CN106374920A - Estimation and compensation method of TIADC system based on polynomial model - Google Patents

Abstract

The invention discloses an estimation and compensation method of a TIADC system based on a polynomial model, and belongs to an estimation and compensation algorithm of digital back-end processing based on a channel transfer function model. Any linear error can be contained, comprising, but not limited to, time errors, gain errors, pole-zero errors, etc. Therefore, by adoption of a correction method based on a channel transfer function, an error effect of any linear filter can be transferred into a frequency domain response mismatch error, and by adoption of the estimation and compensation method disclosed by the invention, estimation and compensation of a high-speed time interleaved analog-to-digital conversion is realized, and the estimation and compensation method has the advantages of good validity, universality and practicability.

Description

A kind of estimation of the tiadc system based on multinomial model and compensation implementation method

Technical field

The present invention relates to the modulus conversion technique field of high speed, more particularly, to a kind of based on multinomial model The estimation of tiadc system and compensation implementation method.

Background technology

With the continuous development of integrated circuit technique, the popularization of digitizing technique, the sampling speed to modulus switching device adc The requirement more and more higher of rate and sampling precision, not requiring nothing more than data collecting system has high sample rate, also will have high sampling Precision.In actual utilization, there is high dependency to real-time sampling speed and sampling precision.But the maximum of adc is adopted Sample rate-constrained, in its resolution, is conflict body between resolution and sampling rate, and high sampling rate requires shorter Conversion time, and high-resolution then requires shorter conversion time.According to current ic design technology, adopting of more high speed to be realized Sample speed is it would be desirable to explore a kind of adc based on new construction and new method.A kind of important method realizing ultra-high speed sampling is just The adc using time-interleaved structure, i.e. tiadc (time-interleaved adc).

The method of the time-interleaved system of this multichannel is that have the single adc of identical sample rate f s using m piece, using simultaneously The structure of row, every adc sampled with the time interval being separated by 1/ (m*fs), with reach sample rate as m*fs (total sampling rate f =m*fs) effect.In theory, the adc structure of this time-interleaved sampling for m passage enables to whole system sampling Rate reaches m times of single dac.But due to manufacturing process shortcoming inherently it is impossible to make the complete mould of often a piece of adc Equally, so will necessarily make there is mismatch error between each passage adc, thus seriously reducing the letter of whole adc system Make an uproar ratio.

Mismatch correction based on early multichannel time-interleaved adc system is usually to repair using to front-end circuit both at home and abroad Adjust, reduce the impact of mismatch error by the circuit of meticulous layout.The shortcoming of this method is exactly when As time goes on, The change of temperature, the aging correction effect that can make circuit of electric elements lost efficacy.Method in order to overcome this front end to revise, The method that back-end processing can be utilized, is currently based at mismatch error and its digital back-end of multichannel time-interleaved adc system The correction algorithm of reason is the key of future development.

Content of the invention

The present invention is at least one defect overcoming described in above-mentioned prior art, provide a kind of based on multinomial model The estimation of tiadc system and compensation method, realize the estimation to high speed time intertexture A/D conversion system and compensation, have very well Effectiveness, popularity and practicality.

For solving above-mentioned technical problem, technical scheme is as follows:

A kind of estimation of the tiadc system based on multinomial model and compensation method, methods described is applied to tiadc system System, tiadc system is sampled to wide steady real-valued signal x (t), and output signal is y [n], the method comprising the steps of:

As reference channel, port number is set to m, using reference channel to other in s1: the a-road-through road of selected tiadc system Channel transfer function do normalized；

S2: normalized channel transfer function h (j ω) (channel-transfer function, ctf) is made p rank many Item formula model decomposition, i.e. h (j ω)=1+g (j ω), wherein,Here the value of p is not less than defeated Enter the frequency spectrum number -1 of signal x (t)；

S3: take ctf parameter a_pEstimated value beObtain the estimated value of ctfEstimation to ctf ValueCarry out inverse discrete Fourier transform and obtain its forms of time and space

S4: make equivalent test correcting filter be

Y [n] is carried out carrying out down-sampling with m=2, obtains 0 phase place and the two paths of signals of 1 phase place, be designated as y₀[n] and y₁ [n], they pass through respectivelyWithObtain z₀[n] and z₁[n], both intertextures can obtain z [n]；

S5: because input signal x (t) is wide steady (wws), ctf is linear, therefore y [n] must be that circulation width is steady (wscs), i.e. generally, r_y[n,n′]≠r_y[1+n, 1+n '], wherein r_y[n, n '] represents its auto-correlation function；

But when equivalent ctf does not comprise frequency domain response mismatch error or equivalent test correcting filterIt is completely counterbalanced by this During error, output y [n] also would is that wide steadily (wws), i.e. r_y[n, n ']=r_y[1+n, 1+n '], therefore, using relationOptimal channel transmission function can be tried to achieveEstimate knot Structure schematic diagram is as shown in Figure 3；

S6: error parameter under normal circumstancesThereforeOrder

$q_n\left(j\mathrm{\ω}\right)={\tilde{h}}_{opt}\left(j\mathrm{\ω}\right)=({\tilde{a}}_0+1)(1+\underset{p=1}{\overset{p}{\mathrm{\σ}}}{\mathrm{\ϵ}}_n^{\left(p\right)}{\left(j\mathrm{\ω}\right)}^p)\≈(1+\underset{p=1}{\overset{p}{\mathrm{\σ}}}{\mathrm{\ϵ}}_n^{\left(p\right)}{\left(j\mathrm{\ω}\right)}^p)$

Wherein

S7: have limit for length's unit impulse response wave filter (linear-phase fir filters) approximate using linear phase Preferably p rank differentiator, with g_pZ (), p=1 ... p represents, corresponding shock response is g_pK (), during one k level of design Become the collocation structure of digital wave filter group, collocation structure figure is as shown in figure 4, make its shock response be WhereinFor the equivalent impulse Response Function of each layer digital wave filter,Obtained by continuous iteration；

The initial condition making iteration isWherein δ (k) is unit sequence of impacts, and rightFor, can pass throughObtain；

InCalculated by following steps: WhereinThe initial condition of iteration isIts Middle δ (k) is unit sequence of impacts；

S8: make output signal y [n] of tiadc system pass through the digital filter group collocation structure h of this k level_nK (), obtains Output y ' [n] after compensation correction=σ ky [n-k] h_n(k)；

S9: the effect compensating is estimated it is considered to optimal reconstruction condition (perfect reconstruction Condition, pr) as standard it is clear that work asWhen, there is y ' [n]=x [n], that is, meet zero defect sampling, therefore work as a_n(j ω) → 1, that is, as | a_n(j ω) -1 | when → 0, compensation effect is best.

Compared with prior art, the beneficial effect of technical solution of the present invention is:

The present invention discloses a kind of estimation of the tiadc system based on multinomial model and compensation method, belongs to based on passage Estimation and backoff algorithm that the digital back-end of transfer function model is processed, can comprise any linearity error, including but not limited to Time error (time-skew error), gain error (gain error) and zero pole point error (pole-zero effect) Deng.Thus, the bearing calibration based on channel transfer function can be shifted the effect of the error of any linear filter for frequency domain Response mismatch error (frequency-response mismatch errors), the present invention realizes to high speed time intertexture modulus The estimation of converting system and compensation, have good effectiveness, popularity and practicality.

Brief description

Fig. 1 is the schematic diagram of multichannel tiadc system.

Fig. 2 is the channel transfer function model schematic of tiadc system.

Fig. 3 is the estimation structure chart based on channel transfer function tiadc model.

Fig. 4 is the tiadc collocation structure schematic diagram based on polynomial module shape parameter.

Fig. 5 is time domain input/output signal (locally) schematic diagram of tiadc.

Fig. 6 is the estimation schematic diagram of Cyclic Autocorrelation Function and first parameter.

Fig. 7 is that Cyclic Autocorrelation Function is intended to the estimation diagram of second and third parameter.

Fig. 8 is input and output frequency spectrum and the compensation result schematic diagram of tiadc.

Fig. 9 is collocation structure error output schematic diagram at different levels.

Figure 10 is estimation and the compensation flowchart of a whole set of tiadc.

Specific embodiment

Being for illustration only property of accompanying drawing illustrates it is impossible to be interpreted as the restriction to this patent；

With reference to the accompanying drawings and examples technical scheme is described further.

Embodiment 1

Below in conjunction with the accompanying drawings the specific embodiment of the present invention is described so that technical staff more fully understands this Bright.It is to be noted that the description of knowledge known to some can desalinate the main contents of the present invention, the description of these knowledge is here not Can be discussed in detail.

Fig. 1 is the schematic diagram of the multichannel tiadc system of the present invention, and Fig. 2 is the channel transfer function model of tiadc system Schematic diagram.Input signal is inputted with m passage, every passage with identical sample rate but different sampling instant (adjacency channel phases Difference t_sMoment) high-rate input signals are sampled, finally merge output signal, the analog-to-digital conversion of high-speed sampling is realized with this.Fig. 2 It is channel transfer function model schematic, this kind of model can transfer to any linearity error the parameter of channel transfer function On, can use unified method to compensate.

The structure of Fig. 3 is used for the parameter estimation of passage transfer function, and the structure of Fig. 4 utilizes the parameter estimation result of previous step It is filtered compensating.

, the test signal of employing is many sinusoidal signals to the present invention taking port number m=2 as a example, and the position of frequency spectrum is 0.4, 0.6,0.8 (normalized frequency), as shown in the figure of Fig. 8 the top, time-domain signal is as shown in Figure 5 for spectrogram.Therefore the taking of parameter p Value at least 2, therefore this example takes p=2.

During estimation, need first to set estimation parameter area, rule of thumb can first take Really Hunting zone can progressively be reduced after determining approximate range and suitably segment step-length, and then target component is estimated.Fig. 6 is rightStep-length precision is 0.0002 Search Results it is seen that working asWhen, circulation is certainly Correlation functionObtain minima 0.5267, similarly as seen from Figure 7, whenWhen, can use and obtain this minima.Estimated result such as table 1 thus can be obtained Shown:

Table 1

When calculating Cyclic Autocorrelation Function, need to calculate the auto-correlation function r of data z_z[n, 0] and r_z[n+1,1], this Invention takes n_max=5.When calculating auto-correlation function, using r_z[m, n]=e [z [m] z^*[n]] calculate.In order that in mathematic expectaion Statistical average adopts time average to replace, and using the cyclo-stationary of tiadc, calculating time difference respectively is Z₀[n] and z₁The auto-correlation function of [n] and cross-correlation functionAgainWith l=2 weave in, obtain r_z[n, 0],With l=2 weave in Weave in, obtains r_z[n+1,1], you can calculated using Cyclic Autocorrelation Function computing formula.

To the parameter estimatedArranged again and normalizing, utilized Relation, be calculated a m × p matrix For mending Compensation structure uses.

When building collocation structure as shown in Figure 4, need using the fdatool of matlab, each order ideal differentiator to be carried out Design, the fir coefficient g of each differentiator obtaining_pK () obtains incoming each straton passage of epsilon matrix etc. together with when estimating Effect wave filterCalculating function in the middle of, using formula Wherein here n=0,1,2,3 ... express time sequence unit, that is,It is a time varing filter, and due to tiadc There are the periodic characteristics with m as cycle, thereforeIn conjunction with m=2's Precondition, therefore only need to consider n=0,1 situation.In the same mannerh_nK () also only need to consider n=0,1 feelings Condition.

WithIt is all unit impact sequence δ (k), the equivalent shock response of each layer digital wave filter isThe compensation knot of total time varying digital filter group Structure shock response isIn the present invention, k takes 4, as 4 metafiltration wave structures.

Tiadc output signal y [n] passes through h respectively₀(k) and h₁K () wave filter, obtains two filtered sequence: y '₀ [n] and y '₁[n] carries out m=2 this two sequences, phase place be respectively 0 and 1 down-sampling operation, then to this two down-samplings after Sequence be interleaved, you can recover compensation sequences y ' [n], as shown in Figure 8.

The effect that frequency domain response mismatch error can be compensated is estimated it is considered to utilize optimal reconstruction condition (a_n(jω) =1) as standard, detection | a_n(j ω) -1 | whether trend towards 0, the action effect of estimation compensation structure.Effect pair before and after compensation Than as shown in Figure 9.Without during overcompensation | a_n(j ω) -1 | averagely about in about -10 (db), after the first order compensates, | a_n (j ω) -1 | averagely drop to about -30 (db), after the second level compensates, | a_n(j ω) -1 | averagely drop to -50 (db) left The right side, after the third level compensates, | a_n(j ω) -1 | averagely drop to about -70～-80 (db), after the fourth stage compensates, | a_n (j ω) -1 | averagely drop to about -100 (db).Error can be compensated and is gradually reduced with the increase of the collocation structure number of plies, weight Structure quality is become better and better.

Generally speaking, the present invention is a kind of to the high speed time intertexture A/D conversion system based on polynomial module shape parameter Estimate and compensate implementation method, integrally realize flow process as shown in Figure 10.Can be seen that the present invention to height from above experimental result The estimation of the time-interleaved A/D conversion system of speed is realized with compensating, and has good effectiveness, popularity and practicality.

Claims (1)

1. a kind of estimation of the tiadc system based on multinomial model and compensation method, methods described is applied to tiadc system, Tiadc system is sampled to wide steady real-valued signal x (t), and output signal is y [n] it is characterised in that methods described includes Following steps:

As reference channel, port number is set to m in s1: the a-road-through road of selected tiadc system, using reference channel to other logical Road transfer function does normalized；

S2: normalized channel transfer function h (j ω) is made p rank multinomial model decomposition, i.e. h (j ω)=1+g (j ω), its In,Here the value of p is not less than the frequency spectrum number -1 of input signal x (t)；

S3: take ctf parameter a_pEstimated value beP=0 ... p obtains the estimated value of ctfEstimated value to ctfCarry out inverse discrete Fourier transform and obtain its forms of time and space

S4: make equivalent test correcting filter be

Y [n] is carried out carrying out down-sampling with m=2, obtains 0 phase place and the two paths of signals of 1 phase place, be designated as y₀[n] and y₁[n], it Pass through respectivelyWithObtain z₀[n] and z₁[n], both intertextures can obtain z [n]；

S5: because input signal x (t) is wide stable, ctf is linear, therefore y [n] must be that circulation width is stable, that is, typically In the case of, r_y[n,n′]≠r_y[1+n, 1+n '], wherein r_y[n, n '] represents its auto-correlation function；

But when equivalent ctf does not comprise frequency domain response mismatch error or equivalent test correcting filterIt is completely counterbalanced by this error When, output y [n] also would is that wide stable, i.e. r_y[n, n ']=r_y[1+n, 1+n '], therefore, using relationOptimal channel transmission function can be tried to achieve

S6: error parameter under normal circumstancesThereforeOrder

$q_n\left(j\mathrm{\ω}\right)={\tilde{h}}_{opt}\left(j\mathrm{\ω}\right)=({\tilde{a}}_0+1)(1+\underset{p=1}{\overset{p}{\σ}}{\mathrm{\ϵ}}_n^{\left(p\right)}{\left(j\mathrm{\ω}\right)}^p)\≈(1+\underset{p=1}{\overset{p}{\σ}}{\mathrm{\ϵ}}_n^{\left(p\right)}{\left(j\mathrm{\ω}\right)}^p)$

WhereinP=1 ... p, n=0,1；

S7: have the p rank differentiator of limit for length's unit impulse response wave filter approximate ideal using linear phase, with g_p(z), p= 1 ... p represents, corresponding shock response is g_p(k), the collocation structure of one k level time varying digital filter group of design, order Its shock response isWhereinFor the equivalent impulse Response Function of each layer digital wave filter,Obtained by continuous iteration；

The initial condition making iteration isWherein δ (k) is unit sequence of impacts, and rightI=1, For 2 ... k, can pass throughObtain；

InI=1,2 ... k is calculated by following steps: Its InThe initial condition of iteration isWherein δ (k) rushes for unit Hit sequence；

S8: make output signal y [n] of tiadc system pass through the digital filter group collocation structure h of this k level_nK (), is compensated Output y ' [n]=∑ after correction_ky[n-k]h_n(k)；

S9: the effect compensating is estimated it is considered to optimal reconstruction condition as standard it is clear that working asWhen, there is y ' [n]=x [n], that is, meet zero defect sampling, therefore work as a_n (j ω) → 1, that is, as | a_n(j ω) -1 | when → 0, compensation effect is best.