CN103873016B - A kind of arbitrarily sampling rate conversion digital reconstruction filter coefficient method for designing - Google Patents

Abstract

The present invention relates to a kind of arbitrarily sampling rate conversion digital reconstruction filter coefficient method for designing, the method designs digital reconstruction filter coefficient based on re-construction theory and FIR filter THE DESIGN OF WINDOW FUNCTION method, window parameter is chosen by minimum attenuation in stop band, intercepted length, reconfigurable filter heterogeneous branch number is determined by sampling rate conversion factor maximum, by above parameter, perfect reconstruction function windowing discrete sampling is obtained reconfigurable filter coefficient and quantifies, the sampling rate conversion reconfigurable filter passband fluctuation of the method design is little, to mirror image suppression preferably, it is prone to FPGA realize, and it is substantially reduced design complexities, in addition the heterogeneous structure storage filter coefficient reading table is used, high performance any sampling rate conversion is achieved with less resource consumption, and variable sample rate scope is big, realize difficulty little.

Description

A kind of arbitrarily sampling rate conversion digital reconstruction filter coefficient method for designing

Technical field

The present invention relates to a kind of reconfigurable filter factor design method, particularly relate to one and be suitable to any sampling rate conversion Digital reconstruction filter coefficient method for designing, belongs to digital signal processing technique field.

Background technology

The most variable even continuous variable of symbol rate of modern software radio communications system, modulated terminal and demodulating end all need Sampling rate conversion to be carried out is to economize on resources, to reduce power consumption.For the situation of the variable even continuous variable of symbol rate, need design Arbitrarily sampling rate conversion reconfigurable filter, the performance of this wave filter determines the performance of signal sampling rate conversion process.

Signal sampling rate conversion can be realized by single-stage digital reconfigurable filter.Single-stage reconfigurable filter realizes there are two kinds of sides Formula: utilized polynomial approximation reconfigurable filter and the mode of a large amount of filter coefficient ROM table reading by a small amount of coefficient.Multinomial is near Seemingly there are Farrow structure based on Lagrange interpolation and B-spline approximation: Farrow structure only need to store less coefficient and not Need to calculate values of powers, but coefficient calculating in real time can cause time delay longer；And a length of L_BB-spline interpolation each be L_BPower meter Calculating, its edge approximation is the most smooth.Although polynomial approximation amount of storage is less, but coefficient calculates in real time so that power consumption is bigger.

Summary of the invention

It is an object of the invention to overcome the above-mentioned deficiency of prior art, it is provided that a kind of arbitrarily sampling rate conversion digital reconstruction Filter coefficient method for designing, the method selects suitable parameter according to sampling rate conversion performance requirement, to perfect reconstruction function Windowing intercepts design reconfiguration filter coefficient, and the sampling rate conversion reconfigurable filter passband fluctuation of the method design is little, to mirror image Suppression is preferably, it is easy to FPGA realizes, and is substantially reduced design complexities.

The above-mentioned purpose of the present invention is mainly achieved by following technical solution:

A kind of arbitrarily sampling rate conversion digital reconstruction filter coefficient method for designing, comprises the steps:

Step (one), according to minimum attenuation in stop band α_sRequirement, select Kaiser window parameter beta and intercept parameter N；

Step (two), according to sampling rate conversion factor L maximum needed for reconfigurable filter_max, select reconfigurable filter branch number M, takes

Wherein:Represent and x is rounded up, and M is positive integer；

Step (three), according to selected Kaiser window parameter beta, intercept parameter N and reconfigurable filter branch number M, use Kaiser window intercepts Sa function and obtains 2MN reconfigurable filter coefficient h (m), between waiting every for reconfigurable filter coefficient h (m) 2N Every being divided into one group, it is divided into M group；

Step (four), according to reconfigurable filter adjacent coefficient maximum difference Δ_maxXmaxh (m)-h (m-1), by following public Formula determines parameter B_h, wherein the quantization digit of reconfigurable filter coefficient h (m) is B_h+ 1:

$\begin{array}{c}{2}^{-(B_h-1)}>{\mathrm{\Δ}}_{\max }>2^{-B_h}\\ B_h+1>1-{\log }_2{\mathrm{\Δ}}_{\max }>B_h\end{array}.$

In above-mentioned any sampling rate conversion digital reconstruction filter coefficient method for designing, Kaiser window ginseng in step () The system of selection of number β and intercepting parameter N comprises the following specific steps that:

(1), β=0.1102 (α is obtained by Kaiser window function characteristic_s-8.7), wherein α_s≥50dB；

(2), parameter is intercepted, and N is positive integer；

Wherein: BW is signal double-side band bandwidth, f_iFor input signal sample rate.

In above-mentioned any sampling rate conversion digital reconstruction filter coefficient method for designing, step (three) uses Kaiser The concrete grammar that window intercepting Sa function obtains 2MN reconfigurable filter coefficient h (m) is as follows:

$h\left(m\right)=\frac{\sin (\mathrm{\πm}/M)}{\mathrm{\πm}/M}\·\frac{I_0\left(\sqrt{1-{((m-\mathrm{MN})/\mathrm{MN})}^2}\right)}{I_0\left(\mathrm{\β}\right)},m\∈[-\mathrm{MN},\mathrm{MN});$

Wherein: I₀Being a class zero Bessel function, m is sequence number and is integer.

In above-mentioned any sampling rate conversion digital reconstruction filter coefficient method for designing, quantization digit B will be obtained_h+ 1 Reconfigurable filter coefficient h (m) stores in ROM, and storage mode is often row 2N, and M row altogether is during reconfigurable filter work, cumulative Calculating address addr=(addr+L/M) mod (M), and round addr and obtain addr', wherein L is actual sample rate multiple, Corresponding reconfigurable filter coefficient h (m) in ROM is read, by reconfigurable filter according to rounding the accumulation calculating address addr' obtained Coefficient h (m) and input signal convolution obtain variable sampling rate signal.

The present invention compared with prior art provides the benefit that:

(1), the present invention selects appropriate parameter, employing FIR filter window function to set according to sampling rate conversion performance requirement Meter method intercepts design sampling rate conversion reconfigurable filter coefficient to perfect reconstruction function windowing, defeated according to sampling rate conversion during use Going out moment position reading coefficient and realize any sampling rate conversion, the method selects suitably ginseng according to sampling rate conversion performance requirement Number, design reconfiguration filter coefficient, the sampling rate conversion reconfigurable filter passband fluctuation of design is little, to mirror image suppression preferably；

(2), the present invention proposes a kind of brand-new based on digital signal re-construction theory and FIR filter THE DESIGN OF WINDOW FUNCTION method Digital reconstruction filter coefficient method for designing, makes full use of digital signal reconfiguration technique and Finite Impulse Response filter method for designing, adopts Store filter coefficient with the heterogeneous structure reading table, achieve high performance any sampling rate conversion with less resource consumption, And variable sample rate scope is big, it is achieved difficulty is little；

(3), the present invention uses ROM storage list structure by the pre-designed on-demand packet of reconfigurable filter coefficient and to deposit Storage, only need to read corresponding coefficient by address when sampling rate conversion processes and be filtered operation, to multiplier and adding when FPGA realizes Musical instruments used in a Buddhist or Taoist mass carries out multiplexing, and its amount of calculation is few, power consumption is little, it is easy to FPGA realizes, and is substantially reduced design complexities.

Accompanying drawing explanation

Fig. 1 is difference minimum stop-band attenuation α of the present invention_sUnder the conditions of design reconfigurable filter spectrogram；

Fig. 2 is reconfigurable filter quantization digit of the present invention and branch's number relation, and wherein 2A is adjacent coefficient maximum difference Δ_maxRelation curve with filter branch number M；2B is quantization digit B_hRelation curve with filter branch number M；

Fig. 3 is that digital reconstruction wave filter FPGA of the present invention realizes structure chart.

Detailed description of the invention

The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings:

The present invention designs digital reconstruction filter coefficient based on re-construction theory and FIR filter THE DESIGN OF WINDOW FUNCTION method, passes through Minimum attenuation in stop band chooses window parameter, intercepted length, sampling rate conversion factor maximum determine the heterogeneous branch of reconfigurable filter Number, is obtained reconfigurable filter coefficient by above parameter to perfect reconstruction function windowing discrete sampling and quantifies.

The present invention any sampling rate conversion digital reconstruction filter coefficient method for designing by perfect reconstruction function h (t)= Sa(πt/T_i) windowing is blocked and discrete sampling realizes.If the intercepting parameter of window function w (n) is N, then reconfigurable filter after intercepting Shock response be:

$h\left(n\right)=\frac{\sin \left(\mathrm{\πn}\right)}{\mathrm{\πn}}.w\left(n\right),\left|n\right|\≤N---\left(1\right)$

According to digital signal re-construction theory, to signal y (nT_i) carry out sampling rate conversion and obtain variable sampling rate signal y ' (mT_o) For:

$\begin{array}{c}{y}^{\′}\left({\mathrm{mT}}_o\right)=y^{\′}({\mathrm{kT}}_i+{\mathrm{\μT}}_i)\\ =\underset{n=-N}{\overset{N}{\mathrm{\Σ}}}y\left({\mathrm{nT}}_i\right)\·\frac{\sin [\mathrm{\π}({\mathrm{kT}}_i+{\mathrm{\μT}}_i-{\mathrm{nT}}_i)/T_i]}{\mathrm{\π}}\·w({\mathrm{kT}}_i+{\mathrm{\μT}}_i-{\mathrm{nT}}_i)\end{array}---\left(2\right)$

Wherein: T_iIt is spaced for input sample；T_oFor the output sampling interval；μ ∈ [0,1) it is output sampling instant mT_oRelative to Input sample moment kT_iNormalized offset.

By discrete for the value of μ in formula (2) the adjustment step-length n ε for finite point during reconfigurable filter design_k.Reconfigurable filter Time resolution ε_kThe least sampling rate conversion precision is the highest.

Sa function windowing intercepting can make reconfigurable filter frequency spectrum produce two changes: one is passband and the resistance of its frequency response There is fluctuation in band；Two are off at frequency being become intermediate zone slowly from precipitous decline.Fluctuation and intermediate zone can affect signal Reconstruction property, it is therefore desirable to choose suitable window function and intercept Sa function design digital reconstruction filter coefficient.Due to Kaiser Window intermediate zone is narrower, minimum attenuation in stop band scalable, has the more preferable suitability, therefore selects Kaiser window design digital reconstruction Filter coefficient.

The design of the present invention any sampling rate conversion digital reconstruction filter coefficient is implemented as follows:

(1), according to minimum attenuation in stop band α_sRequirement select Kaiser window parameter beta and intercept parameter N, Kaiser window time domain Expression formula is:

$w\left(n\right)=\frac{I_0(\mathrm{\β}\·\sqrt{1-{((n-N)/N)}^2})}{I_0\left(\mathrm{\β}\right)},\left|n\right|\≤N$

Wherein:For first kind zero Bessel function, N is positive integer.

Kaiser window function Fourier transformation is:

$\left(\mathrm{\ω}\right)=\left\{\begin{array}{c}\frac{N}{I_0\left(\mathrm{\β}\right)}\·\frac{\sinh \left(\sqrt{{\mathrm{\β}}^2-{(\mathrm{N\ω}/2)}^2}\right)}{\sqrt{{\mathrm{\β}}^2-{(\mathrm{N\ω}/2)}^2}},\left|\mathrm{\ω}\right|\≤\frac{\mathrm{\β}}{N}\\ \frac{N}{I_0\left(\mathrm{\β}\right)}\·\frac{\sin \left(\sqrt{{(\mathrm{N\ω}/2)}^2-{\mathrm{\β}}^2}\right)}{\sqrt{{(\mathrm{N\ω}/2)}^2-{\mathrm{\β}}^2}},\left|\mathrm{\ω}\right|\≥\frac{\mathrm{\β}}{N}\end{array}---\left(4\right)\right.$

In formula, β=0.1102 (α_s-8.7) (α_s>=50dB), α_sFor minimum attenuation in stop band；β value is by α_sUnique decision.β/N is Kaiser window function Fourier transformation W (ω) is become, from sinh (x) approximation, the cut-point that sin (x) approximates.

If the signal initial samples rate of a width of BW of double-side band band is f_i(f_i=1/T_i≥2BW).Digital reconstruction wave filter intercepts Parameter N it suffices that:

$2N\≥\frac{({\mathrm{\α}}_s-7.95)\·f_i}{14.36\mathrm{\Δf}}---\left(5\right)$

Wherein, Δ f is reconfigurable filter intermediate zone.In order to suppress mirror image, generally take Δ f≤f_i-BW。

Δ f≤f_i-BW substitute into formula (5) obtain intercept parameter N scope:

$N\≥\frac{({\mathrm{\α}}_s-7.95)}{28.72\·(1-\mathrm{BW}/f_i)}---\left(6\right)$

Known by formula (6), intercept parameter N and BW/f_iAnd α_sAll it is directly proportional.Take BW/f_iBe 1/2, Kaiser window parameter beta and N with α_sRelation see table:

Table 1Kaiser window parameter beta and N and α_sRelation

Minimum attenuation in stop band αs(dB)	60	65	70	75	80	85	90
								Corresponding β value	5.66	6.21	6.76	7.31	7.86	8.41	8.96

Intercept parameter N lower limit

4

4

5

5

6

6

6

During design, according to minimum attenuation in stop band α_sSelected suitably by table 1 and formula (6) with initial signal BW/fi ratio Window parameter beta and intercepting parameter N.

(2), selecting reconfigurable filter branch number M, the value of branch number M needs to consider the maximum needed for signal reconstruction filtering Precision, branch number M is reconstruct filter time domain precision ε_kInverse.According to the sampling rate conversion factor maximum needed for reconfigurable filter L_max, select reconfigurable filter branch number M, take

Wherein:Representing and round up x, M is positive integer.

(3), according to selected Kaiser window parameter beta, parameter N and reconfigurable filter branch number M Kaiser window are intercepted Intercepting Sa function design sampling rate conversion reconfigurable filter coefficient:

$h\left(m\right)=\frac{\sin (\mathrm{\πm}/M)}{\mathrm{\πm}/M}\·\frac{I_0(\mathrm{\β}\·\sqrt{1-{((m-\mathrm{MN})/\mathrm{MN})}^2})}{I_0\left(\mathrm{\β}\right)},m\∈[-\mathrm{MN},\mathrm{MN})---\left(7\right)$

Wherein: I₀For first kind zero Bessel function, m is sequence number and is integer.

2MN reconfigurable filter coefficient is there are by formula (7).It is divided into one group at equal intervals by every for coefficient 2N, is divided into M Group, then kth system number is:

$h_k=\underset{n=1}{\overset{2N}{\mathrm{\Σ}}}h(\mathrm{nM}+k),k\∈[1,M]---\left(8\right)$

(4) quantization parameter B, is determined_h, the quantization digit of reconfigurable filter coefficient h (m) is B_h+1.Modulated terminal signal to send Generate analogue signal to D/A modular converter to send to radio-frequency head.Signal to noise ratio snr=6.02 (the B of D/A converter_d+1)+1.76(B_d For the D/A input end signal bit number without sign bit).Usually require that the signal to noise ratio of communication system reaches 60dB, so input The quantization digit B of signal_d>=9, quantization parameter B of word reconfigurable filter of similarly peeking_h≥9。

Reconfigurable filter coefficient B_h+ 1 bit quantization, then quantified precision is.In order to represent reconstruct filter accurately Ripple device makes signal reconstruction error less, it is desirable to the maximum difference between adjacent samples point is more than minimum quantization precision, wave filter phase Adjacent coefficient time interval is directly proportional to filter branch number M.If reconfigurable filter adjacent coefficient maximum difference is Δ_max=maxh (m)-h (m-1), then reconfigurable filter coefficient quantization position parameter B_hMeet following condition:

$\begin{array}{c}{2}^{-(B_h-1)}>{\mathrm{\Δ}}_{\max }>2^{-B_h}\\ B_h+1>1-{\log }_2{\mathrm{\Δ}}_{\max }>B_h\end{array}---\left(9\right)$

The quantization digit that reconfigurable filter is minimum is may determine that by formula (9).By calculate can be worked as | x |= When 0.66268, h (x) rate of change is maximum.Quantization digit B when branch number M of the present invention takes 256≤M≤65536_hLower limit such as Fig. 2 Shown in, Fig. 2 is reconfigurable filter quantization digit of the present invention and branch's number relation, and wherein 2A is adjacent coefficient maximum difference Δ_maxWith The relation curve of filter branch number M；2B is quantization digit B_hRelation curve with filter branch number M.Table 2 lists reconstruct When filter branch number M takes different value, filter coefficient quantifies word length B accordingly_hValue:

The quantization digit that table 1 branch number is corresponding

During design from Fig. 2 and Biao 2 can obtain digital reconstruction filter branch number M take different value time, digital reconstruction filter Device corresponding minimum quantization position parameter B_h。

(5), according to obtaining quantization digit B_hReconfigurable filter coefficient h (m) the design digital reconstruction wave filter FPGA knot of+1 Structure, will obtain quantization digit B_hReconfigurable filter coefficient h (m) storage in ROM, storage mode be often row 2N, common M row, Resource-constrained in FPGA, often uses multiplexings such as multipliers.

The FGPA structure of reconfigurable filter realizes structure as it is shown on figure 3, Fig. 3 is digital reconstruction wave filter FPGA of the present invention Figure.In Fig. 3, M is reconstruct filter branch number, and N is that digital reconstruction wave filter intercepts parameter, and L is actual sample rate multiple, h₁, h₂…h_2NThe corresponding system number read from ROM for address addr.y(nT_i) input signal sequence, its sample rate is f_i=1/ T_i, y^′(mT_o) it is resampling postorder row, its output sampling rate is f_o, K=L/M is the frequency control word of NCO.

During reconfigurable filter work, accumulation calculating address addr=(addr+L/M) mod (M), and addr is rounded obtain Addr', reads corresponding reconfigurable filter coefficient h (m) in ROM according to rounding the accumulation calculating address addr' obtained, will reconstruct Filter coefficient h (m) and input signal convolution obtain variable sampling rate signal, i.e. with input signal y (nT_i) convolution obtains sample rate Conversion signal y^′(mT_o)。

It is illustrated in figure 1 difference minimum stop-band attenuation α of the present invention_sUnder the conditions of design reconfigurable filter spectrogram, in figure Give α_s=60,70,80, the 90dB sampling rate conversion reconfigurable filter spectral performance requiring lower design, are found out design by figure Sampling rate conversion reconstruct minimum attenuation in stop band meets design performance demand and passband fluctuation is less.Therefore any sample rate of the present invention Conversion reconfigurable filter factor design can select according to sampling rate conversion performance requirement that suitable parameter designing is high performance adopts Sample rate conversion reconfigurable filter.

Embodiment

Biobelt bandwidth BW=40kHz, input sampling rate f_i=80kHz, communications platform D/A converter work sample rate f_o= 80MHz.Require that reconfigurable filter minimum attenuation in stop band is more than 65dB.

(1) according to minimum attenuation in stop band α_sThe requirement of >=65dB selects Kaiser window parameter beta and intercepts parameter N: taken by table 1 α_s=70dB, then β=6.76, N=5.

(2) reconfigurable filter branch number M is selected according to minimum attenuation in stop band.Sampling rate conversion factor L=f_o/f_i=1000, institute To take M=2¹⁰>L。

(3) according to selecting Kaiser window parameter beta=6.76, intercepting parameter N=5 and reconfigurable filter branch number M=1024, Intercept Sa function with Kaiser window and obtain 10240 reconfigurable filter coefficients.One group it is divided at equal intervals by every for coefficient 2N=10, It is divided into M=1024 group.

(4) selection of the quantization digit of data, according to table 2 by reconfigurable filter branch number M=1024 peek word reconstruction filtering Device quantization parameter B_h=10, i.e. quantization digit is 11.

(5) during the work of digital reconstruction filtration module, accumulation calculating address addr=(addr+L/M) mod (M) also rounds, and reads Take the sampling rate conversion signal after corresponding coefficient and input signal convolution are reconstructed in ROM storage table.

The above, the detailed description of the invention that only present invention is optimal, but protection scope of the present invention is not limited thereto, Any those familiar with the art in the technical scope that the invention discloses, the change that can readily occur in or replacement, All should contain within protection scope of the present invention.

The content not being described in detail in description of the invention belongs to the known technology of professional and technical personnel in the field.

Claims (4)

1. any sampling rate conversion digital reconstruction filter coefficient method for designing, it is characterised in that: comprise the steps:

Step (one), according to minimum attenuation in stop band α_sRequirement, select Kaiser window parameter beta and intercept parameter N；

Step (two), according to sampling rate conversion factor L maximum needed for reconfigurable filter_max, select reconfigurable filter branch number M, take

Wherein:Represent and x is rounded up, and M is positive integer；

Step (three), according to selected Kaiser window parameter beta, intercept parameter N and reconfigurable filter branch number M, use Kaiser window intercepts Sa function and obtains 2MN reconfigurable filter coefficient h (m), between waiting every for reconfigurable filter coefficient h (m) 2N Every being divided into one group, it is divided into M group；

Step (four), according to reconfigurable filter adjacent coefficient maximum difference Δ_max=max | h (m)-h (m-1) |, by following public Formula determines parameter B_h, wherein the quantization digit of reconfigurable filter coefficient h (m) is B_h+1:

$\begin{array}{c}{2}^{-(B_h-1)}>{\mathrm{\Δ}}_{\max }>2^{-B_h}\\ B_h+1>1-{\log }_2{\mathrm{\Δ}}_{\max }>B_h\end{array};$

Wherein: m is sequence number and is integer；B_hQuantization parameter for digital reconstruction wave filter.

One the most according to claim 1 any sampling rate conversion digital reconstruction filter coefficient method for designing, its feature It is: in described step (), the system of selection of Kaiser window parameter beta and intercepting parameter N comprises the following specific steps that:

(1), β=0.1102 (α is obtained by Kaiser window function characteristic_s-8.7), wherein α_s≥50dB；

(2), parameter is interceptedAnd N is positive integer；

Wherein: BW is signal double-side band bandwidth, f_iFor input signal sample rate.

One the most according to claim 1 any sampling rate conversion digital reconstruction filter coefficient method for designing, its feature It is: described step (three) uses Kaiser window intercept Sa function and obtain the concrete side of 2MN reconfigurable filter coefficient h (m) Method is as follows:

$h\left(m\right)=\frac{\sin (\mathrm{\π}m/M)}{\mathrm{\π}m/M}\·\frac{I_0(\mathrm{\β}\·\sqrt{1-{\left(\right(m-MN)/MN)}^2})}{I_0\left(\mathrm{\β}\right)},m\∈\[-MN,MN);$

Wherein: I₀It it is a class zero Bessel function.

4. according to a kind of arbitrarily sampling rate conversion digital reconstruction filter coefficient described in claims 1 to 3 any claim Method for designing, it is characterised in that: quantization digit B will be obtained_hReconfigurable filter coefficient h (m) of+1 stores in ROM, storage side Formula is often row 2N, M row altogether, during reconfigurable filter work, and accumulation calculating address addr=(addr+L/M) mod (M), and right Addr rounds and obtains addr', and wherein L is actual sample rate multiple, reads according to rounding the accumulation calculating address addr' obtained Corresponding reconfigurable filter coefficient h (m) in ROM, obtains variable sampling rate by reconfigurable filter coefficient h (m) and input signal convolution Signal.