 1/2 of the signal value after leaning in two signals in the middle of getting carries out first input signal that the alternative multichannel is selected during as semi-band filtering; With above-mentioned signal u0 (n), u1 (n) ... sample successively maintenance, weighted sum and modulation of uM-2 (n) adds up, and obtains signal y ' (m); Above-mentioned signal y ' (m) is extracted and the convergent-divergent that gains second input signal that the alternative multichannel is selected during as semi-band filtering; Two input signals that above-mentioned alternative multichannel is selected carry out alternately output of periodicity, are the output signal of semi-band filtering, and the speed that replaces output is 2 times of input signal speed.

Wherein to signal u0 (n), u1 (n) ... uM-2 (n) method that keeps of sampling is: with signal u0 (n), u1 (n) ... uM-2 (n) duplicates K time respectively, obtains v0 (m), v1 (m) ... vM-2 (m), signal v0 (m), v1 (m) ... the speed of vM-2 (m) is signal u0 (n), u1 (n) ... the K of uM-2 (n) times, wherein K is the dimension that the semi-band filtering mixed base decomposes, mixed base decomposition precision P according to semi-band filtering chooses $P=-{\log }_2\left({\mathrm{Cr}}_1^{-N}{r}_2^{-(K-1)}\right)+1,$ R1 wherein, r2 is two substrates that the semi-band filtering mixed base decomposes, and C is the normalization factor that the semi-band filtering mixed base decomposes, and N is another dimension that the semi-band filtering mixed base decomposes, it is the decomposition that double band filter factor h (n) carries out that the semi-band filtering mixed base decomposes, promptly $h\left(n\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)},n=\mathrm{0,1},\·\·\·,N_f,$ Wherein

Be to decompose the coefficient that obtains by the semi-band filtering mixed base.

Signal vi (m) (i is from 0 to M-2) wherein is weighted the method for summation, after the every renewal once of signal value of vi (m) (i is from 0 to M-2), in each signal period of vi (m), will finishes following operation:

At first make above-mentioned signal v _i(m) enter N bar individual path, with the signal v on j (j from 0 to N) the bar individual path _i(m) multiply by j, numerical value is

Gain factor, multiply by the periodically time-varying gain factor again

Obtain N weighted results, all signal v _i(m) it is individual that weighted results has N * (M-1); The time-varying gain factor periodically wherein Obtain by semi-band filtering coefficient mixed base decomposition transform, promptly $d_n^i(\mathrm{\μK}+\mathrm{\η})=c_{\mathrm{\μ}+2n}^i\left(\mathrm{\η}\right),$ η=0,1 ..., K-1 and μ=0,1, wherein

By the mixed base decomposition formula $h\left(n\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_n^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)},$ N=0,1 ..., N _fObtain N, the dimension that K decomposes for the semi-band filtering mixed base, r ₁, r ₂Be two substrates that the semi-band filtering mixed base decomposes, h (n) is the semi-band filtering coefficient, and C is the normalization factor that the semi-band filtering mixed base decomposes; With above-mentioned N * (M-1) individual weighted results addition, obtain signal w (m); Above-mentioned signal w (m) is modulated and add up, modulation factor is

Wherein＜m 〉 _KExpression m asks mould surplus to K; When the next signal period arrives, repeat above-mentioned steps, and k increases by 1, up to k=K-1, after this k is clear 0, and accumulation result is zero clearing also.

In the semi-band filtering method of the present invention, the method that signal y ' (m) is extracted is: extraction be the K time accumulation result, and do not extract the intermediate object program of cumulative process, signal rate changes back to the speed of input signal again.The gain zoom factor of back is

r ₁Be the substrate that the semi-band filtering mixed base decomposes, C is the normalization factor that the semi-band filtering mixed base decomposes.

The performance of two semi-band filterings among Fig. 3 has determined the performance of whole filtering.In order to use less hardware resource and to realize the high accuracy data conversion, the semi-band filtering method flow chart that the present invention proposes as shown in Figure 4.This structure is based on the method that the coefficient mixed base decomposes, and combines nearly half coefficient of semi-band filtering and be 0 characteristics, used the design philosophy of multiphase filtering simultaneously.X among Fig. 4 (n) and y (n) are respectively input, output signal.Arrow points among the figure is the direction that data processing transmits.The delay chain of depositing of upper part is used for store data among the figure; "+" is add operation; Sampling keeps operation to realize that this also makes signal rate bring up to original K times with the function of signal replication K time; All triangles are represented doubly taking advantage of of data, and all the method for available displacement realizes; " * " is modulation operations, and also the method with shifter-adder realizes; Adding up of signal finished in the operation that adds up, and whenever finishes the back zero clearing that adds up for K time; Extraction operation then extracts first signal output in every K input signal, be about to the speed that signal rate is reduced to input signal; Switch among the figure is then realized the alternately gating output of two paths of signals up and down, makes that output signal speed is 2 times of input.

Introduce the detailed process of semi-band filtering in the interpolation filtering of digital-analog convertion method of the present invention below in conjunction with Fig. 4: filter factor adopts the mixed base algorithm to decompose in the method, filtering for M rank, if coefficient { h (j), j=0,1,2 ... M-1} normalizes in the scope of [1,1], and its Mixed Radix Representation as the formula (1).

$h\left(j\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}\underset{i=0}{\overset{N-1}{\mathrm{\Σ}}}{c}_j^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)}---\left(1\right)$

r ₁And r ₂Be base,

For belong to 0, ± 1 ..., ± α ₀Set.Integer α ₀Satisfy Here

Expression is not more than the smallest positive integral of t.r ₂Optimal value can determine by (2) formula

$\left({\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C200710064940E00112.png,C200710064940E00114.png"\; state="\{\{state\}\}">r</figure-callout>}}_{2\mathrm{opt}}^{-1}\right)=\frac{r_1-1}{r_1-1+2{\mathrm{\&alpha;}}_0(r_1^N-1)}---\left(2\right)$

C is a normalization factor, is determined by (3) formula

$C=\frac{r_1^N(r_1-1)(1-r_2^{-1})}{r_2^{-(K-1)}(1-r_2^{-1})(r_1-1)+{\mathrm{\&alpha;}}_0(r_1^N-1)(1-r_2^{-K})}---\left(3\right)$

The precision that this method for expressing can reach is

$P=-{\log }_2\left({\mathrm{Cr}}_1^{-N}{r}_2^{-(K-1)}\right)+1---\left(4\right)$

For example get N=3, K=5, r ₁=4, integer α ₀Be 2.The mixed base decomposition result of coefficient h (j)

Belong to set 0, ± 1, ± 2}, therefore the multiplication operations with h (j) can be reduced to a series of displacement and the operation that adds up.

Determine by formula (2) and formula (3) with the value of C.When hardware is realized,

Can be expressed as with 2 integral number power with the value of C $r_{}^{}$ ${}_{2\mathrm{opt}}^{-1}=2^{-6}-2^{-9},$ C=1+2 ^-1+ 2 ^-8The approximation accuracy of being known coefficient by (3) formula can reach 32bit, and this decomposes with traditional base 2 is extremely inaccessible.According to top decomposition, each filter factor can be write as the matrix of a N * K, each data represented factoring of a certain this coefficient of the moment that lists of this matrix, the cycle time variation of these coefficients of data representation on the different lines.For the design, the mixed base split-matrix MR (h) of this coefficient can be expressed as follows:

${\mathrm{MR}}_{h\left(n\right)}=\left[\begin{array}{ccccc}{c}_n^0\left(0\right)& c_n^0\left(1\right)& c_n^0\left(2\right)& c_n^0\left(3\right)& c_n^0\left(4\right)\\ c_n^1\left(0\right)& c_n^1\left(1\right)& c_n^1\left(2\right)& c_n^1\left(3\right)& c_n^1\left(4\right)\\ c_n^2\left(0\right)& c_n^2\left(1\right)& c_n^2\left(2\right)& c_n^2\left(3\right)& c_n^2\left(4\right)\end{array}\right]---\left(5\right)$

By simple linear transform:

$d_n^i(\mathrm{\&mu;K}+\mathrm{\&eta;})=c_{\mathrm{\&mu;}+2n}^i\left(\mathrm{\&eta;}\right),\mathrm{\&eta;}=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,K-1\mathrm{and\&mu;}=\mathrm{0,1}---\left(6\right)$

Mixed base matrix (5) is transformed to:

${M{R}^{*}}_{h\&prime;\left(n^{*}\right)}=\left[\begin{array}{ccccc}{d}_{n^{*}}^0\left(0\right)& d_{n^{*}}^0\left(1\right)& d_{n^{*}}^0\left(2\right)& ...& d_{n^{*}}^0\left(9\right)\\ d_{n^{*}}^1\left(0\right)& d_{n^{*}}^1\left(1\right)& d_{n^{*}}^1\left(2\right)& ...& d_{n^{*}}^1\left(9\right)\\ d_{n^{*}}^2\left(0\right)& d_{n^{*}}^2\left(1\right)& d_{n^{*}}^2\left(2\right)& ...& d_{n^{*}}^2\left(9\right)\end{array}\right]---\left(7\right)$

n ^*＝0，1，…，M-2

The line number that can see matrix does not change, but columns has become original twice.Therefore this conversion reduces hardware spending by the burden that increases sequencing control.Especially, for semi-band filtering, the mixed base matrix of most of coefficients

In the element of the right side 5 row all be 0,---in the semi-band filtering process middle coefficient 0.5---exception of having only a coefficient.On this theoretical foundation, the method (shown in Figure 4) that the present invention proposes has been utilized the thought of multiphase filtering, greatly reduces the time sequence control logic complexity.The foundation of optimizing is the directly displacement output of coefficient 0.5 that semi-band filtering is middle, and without the mixed base resolution process of complexity, this is the thought of multiphase filtering.

In the inventive method, the coefficient HC of compensation filter ₀, HC ₁, HC ₂..., H _{C (N-1)/2}, determine as follows.If there is not compensation filter, can determine the amplitude response H (w) of interpolation filtering by Computer Simulation, this amplitude response has certain decay in the passband edge of signal, and this decay is to cause because of the frequency characteristic of combing value filtering.In the passband of signal, get Frequency point w ₀, w ₁, w ₂..., w _N-1, according to the amplitude response H (w of H (w) calculating interpolation filtering ₀), H (w ₁), H (w ₂) ..., H (w _N-1).The frequency response of corresponding compensation filtering should be 1/H (w ₀), 1/H (w ₁), 1/H (w ₂) ..., 1/H (w _N-1).Can obtain the coefficient HC of compensation filter among Fig. 2 according to the frequency sampling algorithm ₀, HC ₁, HC ₂..., HC _(N-1)/2The value of getting N in the inventive method is 11, promptly to 11 Frequency point w of passband sampling of the frequency response curve of the interpolation filtering that do not add compensation filter ₀, w ₁, w ₂..., w ₁₀Amplitude response value H (w ₀), H (w ₁), H (w ₂) ..., H (w ₁₀), the characteristic of the filtering characteristic of compensation filter on selected Frequency point should be 1/H (w ₀), 1/H (w ₁), 1/H (w ₂) ..., 1/H (w ₁₀), can calculate the coefficient HC of compensation filter according to the frequency sample algorithm ₀, HC ₁, HC ₂..., HC ₅

In the inventive method, the flow chart of comb value filtering is combed value filtering and is divided five second son filtering as shown in Figure 5, and the transfer function that each sub-filtering realizes is (1-z ^-1) ⁴, the data transfer rate that twice is finished in each sub-filtering promotes.

Delta-Sigma modulation in the inventive method is adopted the structure of monocycle single-bit distributed feed-back, and is introduced two LOCAL FEEDBACK, and signal flow graph as shown in Figure 6.Each coefficient a1～a4 among the figure, b1～b5, g1, determining of g2 can be referring to " Delta-sigma data converter principle design and emulation " (Steven R.Norsworthy, Richard Schreier, the Delta-sigma data converters:theory of Gabor C.Temes., design, and simulation.NewYork, IEEE PRESS, 1996.512-513).

Signal after the Delta-Si gma modulation carries out semi digital filtering and analogue low pass filtering, and its hardware configuration as shown in Figure 7.The transfer function that semi digital filtering is realized is:

$H\left(z\right)=\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}h\left(j\right)z^{-j}$

Coefficient realizes that by the current source of weighting the size of current source is directly proportional with the coefficient of filtering.Delay unit among the figure is realized with d type flip flop when hardware is realized.Filtering input DIN is 1 a data flow from aforementioned Delta-Sigma modulator, j the j level time-delay that delay unit is DIN, and j=0,1,2 ..., N.Because input signal is ' 0 ' or ' 1 ', each product term h (j) DINz ^-jValue be ' 0 ' or for h (j), this can be reduced to product term by the switch of delay unit control and realize.Its effect is in single-bit Delta-Sigma digital to analog converter, the digital bit stream of single-bit is converted to analog signal and carries out to a certain degree filtering.Output signal behind the semi digital filtering is as the input signal of analogue low pass filtering, because the output signal of semi digital filtering is a current signal, analogue low pass filtering is converted to voltage signal with this current signal and carries out analogue low pass filtering simultaneously.

Claims (6)

1, a kind of digital-analog convertion method is characterized in that this method comprises the steps:

(1) the data x (n) to input compensates filtering, and the data transfer rate behind compensation filter is identical with data transfer rate before the compensation filter, and the output signal behind the compensation filter is xc (n);

(2) above-mentioned output signal xc (n) is carried out interpolation filtering, output signal is xp (n), and the data transfer rate behind the interpolation filtering rises, and the rising multiple is identical with the over-sampling rate of described digital-to-analogue conversion;

(3) the output xp (n) to above-mentioned interpolation filtering carries out the Delta-Sigma modulation, the data flow xd (n) of output single-bit;

(4) the data flow xd (n) to above-mentioned single-bit carries out semi digital filtering, output analog signal xs;

(5) above-mentioned analog signal xs is carried out analogue low pass filtering, output analog signal y.

2, the method for claim 1 is characterized in that may further comprise the steps importing the method that data x (n) compensate filtering:

(2-1) receives the data-signal x (n) of input continuously, postpones to deposit, and obtains the delay chain of depositing of an input data signal x (n), and the length of delay chain is N, and N is an odd number;

(2-2) obtain signal C with above-mentioned first signal and last signal plus of depositing in the delay chain ₀(n), second signal and penult signal plus obtain signal C ₁(n), and the like, C obtained ₂(n), C ₃(n), C _(N-3)/2(n), Sheng Xia M signal is designated as C _(N-1)/2(n), C ₀(n)～C _(N-1)/2(n) respectively with the coefficient HC of described compensation filter ₀, HC ₁, HC ₂..., HC _(N-1)/2Multiply each other,, obtain xc (n) again with all multiplied result additions.

3, the method for claim 1 is characterized in that wherein said signal xc (n) is carried out may further comprise the steps the method for interpolation filtering:

(3-1) carries out the semi-band filtering first time to the output signal xc (n) of compensation filter, with the input of primary filtering result as the filtering second time, carries out the semi-band filtering second time, has been total to the sample rate that quadruples and has promoted;

Output signal after (3-2) promote above-mentioned sample rate is combed value filtering, and the comb value filtering is finished 32 times sample rate lifting altogether, obtains xp (n).

4, method as claimed in claim 3 is characterized in that the output signal xc (n) to compensation filter carries out the method for semi-band filtering, may further comprise the steps:

(4-1) receives the output signal xc (n) of compensation filter continuously, postpones to deposit, and obtains one and deposits delay chain, and the length of delay chain is Nf/2+3, and wherein Nf is the semi-band filtering exponent number, and Nf/2 is an odd number;

(4-2) are with above-mentioned first signal and last signal plus of depositing in the delay chain, obtain signal u0 (n), second signal and penult signal plus, obtain signal u1 (n), and the like, until remaining middle two signals, the signal plus postscript of middle two signal both sides is uM-2 (n), M=(Nf+6)/4 wherein, 1/2 of the signal value after leaning in two signals in the middle of getting carries out first input signal that the alternative multichannel is selected during as semi-band filtering;

(4-3) with above-mentioned signal u0 (n), u1 (n) ... sample successively maintenance, weighted sum and modulation of uM-2 (n) adds up, and obtains signal y ' (m);

(4-4) (m) are extracted above-mentioned signal y ' and the convergent-divergent that gains, second input signal that the alternative multichannel is selected during as semi-band filtering;

Two input signals that (4-5) select above-mentioned alternative multichannel carry out alternately output of periodicity, are the output signal of semi-band filtering, and the speed that replaces output is 2 times of input signal speed.

5, method as claimed in claim 4, it is characterized in that wherein said signal u0 (n), u1 (n) ... uM-2 (n) method that keeps of sampling is: with signal u0 (n), u1 (n) ... uM-2 (n) duplicates K time respectively, obtain v0 (m), v1 (m) ... vM-2 (m), signal v0 (m), v1 (m) ... the speed of vM-2 (m) is signal u0 (n), u1 (n) ... the K of uM-2 (n) doubly, wherein K is the dimension that the semi-band filtering mixed base decomposes, and decomposes precision P according to the mixed base of semi-band filtering and chooses $P=-{\log }_2\left({\mathrm{Cr}}_1^{-N}{r}_2^{-(K-1)}\right)+1,$ R1 wherein, r2 is two substrates that the semi-band filtering mixed base decomposes, and C is the normalization factor that the semi-band filtering mixed base decomposes, and N is another dimension that the semi-band filtering mixed base decomposes, it is the decomposition that double band filter factor h (n) carries out that the semi-band filtering mixed base decomposes, promptly $h\left(n\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_n^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)},$ N=0,1 ..., N _f, wherein

Be to decompose the coefficient that obtains by the semi-band filtering mixed base.

6, method as claimed in claim 5 is characterized in that wherein said signal v _i(m) (i is from 0 to M-2) is weighted the method for summation and is: work as v _i(m) after the every renewal once of signal value of (i is from 0 to M-2), at v _i(m) will finish following operation in each signal period:

(6-1) makes above-mentioned signal v _i(m) enter N bar individual path, with the signal v on j (j from 0 to N) the bar individual path _i(m) multiply by j, numerical value is

Gain factor, multiply by the periodically time-varying gain factor again

Obtain N weighted results, all signal v _i(m) it is individual that weighted results has N * (M-1); The time-varying gain factor periodically wherein

Obtain by semi-band filtering coefficient mixed base decomposition transform, promptly $d_n^i(\mathrm{\&mu;K}+\mathrm{\&eta;})=c_{\mathrm{\&mu;}+2n}^i\left(\mathrm{\&eta;}\right),$ η=0,1 ..., K-1 and μ=0,1, wherein

By the mixed base decomposition formula $h\left(n\right)={\mathrm{Cr}}_1^{-1}\underset{k=0}{\overset{K-1}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{c}_n^i\left(k\right)r_1^{-i}{r}_2^{-(K-1-k)},$ N=0,1 ..., N _fObtain N, the dimension that K decomposes for the semi-band filtering mixed base, r ₁, r ₂Be two substrates that the semi-band filtering mixed base decomposes, h (n) is the semi-band filtering coefficient, and C is the normalization factor that the semi-band filtering mixed base decomposes;

(6-2) obtain signal w (m) with above-mentioned N * (M-1) individual weighted results addition;

(6-3) are modulated above-mentioned signal w (m) and are added up, and modulation factor is

Wherein＜and m〉K represents that m asks mould surplus to K;

When arrived when the next signal period (6-4), repeating step (6-1), (6-2), (6-3), and k increases by 1, up to k=K-1, after this k is clear 0, and accumulation result is zero clearing also.

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