CN106134514B - Sampling rate converting method based on Farrow Structure Filter and device - Google Patents

Abstract

Based on the sampling rate converting method of Farrow Structure Filter, the sample rate conversion that need to complete data signal for multi-sampling rate system for signal processing, adopt second order power function and four sampled points to build the expression formula of signal after sample rate conversion, sample conversion device adopts 9 delayers, 9 adders, 2 subtracters and 8 multipliers to build sampling filter. With respect to traditional Lagrangian Farrow Structure Filter sampling rate converting method, the multiplier that the inventive method can reduce half uses, in the time that FPGA realizes, can utilize 1/2 hardware resource to realize sample rate conversion, and there is good anti-spectral image and the ability of spectral aliasing, ensure the integrality of signal frequency spectrum after sampling rate conversion.

Description

Sampling rate converting method based on Farrow Structure Filter and device

Technical field

The present invention relates to a kind of conversion method of digital signal samples rate and adopt the sample rate of the method design to turnChanging device.

Background technology

At present, mainly utilize CIC filtering and Farrow filtering to realize sample rate conversion. Wherein CIC filterThe flexibility of wave method is poor, and it is more to take resource, and in engineering practice, application can cause higher hardwareCost, be unfavorable for developing of product, and the sample rate conversion technology of Farrow Structure Filter not onlyThere is flexibility, the more important thing is in the utilization of resources and account for and have great advantage, therefore study FarrowThe sample rate conversion technology of Structure Filter has great engineering practice meaning.

Normally used Farrow Structure Filter as shown in Figure 1, utilizes 12 filter coefficients to do 14Individual multiplying completes sample rate conversion, and its design of filter often utilizes linear interpolation, or cubic spline is insertedValue, or the method for Lagrange's interpolation designs, so that wave filter has good filtering performance. For exampleApplication number is CN00807033.4, and name is called " the continuous variable delay filter of use and multiphase filter combinationThe image interpolation of ripple device and extraction " Chinese patent, and application number is CN200710037143.X, nameBe called the disclosed technical side of Chinese patent of " a kind of Doppler simulation implementation method based on digital interpolative "In case, all use multistage multinomial design Farrow wave filter, Chen Weidong, Sun Dong, Zhang Hua are punched in 2009On year the 6th phase the 35th volume " radio communication technology ", deliver " based on interpolation filter sign synchronizationRealize " use cubic function design Farrow wave filter in a literary composition. A large amount of emulation facts have proved, utilizeAbove-mentioned these interpolation method designing filters, have the ability of good anti-spectral aliasing, but for by samplingThe inhibition ability of the image spectra that rate conversion produces is not also very desirable, in addition, and owing to utilizing above-mentioned these to insertThe filter coefficient of value method design is fixed, and is unfavorable for follow-up optimization.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of filtering performance good,The sampling rate converting method based on Farrow Structure Filter and device that resource utilization is high.

Technical solution of the present invention is: based on the sampling rate converting method of Farrow Structure Filter,Adopt second order power function and four sampled points to represent the signal y (kT after sample rate conversion_i)，

$y\left({\mathrm{kT}}_i\right)=\underset{n=0}{\overset{2}{\Σ}}v\left(n\right){\left(u_k\right)}^n$

Wherein, T_iFor the signal sampling period after conversion, k is integer,

T_sFor the signal sampling period before conversion, m_kFor kT_i/T_sInteger part, u_kFor kT_i/T_sFractional partPoint, x () is sampled signal, c_nAnd c (0)_n(1), n=0,1,2 is and passband and the stopband of sample rate conversion wave filterRelevant undetermined coefficient, m_k，u_kInitial value is 0, u_kWith increment, Ti/Ts increases progressively, u_kRate of change be 1/T_i; Work as u_kU when > 1_k＝u_k-1，m_k＝m_k+1。

Described c_nAnd c (0)_n(1), n=0,1,2 meets relational expression with sample rate conversion wave filter h (t):

Sample rate conversion device based on Farrow Structure Filter, comprise 9 delayers, 9 adders,2 subtracters and 8 multipliers; Wherein every 3 delayers are one group, for to certain fixed timeSampled signal is carried out delay process, obtains three groups of bursts that form by four identical sampled points; Work as nDuring for even number, v (n) adopts 3 adders and 2 multipliers to realize, and in the time that n is odd number, v (n) adopts2 subtracters, 1 adder and 2 multipliers are realized; V (2) first utilizes 1 multiplier and u_kMultiply each other1 adder of rear recycling and v (1) are added, and the result of addition is utilized 1 multiplier and u_kRecycling after multiplying each other1 adder and v (0) are added, and finally obtain y (kT_i) and output.

The present invention's advantage is compared with prior art:

1, the inventive method utilizes the low pass filter of power function design to have good anti-spectral image and frequency spectrumThe ability of aliasing, in the time that Practical Project antagonism spectral image has different requirement from aliasing ability, can be by adjusting6 parameter c 0 (k) and c1 (k), k=0,1,2 size, adjusts pass band and Stopband Performance flexiblyWith meet Practical Project demand;

2, with respect to the wave filter of identical interpolation knot, the Farrow structure of the inventive method based on power functionThe filter coefficient that wave filter uses becomes original half, when coefficient storage, takies storageCapacity has been saved half, in addition, by increasing add operation, the number of multiplier has also been saved than originalHalf, and in engineering practice, while utilizing FPGA to realize, the shared resource of multiplier is high far awayGo out the shared resource of adder, therefore, utilize adder to reduce the method for multiplier, greatly reduceSample rate conversion technology takies resource. In the time utilizing FPGA to carry out signal processing, because of FPGA insideResource-constrained, therefore, in the time of algorithm for design, maximum Consideration is resource utilization issue, the inventive methodUnder the prerequisite of performance that ensures signal processing, reduce to greatest extent resource use, thereby reduced hardPart cost, has great practical value in research and development of products and in producing.

Brief description of the drawings

Fig. 1 is the schematic diagram of traditional Farrow Structure Filter;

Fig. 2 is sample rate conversion Principle of Process figure;

Fig. 3 is the schematic diagram that the present invention is based on the Farrow Structure Filter of power function;

Fig. 4 is the time domain waveform figure of sample rate conversion front signal in the embodiment of the present invention;

Fig. 5 is the spectrogram of signal shown in Fig. 4;

Fig. 6 is the time domain waveform figure of signal after sample rate conversion in the embodiment of the present invention;

Fig. 7 is the spectrogram of signal shown in Fig. 6.

Detailed description of the invention

The present invention proposes a kind of method of utilizing power function to design low pass filter, utilize power function structurePiecewise polynomial represents filter function, utilizes the controllability of each piecewise polynomial coefficient, adjusts flexibly systemNumber size, to change passband and the Stopband Performance of wave filter, make wave filter have good anti-spectral aliasing withSuppress the performance of spectral image.

Sample rate conversion process as shown in Figure 2, its essence is a resampling process, first utilizes low pass filteredRipple device (sample rate conversion wave filter) h (t) is T to sample rate_sInput signal sequence x (n) be reconstructed,And then with sample rate T_iThe signal of reconstruct is carried out to double sampling and obtain output sequence y (k). Said process canShow with following formula table:

$y\left({\mathrm{kT}}_i\right)=\underset{m=-N/2}{\overset{N/2-1}{\Σ}}{h}_m\left(\right(m+u_k\left)T_s\right)x\left(\right(m_k-m\left)T_s\right)---\left(1\right)$

Wherein m_kFor kT_i/T_sInteger part, u_kFor kT_i/T_sFractional part, h_m((m+u_k)T_sFor h((m+u_k)T_sHeterogeneous component, N participates in the interpolation knot number of computing.

According to the character of power function, any one function can utilize the method representation of power function summation,This definition power function g_n(t) as follows

Filter function h (t) can be expressed from the next

$h\left(t\right)=\underset{k=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{L}{\mathrm{\Σ}}}{c}_n\left(k\right)g_n(t-k)---\left(3\right)$

Wherein L is power series g_n(t) top step number. Coefficient c_n(k) adjustable, can be according to Practical Project to frequency spectrumRequirement (passband and stopband characteristic) design different c_n(k), make the frequency spectrum of the wave filter being represented by h (t)Meet the demands, reach good spectral characteristic.

Can design according to following requirement for h (t):

A), in order not introduce interpolated error at interpolation knot, require h (t) to meet following restrictive condition:

$h\left({\mathrm{kT}}_i\right)=\left\{\begin{array}{cc}1,& k=0\\ 0,& k\≠0\end{array}\right.---\left(4\right)$

B), in order to make interpolation filter there is linear phase, require the h (t) should be about t=0 even symmetry, therefore

Require coefficient c_n(k) there is symmetry,

Therefore wave filter h (t) can be expressed as

$h\left(t\right)=\underset{k=0}{\overset{N/2-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{L}{\mathrm{\Σ}}}{c}_n\left(k\right)f_n(t-k)---\left(6\right)$

Wherein

f_n(t-k)＝g_n(t-k)+(-1)ⁿg_n(t+(k+1)) (7)

(6) formula is carried out to frequency domain conversion, obtain

$H\left(f\right)=\underset{k=0}{\overset{N/2-1}{\Σ}}\underset{n=0}{\overset{L}{\Σ}}{c}_n\left(k\right)F_n(n,k,f)---\left(8\right)$

Wherein, F_n(n, k, f) is f_n(t-k) Fourier transformation. By flexible design c_n(k) can makeH (f) meets the demands respectively in passband and stopband.

The sample rate conversion implementation method based on Farrow Structure Filter that the present invention proposes, described in utilizationThe symmetry of the low-pass filter coefficients based on power function, is only used the coefficient of half to carry out computing, will storeThe space of filter coefficient subtracts and is a half. By the sampled point buffer memory with the same product factor is added,The method multiplying each other with Product-factor again, makes multiplication computation amount also subtract and be a half, thereby makes of the present inventionThe realization of Farrow wave filter is used resource to reduce to the half of traditional structure.

The present invention is based on the Farrow Structure Filter of power function, as shown in Figure 3. In figure, D is delayer,For adder,For subtracter,For multiplier, its derivation is as follows:

According to formula (2) and formula (3), between any two input sample points

$\begin{array}{c}h(m+u_k)=\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{L}{\mathrm{\Σ}}}{c}_n\left(m\right)g_n\left(u_k\right)\\ =\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{L}{\mathrm{\Σ}}}{c}_n\left(m\right){\left(u_k\right)}^n\\ =\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}{h}_m(m+u_k)\end{array}---\left(9\right)$

(9) formula substitution (1) formula can be obtained

$\begin{array}{c}y\left({\mathrm{kT}}_i\right)=\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}{h}_m\left(\right(m+u_k)T_s\left)x\left(\right(m_k-m)T_s\right)\\ =\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{L}{\mathrm{\Σ}}}{c}_n\left(m\right){\left(u_k\right)}^{n}x\left(\right(m_k-m)T_s)\end{array}---\left(10\right)$

Exchange summation sequentially with after multiplication order can obtain

$\begin{array}{c}y\left({\mathrm{kT}}_i\right)=\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{L}{\mathrm{\Σ}}}{c}_n\left(m\right)x\left(\right(m_k-m)T_s){\left(u_k\right)}^n\\ =\underset{n=0}{\overset{L}{\mathrm{\Σ}}}\[\underset{m=-N/2}{\overset{N/2-1}{\mathrm{\Σ}}}{c}_n\left(m\right)x\left(\right(m_k-m)T_s)\]{\left(u_k\right)}^n\\ =\underset{n=0}{\overset{L}{\mathrm{\Σ}}}v\left(n\right){\left(u_k\right)}^n\end{array}---\left(11\right)$

In the present invention, use power function lowest-order L=2 to carry out computing, according to the principle of curve, utilize 2Rank multinomial carries out curve fitting to sampled point, at least needs four sampled points, the power letter using in the present inventionNumber top step number is 2, can select N=4. By simulating, verifying, the present invention's 2 rank power function design filteringDevice can be realized the identical spectral performance of 3 rank Lagrange, due to the controllability of power function filter coefficient,By a large amount of simulating, verifyings, design one group of preferably filter coefficient, as shown in table 1. Utilize this filterRipple device coefficient can be realized than better spectral performance of 3 rank Lagranges.

Table 1 is based on power function Farrow Structure Filter optimization coefficient

In the time that Practical Project has different requirement to filter passband from the performance of stopband, can be according to following formula to filteringDevice coefficient magnitude is suitably adjusted.

All can increase operand if increase the value of L or N, thereby the resource can increase hardware and realize time is heldPin. In the time that hardware is realized, except being required to meet suitable performance, the utilization of resources be also an important consideration because ofElement, therefore the final purpose of design is to meet performance requirement, farthest reduce again resource and use,Consider final N=4, the L=2 of selecting in the present invention.

According to the symmetry of describing in formula (5), can obtain

m_k，u_kInitial value is 0, due to x (T_s) in actual signal, do not exist, can think that it is 0; u_kWith increment, Ti/Ts increases progressively, the sample rate f of its rate of change and output_iIdentical (is 1/T_i). Work as u_kWhen > 1 u_k＝u_k-1, m simultaneously_kFrom adding 1, due to m_kVariation, make to participate in four sampled point m of computing_k-2， m_k-1，m_k，m_k+ 1 becomes one group of new sampled point.

Can obtain structure shown in Fig. 3 according to formula (11) and formula (12).

Embodiment

Get interpolation knot number N=4, power function top step number L=2.

1) utilize sinc function, with sample rate f_s=3M/s (is T_s=3.3ms) one group of input letter of generationNumber sequence x (n), as shown in Figure 4, frequency spectrum as shown in Figure 5 for its signal waveform.

2)u_kInitial value is made as 0, then increases progressively with increment Ti/Ts, works as u_kWhen > 1, subtract 1, u_kEvery changeChange the sample rate sequence that once just can obtain an output, therefore u_kWith sample rate T_iBecomeChange, and participate in multiply-add operation.

3) [the m in list entries_k-1，m_k，m_k+1，m_k+ 2] four sampled points participate in computing, its workWorking frequency is Ts, works as u_kWhen > 1, m_k+ 1, produce one group of new sampled point sequence ginsengWith computing, work as u_kWhen < 1, the sampled point that participates in computing remains unchanged, with u_kTake advantage ofThe intermediate variable that adds computing also remains unchanged, and now can save part amount of calculation

By controlling u_k，m_kVariation, output that can control signal, it is new that Fig. 6 and Fig. 7 are respectively outputSample rate f_i=4M/s (is T_i=2.5ms) under signal waveform and frequency spectrum, comparison diagram 4 and Fig. 6, from time domainWaveform is seen, the envelope approximately equal of input signal and output signal, but sample rate is carried to some extent than original sample rateHeight, can think that output signal is to be redeveloped into analog signal by input signal to sample and obtain again, comparison diagram 5 HesFig. 7, from spectrum component, the spectral bandwidth of input signal is between normalized frequency [0.2,0.2], and logicalBe with smooth, the passband of output signal with input signal spectrum consistent, illustrate signal do not have after treatment frequency spectrum mixFolded, not being both of input/output signal frequency spectrum, there is mirror image outward in output signal band, but image spectra all decaysBelow 0db, illustrate that the Farrow Structure Filter that adopts the inventive method to build is well anti-except havingSpectral aliasing ability, also has good anti-spectral image ability.

The content not being described in detail in description of the present invention belongs to those skilled in the art's known technology.

Claims (3)

1. the sampling rate converting method based on Farrow Structure Filter, is characterized in that: adopt second order powerFunction and four sampled points represent the signal y (kT after sample rate conversion_i)，

$y\left({\mathrm{kT}}_i\right)=\underset{n=0}{\overset{2}{\&Sigma;}}v\left(n\right){\left(u_k\right)}^n$

Wherein, T_iFor the signal sampling period after conversion, k is integer,

T_sFor the signal sampling period before conversion, m_kFor kT_i/T_sInteger part, u_kFor kT_i/T_sFractional partPoint, x () is sampled signal, c_nAnd c (0)_n(1), n=0,1,2 is and passband and the stopband of sample rate conversion wave filterRelevant undetermined coefficient, m_k，u_kInitial value is 0, u_kWith increment, Ti/Ts increases progressively, u_kRate of change be 1/T_i; Work as u_kU when > 1_k＝u_k-1，m_k＝m_k+1。

2. the sampling rate converting method based on Farrow Structure Filter according to claim 1, itsBe characterised in that: described c_nAnd c (0)_n(1), n=0,1,2 meets relational expression with sample rate conversion wave filter h (t):

3. the sample rate conversion device based on Farrow Structure Filter, is characterized in that comprising: 9 are prolongedTime device, 9 adders, 2 subtracters and 8 multipliers; Wherein every 3 delayers are one group, useIn the sampled signal of certain fixed time is carried out to delay process, obtain three groups by four identical sampled point structuresThe burst becoming; In the time that n is even number, v (n) adopts 3 adders and 2 multipliers to realize, whenWhen n is odd number, v (n) adopts 2 subtracters, 1 adder and 2 multipliers to realize; V (2) is profit firstWith 1 multiplier and u_kAfter multiplying each other, recycle 1 adder and v (1) and be added, the result of addition utilizes 1 to take advantage ofMusical instruments used in a Buddhist or Taoist mass and u_kAfter multiplying each other, recycle 1 adder and v (0) and be added, finally obtain y (kT_i) and output,

T_iFor the signal sampling period after conversion, k is integer, T_sFor the signal sampling period before conversion, m_kFor kT_i/T_sInteger part, u_kFor kT_i/T_sFractional part, x () is sampled signal, c_nAnd c (0)_n(1), n=0,1,2 is the undetermined coefficient relevant with stopband to the passband of sample rate conversion wave filter, m_k， u_kInitial value is 0, u_kWith increment, Ti/Ts increases progressively, u_kRate of change be 1/T_i; Work as u_kU when > 1_k＝u_k-1， m_k＝m_k+1。