CN100557971C - The time domain implementation method that is used for simple coefficient FIR filter - Google Patents

Abstract

The invention discloses a kind of time domain implementation method that is used for simple coefficient FIR filter, belong to the discrete signal processing technology field.Described method comprises: the impulse response of FIR filter is decomposed into the fixing sub-impulse response of a plurality of length, and the sub-impulse response that each length is fixing is decomposed into the fixing branch cross-talk impulse response of a plurality of length; The input signal of FIR filter obtains a plurality of minutes cross-talk linear convolution results after dividing the cross-talk impulse response by each; Branch cross-talk linear convolution results added with selecting to obtain obtains a plurality of sub-linear convolution results; The delayed addition of each sub-linear convolution result is obtained the time domain output signal of FIR filter.The time domain implementation method of FIR filter provided by the invention has reduced hard-wired complexity, has reduced the quantity of tapped delay unit, has reduced the quantity of adder, has optimized hardware configuration, has realized that the coefficient of FIR filter is configurable.

Description

The time domain implementation method that is used for simple coefficient FIR filter

Technical field

The present invention relates to the discrete signal processing technology field, particularly a kind of time domain implementation method that is used for simple coefficient FIR filter.

Background technology

Discrete filter is the discrete time linear time-invariant system with time-discrete impulse response (Impulse Response) definition.Wherein, the discrete filter of impulse response limited length abbreviates FIR (Finite Impulse Response) filter as.The time domain expression formula of the linear convolution operation of FIR filter is as follows:

$y\left[n\right]=x\left[n\right]*h\left[n\right]=\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}x[n-m]h\left[m\right]$

Wherein * represents discrete linear convolution relation, and input signal is x[n], output signal is y[n], h[n] be the finite impulse response of FIR filter, its length is finite value N.The linear convolution system block diagram of FIR filter as shown in Figure 1, it realizes that principle is: length is the different delayed time that the tapped delay line of N obtains input signal, delay input signal x[n-m] and FIR filter coefficient h[m] multiply each other, summation obtains filtering output to multiplied result.As h[n] when being simple coefficient, multiplication can replace with according to h[m] to x[n-m] do the shifter-adder computing of signed number.In actual applications; transmitting terminal often uses value simple (for example+1;-1) and the sequence of limited length; and sequence is changes persuingization (promptly configurable) as required; for example be used for the frequency expansion sequence of Resistant DS Spread Spectrum System and be used for the PN sequence that the block transmission system protection is filled at interval, correspondingly matched filtering or the coupling related operation at system receiving terminal needs the simple and/or configurable FIR filter of coefficient of coefficient.The major function of FIR filter be finish the input sample delay, filter coefficient multiplies each other and the summation operation of multiplied result.The finite impulse response of FIR filter helps guaranteeing the performance of discrete system, for example the stability of linear phase; Filter coefficient simply helps abbreviation or directly substitutes multiplying; Filter coefficient is configurable then to be realized having higher requirement to filter.

The direct type implementation structure of FIR filter as shown in Figure 2, its implementation structure mainly comprises tapped delay line, multiplication unit and sum unit three parts, the main composition of other implementation structure (as the transposition type) is with directly type is similar.Input signal passes through delay line successively, and the result of its different delay exports by delay line tap; Tap output and filter coefficient multiply each other, and finish the required multiplying of linear convolution, and the filter fixing for coefficient adopts shifter-adder to substitute multiplying usually; Multiplied result obtains the linear convolution result after summation, i.e. filter output signal.

But the hardware of high order FIR filter in integrated circuit or programming device realizes existing usually following several problem:

1. the hardware realization of high order FIR filter can make delay cell quantity and number of taps become too much;

2. the hardware realization of high order FIR filter can make the adder quantity of multiplier or alternative multiplication become too much;

3. for the variable high order FIR filter of coefficient, its hard-wired complexity is multiplied.

Based on above-mentioned high order FIR filter existing problem on hardware is realized, be necessary to propose a kind of new implementation method and reduce its hard-wired complexity.

Summary of the invention

For the hardware that solves high order FIR filter is realized complicated, and the adder quantity of bringing in the hardware implementation procedure is too much and the too much problem of tapped delay element number, the invention provides a kind of time domain implementation method that is used for simple coefficient FIR filter, described method comprises:

Steps A: with the impulse response h[n of FIR filter] be decomposed into the fixing sub-impulse response h of K length _k[n] | _K=1 ^K, and the sub-impulse response h that each length is fixing _k[n] is decomposed into the fixing branch cross-talk impulse response h of J length _{K, j}[n] | _J=1 ^J, obtain K * J branch cross-talk impulse response h _{K, j}[n], 1≤k≤K, 1≤j≤J; Wherein, K described sub-impulse response h _kThe sub-impulse response h of in [n] each _kJ the branch cross-talk impulse response that [n] is corresponding constitutes j component cross-talk impulse response h _{K, j}[n] | _K=1 ^K, every component cross-talk impulse response h _{K, j}[n] | _K=1 ^KCorresponding common segment sum unit, k is that integer, j are that integer, K are that integer, J are integer;

Step B: the input signal of described FIR filter obtains J component cross-talk impulse response h by general tapped delay unit and J common segment sum unit _{K, j}[n] | _K=1 ^KCorresponding K _hIndividual minute cross-talk linear convolution result; Wherein, K _h≤ K * J, K _hBe integer;

Step C: from described K _hSelected among the cross-talk linear convolution result in individual minute with described K sub-impulse response in J corresponding branch cross-talk linear convolution result of each sub-impulse response, and, obtain the individual sub-linear convolution result of K with J branch cross-talk linear convolution results added of each sub-impulse response correspondence in described K the sub-impulse response;

Step D: the time domain output signal that described K the delayed addition of sub-linear convolution result is obtained described FIR filter.

Described step B specifically comprises:

The input signal of described FIR filter obtains J the different segmentation input vector that postpones by general tapped delay unit;

J segmentation input vector in described J segmentation input vector obtains j component cross-talk impulse response h by the j common segment sum unit in described J the common segment sum unit _{K, j}[n] | _K=1 ^KCorresponding K _h ^jIndividual minute cross-talk linear convolution result; Wherein, K _h ^jBe integer, K _h ^j≤ K, $\underset{j=1}{\overset{j=J}{\mathrm{\Σ}}}{K_h}^j=K_h.$

Described step C specifically comprises: from described j component cross-talk impulse response h _{K, j}[n] | _K=1 ^KCorresponding K _h ^jAmong the individual minute cross-talk linear convolution result, select to obtain k sub-impulse response h _kJ the branch cross-talk linear convolution of [n] correspondence be y as a result _{K, j}[n], 1≤j≤J, 1≤k≤K;

With described k sub-impulse response h _kJ the branch cross-talk linear convolution of [n] correspondence be y as a result _{K, j}[n] | _J=1 ^JAddition obtains k sub-linear convolution y as a result _k[n], 1≤k≤K.

Described step D is specially: described K sub-linear convolution result is obtained the time domain output signal of described FIR filter by incremental delay sum unit or the fixed delay unit that adds up.

The beneficial effect of technical scheme provided by the invention is: the time domain implementation method of FIR filter provided by the invention has reduced hard-wired complexity, reduced the quantity of tapped delay unit, reduced the quantity of adder, optimized hardware configuration, realized that the coefficient of FIR filter is configurable.

Description of drawings

Fig. 1 is the schematic diagram of the linear convolutional system explained block diagram of FIR filter in the prior art;

Fig. 2 is the direct type implementation structure schematic diagram of FIR filter in the prior art;

Fig. 3 is the time domain approach principle schematic that application subfilter group provided by the invention and incremental delay sum unit realize simple coefficient FIR filter;

Fig. 4 is that the time domain approach principle schematic of simple coefficient FIR filter is realized in application subfilter group provided by the invention and the fixed delay unit that adds up;

Fig. 5 provided by the inventionly realizes the time domain approach principle schematic of simple coefficient FIR filter by tapped delay unit, partial summation unit, selected cell and the fixed delay unit that adds up;

Fig. 6 is the flow chart that is used for the time domain implementation method of simple coefficient FIR filter provided by the invention;

Fig. 7 is subfilter h provided by the invention _kThe principle schematic that [n] segmentation realizes;

Fig. 8 is subfilter h provided by the invention _k[n] realizes dividing the principle schematic of cross-talk filtering by tapped delay unit and partial summation unit;

Fig. 9 is the subfilter h for the configurable FIR filter of coefficient provided by the invention _k[n] realizes dividing the principle schematic of cross-talk filtering by tapped delay unit, partial summation unit and selected cell.

Embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, embodiment of the present invention is described further in detail below in conjunction with accompanying drawing.

The invention provides a kind of time domain implementation method that is used for simple coefficient FIR filter, this method realizes high order FIR filter with low order subfilter group and incremental delay sum unit, perhaps realize with low order subfilter group and the fixed delay unit that adds up, and use the parallel filtering structure, as shown in Figure 3 and Figure 4.This method is applicable to that coefficient is the system of simple real integer or complex integers, is applicable to matched filtering or coupling related system, is applicable to high order system, is applicable to the high power sampling system that all-digital receiver is common, is applicable to the configurable system of coefficient.

Be that example is set forth the realization technical solutions according to the invention with the unit that adds up with low order subfilter group and fixed delay below.

The input signal of supposing the FIR filter is x[n], output signal is y[n], then the time domain expression formula of the linear convolution operation of FIR filter is:

$y\left[n\right]=x\left[n\right]*h\left[n\right]=\underset{m=0}{\overset{N-1}{\mathrm{\Σ}}}x[n-m]h\left[m\right]$

Wherein, impulse response h[n] length be N, N=K * L=K * J * I, integer K, L, J, I is the parameter according to FIR filter implementation method design, and the time domain implementation method that is used for simple coefficient FIR filter provided by the invention thus specifically may further comprise the steps, referring to Fig. 5 and Fig. 6:

Step 101: with the impulse response h[n of high order FIR filter] be decomposed into the sub-impulse response sum that K length is L;

Impulse response h[n] be decomposed into K length be L sub-impulse response sum specifically:

$h\left[n\right]=\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}{h}_k[n-\mathrm{kL}]$

Wherein, h _k[n] is the impulse response of k the branch road (being subfilter k) of subfilter group, and its exponent number is the 1/K of original FIR filter order; The subfilter group is by K subfilter h _k[n] | _K=0 ^K-1The parallel composition, as shown in Figure 3 and Figure 4;

Step 102: use the parallel filtering structure, with high order FIR filter linear convolution y[n as a result] be decomposed into K sub-linear convolution sum as a result;

The high order FIR filter linear convolution is y[n as a result] sum is specifically as a result to be decomposed into K sub-linear convolution:

$y\left[n\right]=x\left[n\right]*h\left[n\right]=\underset{k=0}{\overset{K-1}{\mathrm{\Σ}}}{y}_k[n-\mathrm{kL}]$ y _k[n]＝x[n]*h _k[n]

Wherein, y _k[n] is the sub-linear convolution result of k branch road of subfilter group, promptly passes through subfilter h _kThe sub-linear convolution result of [n];

Step 103: with subfilter h _kThe branch cross-talk impulse response h that [n] is decomposed into J length is I _{K, j}[n] | _J=0 ^J-1Sum, correspondingly, with sub-linear convolution y as a result _k[n] is decomposed into J branch cross-talk linear convolution y as a result _{K, j}[n] | _J=0 ^J-1Sum;

In order further to reduce the exponent number of subfilter, subfilter h _k[n] realize by segmentation, as shown in Figure 7, and according to hypothesis L=J * I, with subfilter h _kThe branch cross-talk impulse response sum that [n] is decomposed into J length is I is specifically:

$h_k\left[n\right]=\underset{j=0}{\overset{J-1}{\mathrm{\Σ}}}{h}_{k,j}[n-\mathrm{jI}]$

With sub-linear convolution y as a result _k[n] is decomposed into J branch cross-talk linear convolution, and sum is specifically as a result:

$y_k\left[n\right]=x\left[n\right]*h_k\left[n\right]=\underset{j=0}{\overset{J-1}{\mathrm{\Σ}}}{y}_{k,j}\left[n\right]$

y _k，j[n]＝x[n-jI]*h _k，j[n-jI]

Step 104: k subfilter passed through J tapped delay cells D _j, a J partial summation cell S _{K, j}(the individual selected cell Q of K * J) _{K, j}Obtain branch cross-talk linear convolution y as a result _{K, j}[n];

As shown in Figure 8, input signal x[n] by J tapped delay cells D _jAfter obtain the different segmentation input vectors formed of postponing

Promptly $\stackrel{\→}{x_j}=\left\{\begin{array}{cccc}x[x-(j-1)I]& x[n-(j-1)I+1]& ...& x[n-(j-1)I+I-1]\end{array}\right\},$ Segmentation subfilter h _{K, j}The coefficient of [n] is formed coefficient vector

Promptly $\stackrel{\→}{h_{k,j}}=\left\{\begin{array}{cccc}{h}_{k,j}\left[(j-1)I\right]& h_{k,j}[(j-1)I+1]& ...& h_{k,j}[(j-1)I+I-1]\end{array}\right\},$ The partial summation cell S _{K, j}Calculate the segmentation input vector

Coefficient vector with correspondence

Inner product obtain branch cross-talk linear convolution y as a result _{K, j}[n], promptly $y_{k,j}\left[n\right]=x[n-\mathrm{jI}]*h_{k,j}[n-\mathrm{jI}]=\stackrel{\→}{x_j}\·\stackrel{\→}{h_{k,j}};$

As can be seen from Figure 8 the tapped delay unit of a plurality of subfilters all is identical, so the general tapped delay of called after unit again, tapped delay unit, and a plurality of like this subfilters can be shared one group of general tapped delay unit;

Length is that the FIR filter of N uses K subfilter altogether, and each subfilter all has the identical partial summation unit of structure, with j partial summation unit group S _{K, j}| _K=0 ^K-1Be example, to different subfilters, its segmentation input vector is consistent, promptly

Coefficient vector is by the coefficient decision of FIR filter, promptly

For the simple high price of coefficient FIR filter, the likelihood ratio that K coefficient vector has nothing in common with each other is less, and the value space of supposing the FIR filter coefficient is H, and N is wherein arranged _hIndividual element is supposed K coefficient vector

K is arranged _hIndividual vector is mutually different, then K _h≤ K and K _h≤ N _h ^I, for simple coefficient FIR filter, N _hUsually very little, N for example _h=2, I=3, then K _h≤ 2 ³=8, therefore can pass through the shared portion sum unit, with j partial summation unit group S _{K, j}| _K=0 ^K-1The partial summation operation times reduce to K from K _h, the partial summation unit called after common segment sum unit that a plurality of subfilters are shared is with S _jExpression, total J common segment sum unit in Fig. 8;

When the coefficient of FIR filter is configurable, common segment sum unit S _jExport all possible partial summation result; Selected cell Q _{K, j}Select required partial summation result according to pre-configured coefficient, as shown in Figure 9, for example the FIR filter has M coefficient to dispose, and then mostly to be M most individual for the summation operation that need finish of each partial summation unit, by common segment sum unit S _j, j partial summation unit group S of alternative M subfilter _{K, j}| _K=0 ^K-1, then the number of times that calculates of partial summation is from (the individual K that is reduced to of K * M) at most _hIndividual, K wherein _h≤ (K * M) and K _h≤ N _h ^IAs can be seen, M=1 is the configurable special case of FIR coefficient, the FIR filter that coefficient of correspondence is fixing, and can save selected cell this moment;

Step 105: will divide cross-talk linear convolution y as a result _{K, j}[n] addition obtains sub-linear convolution y as a result _k[n];

Step 106: with all sub-linear convolutions y as a result _k[n] | _K=0 ^K-1Obtain linear convolution y[n as a result through the fixed delay unit that adds up].

In addition, can also substitute the fixed delay unit that adds up with the incremental delay sum unit and realize the present invention, except that first branch road (first branch road is delay not) like this, the delay of each branch road is along with branch road sequence number k increases progressively, and all sub-linear convolutions are y as a result _k[n] | _K=0 ^K-1Through obtaining final linear convolution y[n as a result after the incremental delay sum unit].Adopt the incremental delay sum unit to realize that technical scheme of the present invention is the same with present embodiment, repeats no more here.

In actual applications, FIR filter for length N=K * L=K * J * I, by configuration parameter J and I, can between delay cell and number of taps, number of adders, configurable these three performances of coefficient, select, obtain meeting the optimum time domain implementation structure of design requirement.If there is not suitable integer K, L, J, I satisfy equation N=K * L=K * J * I, then can increase the length N of FIR filter by the mode of zero padding, to select suitable integer K, L, J, I, the length N of increase FIR filter can not increase FIR filter construction complexity; And can use segmentation method flexibly, as L=I ₁+ I ₂+ ... + I _J, section length I wherein _jCan be different.

The time domain implementation method of FIR filter provided by the invention has reduced the complexity that the FIR filter hardware is realized, has reduced delay cell quantity, number of taps and adder quantity, has optimized hardware configuration, has realized the coefficient of FIR filter configurable.

The above only is preferred embodiment of the present invention, and is in order to restriction the present invention, within the spirit and principles in the present invention not all, any modification of being done, is equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (4)

1. time domain implementation method that is used for simple coefficient FIR filter is characterized in that described method comprises:

Steps A: with the impulse response h[n of FIR filter] be decomposed into the fixing sub-impulse response h of K length _k[n] | _K=1 ^K, and the sub-impulse response h that each length is fixing _k[n] is decomposed into the fixing branch cross-talk impulse response h of J length _{K, j}[n] | _J=1 ^J, obtain K * J branch cross-talk impulse response h _{K, j}[n], 1≤k≤K, 1≤j≤J; Wherein, K described sub-impulse response h _kThe sub-impulse response h of in [n] each _kJ the branch cross-talk impulse response that [n] is corresponding constitutes j component cross-talk impulse response h _{K, j}[n] | _K=1 ^K, every component cross-talk impulse response h _{K, j}[n] | _K=1 ^KCorresponding common segment sum unit, k is that integer, j are that integer, K are that integer, J are integer;

Step B: the input signal of described FIR filter obtains J component cross-talk impulse response h by general tapped delay unit and J common segment sum unit _{K, j}[n] | _K=1 ^KCorresponding K _hIndividual minute cross-talk linear convolution result; Wherein, K _h≤ K * J, K _hBe integer;

Step C: from described K _hSelected among the cross-talk linear convolution result in individual minute with described K sub-impulse response in J corresponding branch cross-talk linear convolution result of each sub-impulse response, and, obtain the individual sub-linear convolution result of K with J branch cross-talk linear convolution results added of each sub-impulse response correspondence in described K the sub-impulse response;

Step D: the time domain output signal that described K the delayed addition of sub-linear convolution result is obtained described FIR filter.

2. the time domain implementation method that is used for simple coefficient FIR filter as claimed in claim 1 is characterized in that described step B specifically comprises:

The input signal of described FIR filter obtains J the different segmentation input vector that postpones by general tapped delay unit;

J segmentation input vector in described J segmentation input vector obtains j component cross-talk impulse response h by j common segment sum unit in described J the common segment sum unit _{K, j}[n] | _K=1 ^KCorresponding K _h ^jIndividual minute cross-talk linear convolution result; Wherein, K _h ^jBe integer, K _h ^j≤ K, $\underset{j=1}{\overset{j=J}{\mathrm{\Σ}}}{K_h}^j=K_h.$

3. the time domain implementation method that is used for simple coefficient FIR filter as claimed in claim 2 is characterized in that described step C specifically comprises:

From described j component cross-talk impulse response h _{K, j}[n] _K=1 ^KCorresponding K _h ^jAmong the individual minute cross-talk linear convolution result, select to obtain k sub-impulse response h _kJ the branch cross-talk linear convolution of [n] correspondence be y as a result _{K, j}[n], 1≤j≤J, 1≤k≤K;

With described k sub-impulse response h _kJ the branch cross-talk linear convolution of [n] correspondence be y as a result _{K, j}[n] | _J=1 ^JAddition obtains k sub-linear convolution y as a result _k[n], 1≤k≤K.

4. the time domain implementation method that is used for simple coefficient FIR filter as claimed in claim 1, it is characterized in that described step D is specially: described K sub-linear convolution result is obtained the time domain output signal of described FIR filter by incremental delay sum unit or the fixed delay unit that adds up.

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