CN102741805B - Method and device for using one multiplier to implement multiplication of complex numbers - Google Patents

Abstract

The present invention provides a method and a device for using one multiplier to implement multiplication of complex numbers. The method comprises: receiving a first complex number signal a+ci and a second complex number signal b+di, the first complex number signal and the second complex number signal being both digital communication signals; performing shift processing according to a first real part a and a first imaginary part c of the first complex number signal to acquire a first transformed value s, and performing shift processing according to a second real part b and a second imaginary part d of the second complex number signal to acquire a second transformed value t; according to the first transformed value s and the second transformed value t, performing calculation by using a multiplier to acquire a first reference value w1=st; and acquiring the real part and the imaginary part of the product of the first complex number and the second complex number according to the first reference value w1. The present invention further provides a corresponding device. The technical solutions of the present invention can overcome the disadvantage in the prior art that the utilization ratio of the multiplier is low.

Description

A multiplier is used to realize the method and apparatus of complex multiplication

Technical field

The present invention relates to Digital Signal Processing, particularly relate to a kind of method and apparatus using a multiplier to realize complex multiplication, belong to communication technical field.

Background technology

In the digital signal processing of communication technical field, often need to carry out multiplying to a large amount of complex signals, above-mentioned complex multiplication operation can be realized by multiplier.The complex multiplication be such as calculated as follows:

(a+ci)·(b+di)＝(ab-cd)+(ad+bc)i

Scheme conventionally, needs four multipliers to calculate the value of ab, cd, ad and bc respectively, and then calculates the value of ab-cd and ad+bc, draw net result.

Along with the fast development of computing machine and infotech, need quantity of information to be processed increasing, when carrying out complex multiplication operation, need to use a large amount of multipliers, and usually in the treatment facility of data-signal, such as field programmable gate array (Fie1d-Programmable Gate Array, hereinafter referred to as: FPGA), wherein the quantity of multiplier is all limited, and carries out complex multiplication and need to use nearly four multipliers.As can be seen here, when carrying out complex multiplication operation in prior art, the defect that ubiquity multiplier utilization ratio is low.

Summary of the invention

The invention provides a kind of method and apparatus using multiplier to realize complex multiplication, for solving the low defect of the multiplier utilization ratio that exists in prior art.

The invention provides a kind of method using a multiplier to realize complex multiplication, comprising:

Receive the first complex signal a+ci and the second complex signal b+di, described first complex signal and the second complex signal are all the digital signals that communicates;

Carry out shifting processing according to the first real part a of described first complex signal and the first imaginary part c and obtain the first transformed value s, and carry out shifting processing according to the second real part b of described second complex signal and the second imaginary part d and obtain the second transformed value t;

According to described first transformed value s and described second transformed value t, multiplier is utilized to carry out calculating acquisition first reference value w ₁=st;

According to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number.

Present invention also offers the device that a kind of use multiplier realizes complex multiplication, comprising:

First receiver module, for receiving the first complex signal a+ci and the second complex signal b+di, described first complex signal and the second complex signal are all the digital signals that communicates;

First acquisition module, obtain the first transformed value s for carrying out shifting processing according to the first real part a of described first complex signal and the first imaginary part c, and carry out shifting processing according to the second real part b of described second complex signal and the second imaginary part d and obtain the second transformed value t;

First computing module, for according to described first transformed value s and described second transformed value t, utilizes multiplier to carry out calculating acquisition first reference value w ₁=st;

Second acquisition module, for according to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number.

The use that the embodiment of the present invention provides multiplier realizes the method and apparatus of complex multiplication, by when carrying out complex multiplication, the first transformed value and the second transformed value is obtained according to complex signal, then multiplier is utilized to carry out calculating acquisition first reference value, and the real part ab-cd of the product of the first plural number and the second plural number further can be obtained according to the first reference value, and the first imaginary part ad+bc of product of plural number and the second plural number, only need in this technical scheme to use multiplier when calculating the first reference value, a multiplier is only needed to realize in whole complex multiplication computation process, therefore, technical scheme of the present invention can save multiplier resources effectively.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 uses a multiplier to realize the schematic flow sheet of the method for complex multiplication in the embodiment of the present invention;

Fig. 2 is the schematic flow sheet one carrying out complex multiplication in the specific embodiment of the invention;

Fig. 3 is the schematic flow sheet two carrying out complex multiplication in the specific embodiment of the invention;

Fig. 4 is the schematic flow sheet three carrying out complex multiplication in the specific embodiment of the invention;

Fig. 5 is the schematic flow sheet of another implementation of complex multiplication calculation procedure shown in Fig. 3;

Fig. 6 is the data structure diagram of the first reference value w1 in another specific embodiment of the present invention;

Fig. 7 is w in another specific embodiment of the present invention ₁+ (2 ^2k-1) data structure diagram;

Fig. 8 is the schematic flow sheet four carrying out complex multiplication in the specific embodiment of the invention;

Fig. 9 is the schematic flow sheet five carrying out complex multiplication in the specific embodiment of the invention;

Figure 10 is the schematic flow sheet six carrying out complex multiplication in the specific embodiment of the invention;

Figure 11 is the schematic flow sheet seven carrying out complex multiplication in the specific embodiment of the invention;

Figure 12 is the schematic flow sheet eight carrying out complex multiplication in the specific embodiment of the invention;

Figure 13 is the schematic flow sheet nine carrying out complex multiplication in the specific embodiment of the invention;

Figure 14 is the schematic flow sheet ten carrying out complex multiplication in the specific embodiment of the invention;

Figure 15 is the schematic flow sheet 11 carrying out complex multiplication in the specific embodiment of the invention;

Figure 16 is the schematic flow sheet 12 carrying out complex multiplication in the specific embodiment of the invention;

Figure 17 is the schematic flow sheet 13 carrying out complex multiplication in the specific embodiment of the invention;

Figure 18 is the schematic flow sheet 14 carrying out complex multiplication in the specific embodiment of the invention;

Figure 19 is the schematic flow sheet 15 carrying out complex multiplication in the specific embodiment of the invention;

Figure 20 is the schematic flow sheet 16 carrying out complex multiplication in the specific embodiment of the invention;

Figure 21 is the schematic flow sheet 17 carrying out complex multiplication in the specific embodiment of the invention;

Figure 22 is the schematic flow sheet 18 carrying out complex multiplication in the specific embodiment of the invention;

Figure 23 is the schematic flow sheet 19 carrying out complex multiplication in the specific embodiment of the invention;

Figure 24 is the schematic flow sheet 20 carrying out complex multiplication in the specific embodiment of the invention;

Figure 25 is the schematic flow sheet 21 carrying out complex multiplication in the specific embodiment of the invention;

Figure 26 is the schematic flow sheet 22 carrying out complex multiplication in the specific embodiment of the invention;

Figure 27 is the schematic flow sheet 23 carrying out complex multiplication in the specific embodiment of the invention;

Figure 28 uses a multiplier to realize the structural representation one of the device of complex multiplication in the embodiment of the present invention;

Figure 29 uses a multiplier to realize the structural representation two of the device of complex multiplication in the embodiment of the present invention;

Figure 30 uses a multiplier to realize the structural representation three of the device of complex multiplication in the embodiment of the present invention;

Figure 31 uses a multiplier to realize the structural representation four of the device of complex multiplication in the embodiment of the present invention.

Embodiment

For making the object of the embodiment of the present invention, technical scheme and advantage clearly, below in conjunction with the accompanying drawing in the embodiment of the present invention, technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is the present invention's part embodiment, instead of whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.

For in prior art, when carrying out multiplication calculating for complex signal, need to use a large amount of multipliers to cause the defect that multiplier utilization factor is low, the invention provides a kind of technical scheme, wherein only use a multiplier just can realize the multiplication of complex signal.

Fig. 1 uses a multiplier to realize the schematic flow sheet of the method for complex multiplication in the embodiment of the present invention, as shown in Figure 1, the method comprises following step:

Step 101, receive the first complex signal a+ci and the second complex signal b+di; Wherein the absolute value of the first real part a, the first imaginary part c, the second real part b and the second imaginary part d is all less than or equal to 2 ^k-1-1, wherein k is positive integer, and described first complex signal and the second complex signal are all the digital signals that communicates;

Step 102, carry out shifting processing according to the first real part a of described first complex signal and the first imaginary part c and obtain the first transformed value s, and carry out shifting processing according to the second real part b of described second complex signal and the second imaginary part d and obtain the second transformed value t;

Step 103, according to described first transformed value s and described second transformed value t, carry out calculating acquisition first by multiplier and examine value w ₁=st;

Step 104, according to the first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number.

The technical scheme that the above embodiment of the present invention provides, wherein when carrying out complex multiplication, the first transformed value and the second transformed value is obtained according to complex signal, then multiplier is utilized to carry out calculating acquisition first reference value, and the real part of the product of the first plural number and the second plural number further can be obtained according to the first reference value, and first imaginary part of product of plural number and the second plural number, only need in this technical scheme to use multiplier when calculating the first reference value, a multiplier is only needed to realize in whole complex multiplication computation process, therefore, technical scheme of the present invention can save multiplier resources effectively.

In the above embodiment of the present invention, wherein for the first real part a, the first imaginary part c of the first complex signal, and the second real part b of described second complex signal and the absolute value of the second imaginary part d are all less than or equal to 2 ^k-1-1, wherein k is positive integer; And wherein according to the first transformed value s=a2 that the first complex signal obtains ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d; And the first reference value w ₁=st=ab2 ^4k+ (ab+bc) 2 ^2k+ cd.

In these cases, can needs as the case may be, further calculate the second reference value $w_2=\frac{(w_1-\mathrm{cd})}{2^{2k}}$ And/or the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}}.$

In the embodiment of the present invention, for the first complex signal a+ci and the second complex signal b+di, wherein the absolute value of the first real part a, the first imaginary part c, the second real part b and the second imaginary part d is all less than or equal to 2 ^k-1-1, namely | a|, | b|, | c|, | d|≤2 ^k-1-1, k is here positive integer.2 are less than or equal to by this absolute value ^k-1the constraint of-1, can for the first transformed value s=a2 ^2k+ c, the second transformed value t=b2 ^2k+ d, its absolute value is all less than 2 ^3k-1-1, namely | s|, | t|≤2 ^3k-1-2 ^2k+ 2 ^k-1-1 < 2 ^3k-1-1, therefore, s, t are the signed integer of 3k bit.

For the first reference value w ₁, its value is taken as w ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd, and due to-2 ^k-1+ 1≤a, b, c, d≤2 ^k-1-1, therefore can draw:

-(2 ^k-1-1) ²≤ab，ad，bc，cd≤(2 ^k-1-1) ²

-2(2 ^k-1-1) ²≤ad+bc≤2(2 ^k-1-1) ²

Thus obtain first party formula:

0＜-(2 ^k-1-1) ²+(2 ^2k-1-1)≤cd+(2 ^2k-1-1)≤(2 ^k-1-1) ²+(2 ^2k-1-1)＜2 ^2k-1

0＜-(2 ^k-1-1) ²+(2 ^2k-1-1)≤ab+(2 ^2k-1-1)≤(2 ^k-1-1) ²+(2 ^2k-1-1)＜2 ^2k-1

0＜-2(2 ^k-1-1) ²+(2 ^2k-1-1)≤ad+bc+(2 ^2k-1-1)≤2(2 ^k-1-1) ²+(2 ^2k-1-1)＜2 ^2k-1

Second party formula:

0＜-(2 ^k-1-1) ²+(2 ^2k-1+1)≤-cd+(2 ^2k-1+1)≤(2 ^k-1-1) ²+(2 ^2k-1+1)＜2 ^2k-1

0＜-(2 ^k-1-1) ²+(2 ^2k-1+1)≤-ab+(2 ^2k-1+1)≤(2 ^k-1-1) ²+(2 ^2k-1+1)＜2 ^2k-1

0＜-2(2 ^k-1-1) ²+(2 ^2k-1+1)≤-(ad+bc)+(2 ^2k-1+1)≤2(2 ^k-1-1) ²+(2 ^2k-1+1)≤2 ^2k-1

In above formula, the rightmost sign of inequality of last inequality is due to k >=1, and gets equal sign when k=1.

According to above-mentioned first party formula, and congruence property can obtain congruence expression below:

cd＝mod(w ₁+(2 ^2k-1-1)，2 ^2k)-(2 ^2k-1-1)

Wherein mod (a, b) represents the remainder (for integer) that integer a obtains divided by integer b, and the scope of remainder is less than or equal to b-1 for being more than or equal to 0, and namely a has Unique Decomposition of Ring: a=qb+mod (a, b), and wherein q is integer.

In like manner, if the second reference value then can solve:

ad+bc＝mod(w ₂+(2 ^2k-1-1)，2 ^2k)-(2 ^2k-1-1)

If the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}},$ Then can solve:

ab＝mod(w ₂+(2 ^2k-1-1)，2 ^2k)-(2 ^2k-1-1)

Concrete, when the complement code of carrying out plural number calculates, first the second reference value and the 3rd reference value can be obtained, when further obtaining the product cd of the first imaginary part and the second imaginary part according to above-mentioned first reference value according to the first reference value, can be calculated by following mode, if w ₁+ (2 ^2k-1-1), when>=0, w is obtained ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of cd.

And by w ₁+ (2 ^2k-1-1) < 0, can obtain:

-[w ₁+ (2 ^2k-1-1)]=[-ab2 ^2k-(ad+bc)] 2 ^2k+ [-cd-(2 ^2k-1-1)] > 0, that is:

-[w ₁+(2 ^2k-1-1)]＝[-ab·2 ^2k-(ad+bc)-1]·2 ^2k+[-cd+(2 ^2k-1+1)]＞0

Second party formula is utilized to obtain:

0＜-cd+(2 ^2k-1+1)＜2 ^2k-1

Acquisition-[w ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of cd.

In addition, for according to the second reference value w ₂obtain the product of the first real part and the second imaginary part, and during the sum of products of the first imaginary part and the second real part, can be concrete comprise following content, one is at w ₂+ (2 ^2k-1-1), when>=0, w is obtained ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of ad+bc.

And at w ₂+ (2 ^2k-1-1) during < 0, according to second party formula and above-mentioned similar calculating, acquisition-[w ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of ad+bc.

The product ab obtaining the first real part and the second real part according to described 3rd reference value can specifically comprise following content, and one is at w ₃+ (2 ^2k-1-1), when>=0, w is obtained ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of ab, at w ₃+ (2 ^2k-1-1), during < 0, according to second party formula and above-mentioned similar calculating ,-[w can be retrieved as ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of ab.The value that can obtain ab-cd is subsequently as the real part of the product of described first plural number and the second plural number.

Concrete, the computation process of above-described embodiment can as shown in Figure 2, Figure 3 and Figure 4, namely first in a first step, by the value of a, c, b, d, be input in calculation element with the form of complement code, wherein by a, b to moving to left 2 ^2kposition, obtains a2 ^2kand b2 ^2k, and further carry out additive operation, obtain the first transformed value s=a2 ^2k+ c and the second transformed value t=b2 ^2k+ d, then utilizes multiplier to carry out calculating acquisition first reference value w ₁=st=ab2 ^4k+ (ab+bc) 2 ^2k+ cd.

As shown in Figure 3, in second step, first input the above-mentioned w calculated ₁, and calculating parameter z=w ₁+ 2 ^2k-1-1, judge whether z < 0 sets up, as set up, then get parameter u=-z, and get parameter v=u [0:2k-1], parameter x=2 ^2k-1+ 1-v, when being false for above formula in addition, gets parameter v=z [0:2k-1], parameter x=v-2 ^2k-1the value of+1, output parameter x is as the value of cd.Further, w can be calculated ₂=w ₁-x, then carries out right shift process by w2, obtains w ₂=w ₂/ 2 ^k.Obtaining above-mentioned w ₂after, again can utilize w ₂perform above-mentioned steps, the value of the current parameter x obtained is the value of ad+bc, and also further can calculate w ₃=w ₂-x, then by w ₃carry out right shift process, obtain w ₃=w ₃/ 2 ^k, and further, by w ₃value substitute into above-mentioned steps, the value of the parameter x wherein obtained is the value of ab.

After the value of above-mentioned acquisition cd and ab, as shown in Figure 4 in the 3rd step, the real part r=ab-cd of the product of the first plural number and the second plural number can be obtained by subtraction, the imaginary part i=ad+bc of the product of other first plural number and the second plural number.

In above-mentioned plural computation process, only need use multiplier to realize, significantly can reduce the usage quantity of multiplier relative to prior art, avoid the wasting of resources.

In addition, there is w in above-described embodiment ₁+ (2 ^2k-1-1) < 0, w ₂+ (2 ^2k-1-1) < 0 and w ₃+ (2 ^2k-1-1) situation of < 0, and consider the character of remainder, variously can add numerical value K respectively for above-mentioned _i2 ^2k, wherein Ki is positive integer, and w ₁+ (2 ^2k-1-1)+K _i2 ^2k>=0, w ₂+ (2 ^2k-1-1)+K _i2 ^2k>=0, w ₃+ (2 ^2k-1-1)+K _i2 ^2k>=0.Now obtain the product cd of the first imaginary part and the second imaginary part according to described first reference value w1, be specially and obtain w ₁+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of cd; According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part, be specially and obtain w ₂+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of ad+bc; According to described 3rd reference value w ₃obtain the product ab of the first real part and the second real part, be specially and obtain w ₃+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of ab.

For above-mentioned K _i, a kind of simple obtaining value method equals 2 for making this value ^6k(other obtaining value method can be had, only need meet w ₁+ (2 ^2k-1-1)+K _i2 ^2k>=0, w ₂+ (2 ^2k-1-1)+K _i2 ^2k>=0, w ₃+ (2 ^2k-1-1)+K _i2 ^2k>=0), modify to the computation process shown in above-mentioned Fig. 3, concrete can be shown in Figure 5, first inputs above-mentioned w ₁, and further calculating parameter z=w ₁+ (2 ^2k-1-1)+2 ^6k, the v=z that gets parms [0:2k-1], and parameter x=v-2 ^2k-1the value of-1, output parameter x, as the value of cd, further, can calculate w ₂=w ₁-x, then by w ₂carry out right shift process, obtain w ₂=w ₂/ 2 ^k.Obtaining above-mentioned w ₂after, again can utilize w ₂perform above-mentioned steps, the value of the current parameter x obtained is the value of ad+bc, and also further can calculate w ₃=w ₂-x, then by w ₃carry out right shift process, obtain w ₃=w ₃/ 2 ^k, and further, by w ₃value substitute into perform above-mentioned steps, the value of the parameter x wherein obtained is the value of ab.

The embodiment of the present invention additionally provides another embodiment, namely from the above embodiments:

-(2 ^k-1-1) ²≤ab，ad，bc，cd≤(2 ^k-1-1) ²

-2(2 ^k-1-1) ²≤ad+bc≤2(2 ^k-1-1) ²

Can be obtained by above-mentioned two formulas:

0＜-(2 ^k-1-1) ²+(2 ^2k-1)≤cd+(2 ^2k-1)≤(2 ^k-1-1) ²+(2 ^2k-1)≤2 ^2k-1

0＜-(2 ^k-1-1) ²+(2 ^2k-1)≤ab+(2 ^2k-1)≤(2 ^k-1-1) ²+(2 ^2k-1)≤2 ^2k-1

0＜-2(2 ^k-1-1) ²+(2 ^2k-1)≤ad+bc+(2 ^2k-1)≤2(2 ^k-1-1) ²+(2 ^2k-1)＜2 ^2k-1

Following congruence expression can be obtained by congruence property:

cd＝mod(w ₁+(2 ^2k-1)，2 ^2k)-(2 ^2k-1)

In addition, if $w_2=\frac{(w_1-\mathrm{cd})}{2^{2k}},$ Can obtain thus:

ad+bc＝mod(w ₂+(2 ^2k-1)，2 ^2k)-(2 ^2k-1)

If $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}},$ Can obtain thus:

ab＝mod(w ₂+(2 ^2k-1)，2 ^2k)-(2 ^2k-1)

First the calculating of the product cd of the first imaginary part and the second imaginary part is considered, w ₁value can represent as Fig. 6, it comprises from 0 to 6k-1, altogether 6k bit, w in Fig. 6 _hfor signed integer, w _lfor signless integer, w ₁+ (2 ^2k-1) can represent as Fig. 7, wherein w ' _hfor signed integer, w ' _lfor signless integer.In addition, for w ' _lthe bit of 0 to 2k-2 and w _lthe bit identical (be numbered from low level to high bit number, and lowest order being numbered 0) of 0 to 2k-2, and w ' _l2k-1 bit and w ₁the value of 2k-1 bit contrary.Due to w ₁for signless integer, therefore can obtain:

Mod (w ₁+ (2 ^2k-1), 2 ^2k)=w ' _l, i.e. cd=w ' _l-(2 ^2k-1).

Wherein, cd is signed integer, and w ' _lthe the 0th to 2k-2 bit identical to the bit of 2k-2 with the 0th of cd, and w ' _l2k-1 bit contrary with the 2k-1 bit of cd, thus cd is and w _lthere is the signed integer that same bits represents.

In addition, w is considered ₂calculating, due to carry out conversion to it to obtain:

$w_2=\frac{(w_1+2^{2k-1})-(\mathrm{dc}+2^{2k-1})}{2^{2k}}=\frac{(w_1+2^{2k-1})-{w^{\&prime;}}_L}{2^{2k}}=\frac{{w^{\&prime;}}_H\&CenterDot;2^{2k}+{w^{\&prime;}}_L-{w^{\&prime;}}_L}{2^{2k}}={w^{\&prime;}}_H$

Based on the additive operation of complement code, can obtain:

If w ₁2k-1 bit be 0, then w ' _h=w _h;

If w ₁2k-1 bit be 1, then w ' _h=w _h+ 1.

Namely $w_2=\left\{\begin{array}{cc}{w}_H,& w_1[2k-1]=0\\ w_H+1,& w_1[2k-1]=1\end{array}\right.,$ Wherein w ₁[2k-1] represents w ₁2k-1 bit (lowest bit position is from 0 open numbering).

Wherein w _h=w ₁[6k-1:2k], w ₁[6k-1:2k] represents w ₁from 2k to the value of 6k-1 bit.In this embodiment, only need according to the first reference value w ₁obtain the second reference value and according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part:

Obtain w ₁the signed integer (being likely negative here, lower same) of the value formation of a low 2k bit is the value of cd;

Then the product of the first real part and the second imaginary part is obtained according to described second reference value, and the sum of products ad+bc of the first imaginary part and the second real part:

Obtain w ₂the signed integer that the value of a low 2k bit is formed is the value of ad+bc, i.e. cd=w ₂[2k-1:0]; And wherein at w ₁the value of 2k-1 bit when being 0, w ₂value be w ₁2k to the value of 6k-1 bit; At w ₁the value of 2k-1 bit be 1, w ₂value be w ₁2k add 1 to the value of 6k-1 bit.

The product of the first real part and the second real part is obtained according to described second reference value:

At w ₂the value of 2k-1 bit when being 0, obtain w ₂the signed integer that forms to the value of 4k-1 bit of 2k be the value of ab, at w ₂the value of 2k-1 bit when being 0, obtain w ₂the signed integer that forms to the value of 4k-1 bit of 2k add that 1 signed integer obtained is the value of ab, namely

$\mathrm{ab}=\left\{\begin{array}{cc}{w}_2[4k-1:2k],& w_2[2k-1]=0\\ w_2[4k-1:2k]+1,& w_2[2k-1]=1\end{array}\right..$

Wherein, at w ₁the value of 2k-1 bit when being 0, above-mentioned w ₂value be w ₁2k to the value of 6k-1 bit, at w ₁the value of 2k-1 bit be 1, w ₂value be w ₁2k add 1 to the value of 6k-1 bit.On the basis of above-described embodiment, the value that can obtain ab-cd is as the real part of the product of described first plural number and the second plural number.

In the present embodiment, its concrete computation process can as shown in Figure 8, the w first will calculated ₁be input in calculation element, obtain w ₁the the 0 to the 2k-1 bit value as cd complement code and export, judge w simultaneously ₁the value of 2k-1 bit whether be 0, if so, getting the second reference value is w ₂=w ₁[6k-1:2k], otherwise getting the second reference value is w ₂=w ₁[6k-1:2k]+1.

After obtaining the second above-mentioned reference value, judge the second reference value w ₂the value of 2k-1 bit whether be 0, if so, then ab=w ₂[4k-1:2k]; Otherwise, ab=w ₂[4k-1:2k]+1.For ad+bc, its value gets cd=w ₂[2k-1:0].

In concrete computation process, also can carry out suitable adjustment, namely as shown in Figure 9, no longer judge w ₁the value of 2k-1 bit whether be 0, but directly make w ₂=w ₁[6k-1:2k]+w ₁[2k-1], like this at w ₁2k-1 bit when being 0, be equivalent to w ₂=w ₁[6k-1:2k], and at w ₁2k-1 bit when being 1, be equivalent to w ₂=w ₁the value of [6k-1:2k] increases by 1.Further, do not need to judge w yet ₂the value of 2k-1 bit whether be 0, but directly make ab=w ₂[4k-1:2k]+w ₂[2k-1], like this at w ₂2k-1 bit when being 0, be equivalent to ab=w ₂[4k-1:2k], and at w ₂2k-1 bit when being 1, be equivalent to ab=w ₂[4k-1:2k] value increases by 1.

In the above embodiment of the present invention, value for the first real part a, the first imaginary part c, the second real part b and the second imaginary part d is all more than or equal to the situation of 0, due to the singularity of nonnegative integer, it will be more simple that computing machine realizes, and digital scope can have larger span.

This scope is because above-mentioned each value is integer, then can obtain:

0≤a，b，c，d≤2 ^k-1

Now the first transformed value s=a2 ^2k+ c, the second transformed value t=b2 ^2k+ d, can obtain:

0≤s，t≤(2 ^k-1)·2 ^2k+2 ^k-1＜2 ^3k-1

And above-mentioned s and t is the signless integer of 3k bit.

Calculate the first reference value to obtain: w ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd

Due to $0\&le;a,b,c,d\&le;\sqrt{\frac{2^{2k}-1}{2}},$ Therefore can obtain:

$0\&le;\mathrm{ab},\mathrm{ad},\mathrm{bc},\mathrm{cd}\&le;\frac{2^{2k}-1}{2}<2^{2k}-1$

$0\&le;\mathrm{ad}+\mathrm{bc}\&le;2\&CenterDot;\frac{2^{2k}-1}{2}=2^{2k}-1.$

Congruence property is utilized to obtain congruence expression:

Cd=mod (w ₁, 2 ^2k), in like manner establish the second reference value can obtain:

ad+bc＝mod(w ₂，2 ^2k)

If the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}},$ Then can obtain:

ab＝mod(w ₃，2 ^2k)

Because above-mentioned computation process and result of calculation are nonnegative integer, subtraction above, remainder, divided by 2 ^2koperation all can simplify, wherein the value of cd can be taken as w ₁the 0th nonnegative integer formed to the value of 2k-1 bit; The value of ad+bc is w ₁the nonnegative integer that forms of the value of 2k to 4k-1 bit, the nonnegative integer that namely, the value of 2k bit is formed, it can be used as the imaginary part of the product of the first plural number and the second plural number; The value of ab is w ₁the nonnegative integer that forms of the value of 4k to 6k-1 bit, i.e. the nonnegative integer that forms of the value of last 2k bit, the value that can obtain ab-cd is subsequently as the real part of the product of described first plural number and the second plural number.

The computation process of the present embodiment can be as shown in Figure 10, first above-mentioned the first real part a, the first imaginary part c, the second real part b and the second imaginary part d is inputted, and further the first real part a is carried out shifting processing, move to right 2k bit, and low k bit is wherein filled to the first imaginary part c, namely obtain the first transformed value s=a2 ^2k+ c, separately carries out shifting processing by the second real part b, and move to right 2k bit, and a low k bit is filled to the second imaginary part d, namely obtains the second transformed value t=b2 ^2k+ d.Then utilize multiplier that the first above-mentioned transformed value and the second transformed value are carried out multiplication process and obtain w ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd, on this basis, the value can getting cd is w ₁the 0th nonnegative integer formed to the value of 2k-1 bit, the value of ad+bc is w ₁2k to 4k-1 bit value form nonnegative integer, the value of ab is w ₁4k to 6k-1 bit value form nonnegative integer.The definition of recycling complex multiplication obtains real part ab-cd and the imaginary part ad+bc of complex multiplication result respectively.

In the above embodiment of the present invention, the value for the first real part a, the first imaginary part c, the second real part b and the second imaginary part d is all more than or equal to 0, and during the larger situation of span, i.e. 0≤a, b, c, d≤2 ^k-1, wherein k is positive integer, and namely a, b, c, d are the signless integer of k bit, uses following transformed value.First transformed value s=a2 ^2k+1+ c, the second transformed value t=b2 ^2k+1+ d, can obtain:

0≤s，t≤(2 ^k-1)·2 ^2k+1+2 ^k-1＜2 ^3k+1-1

And above-mentioned s and t is the signless integer of 3k+1 bit.

Calculate the first reference value to obtain: w ₁=st=ab2 ^4k+2+ (ad+bc) 2 ^2k+1+ cd

Due to 0≤a, c, b, d≤2 ^k-1, therefore can obtain:

0≤ab，ad，bc，cd≤(2 ^k-1) ²＝2 ^2k+1-2 ^k+1＜2 ^2k-1

0≤ad+bc＜2·(2 ^2k-1)＜2 ^2k+1-1

Congruence property is utilized to obtain congruence expression:

Cd=mod (w ₁, 2 ^2k), in like manner establish the second reference value can obtain:

ad+bc＝mod(w ₂，2 ^2k+1)

If the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k+1}},$ Then can obtain:

ab＝mod(w ₃，2 ^2k)

Because above-mentioned computation process and result of calculation are nonnegative integer, subtraction above, remainder, divided by 2 ^2koperation all can simplify, concrete, can w be obtained ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number, namely obtain ad+bc; Obtain w ₁the nonnegative integer that forms of the value of 4k+2 to 6k+1 bit as the imaginary part ab of product of described first plural number and the second plural number; Further, the value that can obtain ab-cd is as the real part of the product of described first plural number and the second plural number;

The computation process of the present embodiment can be as shown in figure 11, first above-mentioned the first real part a, the first imaginary part c, the second real part b and the second imaginary part d is inputted, and by further just the first real part a carry out shifting processing, move to left 2k+1 bit, and low k bit is wherein filled to the first imaginary part c, namely obtain the first transformed value s=a2 ^2k+1+ c, separately carries out shifting processing by the second real part b, and move to left 2k+1 bit, and a low k bit is filled to the second imaginary part d, namely obtains the second transformed value t=b2 ^2k+1+ d.Then utilize multiplier that the first above-mentioned transformed value and the second transformed value are carried out multiplication process and obtain w ₁=st=ab2 ^2k+2+ (ad+bc) 2 ^2k+1+ cd, on this basis, the value can getting cd is w ₁the 0th nonnegative integer formed to the value of 2k-1 bit, the value of ad+bc is w ₁2k+1 to 4k+1 bit value form nonnegative integer, the value of ab is w ₁the nonnegative integer that forms of the value of 4k+2 to 6k+1 bit, then the value obtaining ab-cd is as the real part of the product of described first plural number and the second plural number.

Utilize the above-mentioned real part for two complex signals and imaginary part to be the embodiment of signless integer, can construct and use the less multiplier of bit to complete a complex multiplication.In embodiments of the present invention, for the first complex signal a+ci and the second complex signal b+di, wherein the first real part a, the first imaginary part c, the second complex signal the second real part b and the second imaginary part d is k+1 bit signed integer and their absolute value is all less than or equal to 2 ^k-1, namely | a|, | b|, | c|, | d|≤2 ^k-1, k>=0 here.

First calculate a '=-a, b '=-b, c '=-c, d '=-d, these numerical value can realize by calculating opposite number, for computing machine complement code, can add 1 realization by negate.

Divide 16 kinds of situations to calculate the product of the first complex signal a+ci and the second complex signal b+di below, use the multiplier in above-described embodiment method respectively.

A>=0 in a first scenario, c>=0, b>=0, d>=0, this situation can see the embodiment shown in above-mentioned Figure 11, concrete see Figure 12, according to the second real part b and the second imaginary part d of the first real part a, the first imaginary part c, the second complex signal, the method for displacement is utilized to obtain the first transformed value s=a2 ^2k+1+ c and the second transformed value t=b2 ^2k+1+ d, then uses multiplier to obtain the first reference value w ₁=st=ab2 ^4k+2+ (ad+bc) 2 ^2k+1+ cd, and the product x+yi that can obtain the first complex signal a+ci and the second complex signal b+di according to method embodiment illustrated in fig. 11, x=ab-cd, y=ad+bc.

In the latter case, wherein all be less than 0 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the value of the second imaginary part d, i.e. a < 0, c < 0, b < 0, d < 0, and its absolute value is all less than 2 ^kwhen-1, wherein k is nonnegative integer; As shown in figure 13, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a ' 2 ^2k+1+ c ', described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', the wherein a ' opposite number that is a, the opposite number that b ' is b, the opposite number that c ' is c, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=a ' b ' 2 ^4k+2+ (a ' d '+b ' c ') 2 ^2k+1+ c ' d ', further according to the first reference value w ₁the product x+yi of described first plural number and the second plural number can be obtained, x=a ' b '-c ' d ', y=a ' d '+b ' c ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number, i.e. y=ad+bc;

Obtain w ₁the nonnegative integer that forms of the value of 4k+2 to 6k+1 bit as the value of ab;

The value obtaining ab-cd as the real part of product of described first plural number and the second plural number, i.e. x=ab-cd.

In a third case, wherein all 2 are less than at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the second imaginary part d absolute value ^k-1, and a>=0, during c < 0, b>=0, d < 0, wherein k is nonnegative integer; As shown in figure 14, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a2 ^2k+1'+c ', described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d ', the wherein c ' opposite number that is c, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=ab2 ^4k+2+ (ad '+bc ') 2 ^2k+1+ c ' d ', further according to the first reference value w ₁the product x-yi of described first plural number and the second plural number can be obtained, x=ab-c ' d ', y=ad '+bc ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number, i.e. y=-(ad+bc), the opposite number calculating y is as the imaginary part of product of described first plural number and the second plural number.

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer as value ab;

The value obtaining ab-cd as the real part of product of described first plural number and the second plural number, i.e. x=ab-cd.

In the fourth case, wherein all 2 are less than at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and when a < 0, c>=0, b < 0, d>=0, wherein k is nonnegative integer; As shown in figure 15, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a ' 2 ^2k+1+ c, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d, the wherein c ' opposite number that is c, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=a ' b ' 2 ^4k+2+ (a ' d+b ' c) 2 ^2k+1+ cd, further according to the first reference value w ₁the product x-yi of described first plural number and the second plural number can be obtained, x=a ' b '-cd, y=a ' d+b ' c:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number, i.e. y=-(ad+bc), the opposite number calculating y is as the imaginary part of product of described first plural number and the second plural number.

Obtain w ₁the nonnegative integer that forms of the value of 4k+2 to 6k+1 bit as the value of ab;

The value obtaining ab-cd as the real part of product of described first plural number and the second plural number, i.e. x=ab-cd.

In a fifth case, wherein all 2 are less than at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, c>=0, during b < 0, d < 0, wherein k is nonnegative integer; As shown in figure 16, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a2 ^2k+1+ c, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', the wherein b ' opposite number that is b, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=ab ' 2 ^4k+2+ (ad '+b ' c) 2 ^2k+1+ cd ', further according to the first reference value w ₁product-the x-yi of described first plural number and the second plural number can be obtained, x=ab '-cd ', y=ad '+b ' c:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number, i.e. y=-(ad+bc), the opposite number calculating y is as the imaginary part of product of described first plural number and the second plural number;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab;

The opposite number obtaining the value of x=(-ab)-(-cd) is as the real part of the product of described first plural number and the second plural number.

In a sixth case, wherein all 2 are less than at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and when a < 0, c < 0, b>=0, d>=0, wherein k is nonnegative integer; As shown in figure 17, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a ' 2 ^2k+1+ c ', described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d, the wherein a ' opposite number that is a, the opposite number that c ' is c, then uses multiplier to obtain the first reference value w ₁=st=a ' b2 ^4k+2+ (a ' d+bc ') 2 ^2k+1+ c ' d, further according to the first reference value w ₁product-the x-yi of described first plural number and the second plural number can be obtained, x=a ' b-c ' d, y=a ' d+bc ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number, i.e. y=-(ad+bc), the opposite number calculating y is as the imaginary part of product of described first plural number and the second plural number.

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab;

The opposite number obtaining the value of x=(-ab)-(-cd) is as the real part of the product of described first plural number and the second plural number.

In the 7th kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, when c < 0, b < 0, d>=0, wherein k is nonnegative integer; As shown in figure 18, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a2 ^2k+1+ c ', described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d, the wherein c ' opposite number that is c, the opposite number that b ' is b, then uses multiplier to obtain the first reference value w ₁=st=ab ' 2 ^4k+2+ (ad+b ' c ') 2 ^2k+1+ c ' d, further according to the first reference value w ₁product-the x+yi of described first plural number and the second plural number can be obtained, x=ab '-c ' d, y=ad+b ' c ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number, i.e. y=ad+bc;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab;

The opposite number obtaining the value of x=(-ab)-(-cd) is as the real part of the product of described first plural number and the second plural number.

In the 8th kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and during a < 0, c>=0, b>=0, d < 0, wherein k is nonnegative integer; As shown in figure 19, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a ' 2 ^2k+1+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d ', the wherein a ' opposite number that is a, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=a ' b2 ^4k+2+ (a ' d '+bc) 2 ^2k+1+ cd ', further according to the first reference value w ₁product-the x+yi of described first plural number and the second plural number can be obtained, x=a ' b-cd ', y=a ' d '+bc:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number, i.e. y=ad+bc;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab;

The opposite number obtaining the value of x=(-ab)-(-cd) is as the real part of the product of described first plural number and the second plural number.

In the 9th kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, c>=0, b>=0, during d < 0, wherein k is nonnegative integer; As shown in figure 20, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a2 ^2k+1+ c, described the second transformed value t=d ' 2 obtained according to the second complex signal ^2k+1+ b, wherein d ' the opposite number that is d, then uses multiplier to obtain the first reference value w ₁=st=ad ' 2 ^4k+2+ (ab+cd ') 2 ^2k+1+ bc, further according to the first reference value w ₁the product y-xi of described first plural number and the second plural number can be obtained, y=ab+cd ', x=ad '-bc:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of bc;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number, i.e. y=ab-cd;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ad;

The opposite number obtaining the value of x=(-ad)-(bc) is as the imaginary part of the product of described first plural number and the second plural number.

In the tenth kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, c>=0, b>=0, during d < 0, wherein k is nonnegative integer; As shown in figure 21, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=c ' 2 ^2k+1+ a, described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d, wherein c ' the opposite number that is c, then uses multiplier to obtain the first reference value w ₁=st=bc ' 2 ^4k+2+ (ab+c ' d) 2 ^2k+1+ ad, further according to the first reference value w ₁the product y-xi of described first plural number and the second plural number can be obtained, y=ab+cd ', x=bc '-ad:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of ad;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number, i.e. y=ab-cd;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-bc;

The opposite number obtaining the value of x=(-bc)-(ad) is as the imaginary part of the product of described first plural number and the second plural number.

In the 11 kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, c>=0, during b < 0, d>=0, wherein k is nonnegative integer; As shown in figure 22, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a2 ^2k+1+ c, described the second transformed value t=d2 obtained according to the second complex signal ^2k+1+ b ', wherein b ' the opposite number that is b, then uses multiplier to obtain the first reference value w ₁=st=ad2 ^4k+2+ (ab '+cd) 2 ^2k+1+ b ' c, further according to the first reference value w ₁product-the y+xi of described first plural number and the second plural number can be obtained, y=ab '+cd, x=ad-b ' c:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-bc;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number, i.e. y=-ab+cd, the opposite number calculating y is as the real part of product of described first plural number and the second plural number.

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ad;

The value obtaining x=(ad)-(-bc) is as the imaginary part of the product of described first plural number and the second plural number.

In the 12 kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and during a < 0, c>=0, b>=0, d>=0, wherein k is nonnegative integer; As shown in figure 23, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=c2 ^2k+1+ a ', described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d, wherein a ' the opposite number that is a, then uses multiplier to obtain the first reference value w ₁=st=ad2 ^4k+2+ (ab '+cd) 2 ^2k+1+ b ' c, further according to the first reference value w ₁product-the y+xi of described first plural number and the second plural number can be obtained, y=a ' b+cd, x=bc-a ' d:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-ad;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number, i.e. y=-ab+cd, the opposite number calculating y is as the real part of product of described first plural number and the second plural number.

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of bc;

The value obtaining x=(bc)-(-ad) is as the imaginary part of the product of described first plural number and the second plural number.

In the 13 kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and during a < 0, c < 0, b>=0, d < 0, wherein k is nonnegative integer; As shown in figure 24, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a ' 2 ^2k+1+ c ', described the second transformed value t=d ' 2 obtained according to the second complex signal ^2k+1+ b, a ' be the opposite number of a, the opposite number that c ' is c, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=a ' d ' 2 ^4k+2+ (a ' b+c ' d ') 2 ^2k+1+ bc ', further according to the first reference value w ₁product-the y+xi of described first plural number and the second plural number can be obtained, y=a ' b+c ' d ', x=a ' d '-bc ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-bc;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number, i.e. y=-ab+cd, the opposite number calculating y is as the real part of product of described first plural number and the second plural number.

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ad;

The value obtaining x=(ad)-(-bc) is as the imaginary part of the product of described first plural number and the second plural number.

In the 14 kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, during c < 0, b < 0, d < 0, wherein k is nonnegative integer; As shown in figure 25, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=c ' 2 ^2k+1+ a, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', the wherein b ' opposite number that is b, the opposite number that c ' is c, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=b ' c ' 2 ^4k+2+ (ab '+c ' d ') 2 ^2k+1+ ad ', further according to the first reference value w ₁product-the y+xi of described first plural number and the second plural number can be obtained, y=ab '+c ' d ', x=b ' c '-ad ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-ad;

Obtain w ₁2k+1 to 4k+1 bit value form nonnegative integer, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number, i.e. y=-ab+cd, the opposite number calculating y is as the real part of product of described first plural number and the second plural number.

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of bc;

The value obtaining x=(bc)-(-ad) is as the imaginary part of the product of described first plural number and the second plural number.

In the 15 kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and during a < 0, c < 0, b < 0, d>=0, wherein k is nonnegative integer; As shown in figure 26, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=a ' 2 ^2k+1+ c ', described the second transformed value t=d2 obtained according to the second complex signal ^2k+1+ b ', the wherein a ' opposite number that is a, the opposite number that b ' is b, the opposite number that c ' is c, then uses multiplier to obtain the first reference value w ₁=st=a ' d2 ^4k+2+ (a ' b '+c ' d) 2 ^2k+1+ b ' c ', further according to the first reference value w ₁the product y-xi of described first plural number and the second plural number can be obtained, y=a ' b '+c ' d, x=a ' d-b ' c ':

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of bc;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number, i.e. y=ab-cd;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ad;

The opposite number obtaining the value of x=(-ad)-(bc) is as the imaginary part of the product of described first plural number and the second plural number.

In the 16 kind of situation, be wherein all less than 2 at the second real part b of the first real part a, the first imaginary part c, the second complex signal and the absolute value of the second imaginary part d ^k-1, and a>=0, during c < 0, b < 0, d < 0, wherein k is positive integer; As shown in figure 27, first transformed value that can obtain obtaining according to the first complex signal by shifting processing is s=c ' 2 ^2k+1+ a, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', the wherein b ' opposite number that is b, the opposite number that c ' is c, the opposite number that d ' is d, then uses multiplier to obtain the first reference value w ₁=st=b ' c ' 2 ^4k+2+ (ab '+c ' d ') 2 ^2k+1+ ad ', further according to the first reference value w ₁real part y=a ' b '+cd ' of the product-y+xi of described first plural number and the second plural number can be obtained, and the imaginary part x=b ' c-a ' d ' of the product of described first plural number and the second plural number:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of ad;

Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number, i.e. y=ab-cd;

Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-bc;

The opposite number obtaining the value of x=(-bc)-(ad) is as the imaginary part of the product of described first plural number and the second plural number.

Different from following the example of of the first transformed value in the first embodiment and the second transformed value in the present embodiment, for identical scope | a|, | b|, | c|, | d|≤2 ^k-1, calculate the product of the first complex signal a+ci and the second complex signal b+di, first embodiment needs the multiplier using 3k+3 bit, the present embodiment needs the multiplier using 3k+1 bit, but need the judgement of extra different situations and calculate opposite number, namely negate carried out to complement code and add the operation of 1.

Present invention also offers a kind of device using multiplier to realize complex multiplication, Figure 28 uses a multiplier to realize the structural representation one of the device of complex multiplication in the embodiment of the present invention, as shown in figure 28, this device comprises the first receiver module 11, first acquisition module 12, first computing module 13 and the second acquisition module 14, the first receiver module 11 is wherein for receiving the first complex signal a+ci and the second complex signal b+di, and described first complex signal and the second complex signal are all the digital signals that communicates; First acquisition module 12 obtains the first transformed value s for carrying out shifting processing according to the first real part a of described first complex signal and the first imaginary part c, and carries out shifting processing according to the second real part b of described second complex signal and the second imaginary part d and obtain the second transformed value t; First computing module 13, for according to described first transformed value s and described second transformed value t, utilizes multiplier to carry out calculating acquisition first reference value w ₁=st; Second acquisition module 14 is for according to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number.

The technical scheme that the above embodiment of the present invention provides, wherein when carrying out complex multiplication, first acquisition module obtains the first transformed value and the second transformed value according to complex signal, then the first computing module utilizes multiplier to carry out calculating acquisition first reference value, and the real part of the product of the first plural number and the second plural number further can be obtained according to the first reference value, and the first imaginary part ad+bc of product of plural number and the second plural number, the first computing module is only needed to use multiplier when calculating the first reference value in this technical scheme, a multiplier is only needed to realize in whole complex multiplication computation process, therefore, technical scheme of the present invention can save multiplier resources effectively.

In the above embodiment of the present invention, the first real part a of the first complex signal that the first receiver module 11 wherein receives and the first imaginary part c, and the second real part b of described second complex signal and the absolute value of the second imaginary part d are all less than or equal to 2 ^k-1-1, wherein k is positive integer; The first transformed value s=a2 that described first acquisition module 12 obtains according to the first complex signal ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d; The first reference value w that described first computing module 13 calculates ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd.

Concrete, corresponding with said method embodiment, second acquisition module 14 above-mentioned according to different situations can comprise different functional modules, such as shown in Figure 29, first reference value acquiring unit 141 and the first coefficient acquiring unit 142, and the first reference value acquiring unit 141 is wherein for according to described first reference value w ₁obtain the second reference value with the 3rd reference value first coefficient acquiring unit 142 is for according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part, namely at w ₁+ (2 ^2k-1-1), when>=0, w is obtained ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of cd, at w ₁+ (2 ^2k-1-1) during < 0, acquisition-[w ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of cd; According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number, namely at w ₂+ (2 ^2k-1-1), when>=0, w is obtained ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 as the imaginary part of the product of described first plural number and the second plural number, at w ₂+ (2 ^2k-1-1) during < 0, acquisition-[w ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is as the imaginary part of the product of described first plural number and the second plural number; And according to described 3rd reference value w ₃obtain the product ab of the first real part and the second real part, namely at w ₃+ (2 ^2k-1-1), when>=0, w is obtained ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of ab, at w ₃+ (2 ^2k-1-1) during < 0, acquisition-[w ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

Or as shown in figure 30, the second above-mentioned acquisition module 14 comprises the first reference value acquiring unit 141 and the second coefficient acquiring unit 143, wherein the first reference value acquiring unit 141 is for according to described first reference value w ₁obtain the second reference value with the 3rd reference value second coefficient acquiring unit 143 is for according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part, namely obtain w ₁+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of cd, wherein K _ifor positive integer, and w ₁+ (2 ^2k-1-1)+K _i2 ^2k>=0; Obtain the product of the first real part and the second imaginary part according to described second reference value, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number, namely obtains w ₂+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 as the imaginary part of the product of described first plural number and the second plural number, wherein K _ifor positive integer, and w ₂+ (2 ^2k-1-1)+K _i2 ^2k>=0; And the product ab of the first real part and the second real part is obtained according to described 3rd reference value, namely obtain w ₃+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of ab, wherein K _ifor positive integer, and w ₃+ (2 ^2k-1-1)+K _i2 ^2k>=0; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

Or as shown in figure 31, the second acquisition module 14 comprises the second reference value acquiring unit 144 and the 3rd coefficient acquiring unit 145, wherein the second reference value acquiring unit 144 is for according to described first reference value w ₁obtain the second reference value 3rd coefficient acquiring unit 145 is for according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part, namely obtain w ₁the signed integer that the value of low 2k bit is formed is the value of cd; According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number, namely obtains w ₂the signed integer that the value of low 2k bit is formed as the imaginary part of the product of described first plural number and the second plural number, and wherein at w ₁the value of 2k-1 bit when being 0, w ₂value equal w ₁2k to the value of 6k-1 bit; At w ₁the value of 2k-1 bit be 1, w ₂value equal w ₁2k add 1 to the value of 6k-1 bit; According to described second reference value w ₂obtain the product ab of the first real part and the second real part, namely at w ₂the value of 2k-1 bit when being 0, obtain w ₂2k to 4k-1 bit value form signed integer be the value of ab, at w ₂the value of 2k-1 bit when being 0, obtain w ₂2k to 4k-1 bit value form signed integer add that 1 signed integer obtained is the value of ab; Wherein, described w ₂value at w ₁the value of 2k-1 bit equal w when being 0 ₁2k to the value of 6k-1 bit, at w ₁the value of 2k-1 bit be 1, w ₂value equal w ₁2k add 1 to the value of 6k-1 bit; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

In other embodiment, first real part a, the first imaginary part c of the first complex signal that the first above-mentioned receiver module 11 receives, the second real part b of the second complex signal and the value of the second imaginary part d are the integer being more than or equal to 0, the first transformed value s=a2 that described first acquisition module 12 obtains according to the first complex signal ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d, and the first reference value w that described first computing module 13 calculates ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd, wherein k is positive integer; And the second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd, obtain w ₁the nonnegative integer that forms of the value of 2k to 4k-1 bit as the imaginary part of product of described first plural number and the second plural number, acquisition w ₁4k to 6k-1 bit value form nonnegative integer be the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

The multiplier of use as shown in figure 28 realizes the device of complex multiplication, the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the value of the second real part b of the second complex signal and the second imaginary part d are the integer being more than or equal to 0, and are less than or equal to 2 ^kwhen-1, wherein k is nonnegative integer; The first transformed value s=a2 that described first acquisition module 12 obtains according to the first complex signal ^2k+1+ c, according to the second transformed value t=b2 that the second complex signal obtains ^2k+1+ d, the first reference value w that the first computing module 13 calculates ₁=st=ab2 ^4k+2+ (ad+bc) 2 ^2k+1+ cd; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the value of the second real part b of the second complex signal and the second imaginary part d are all less than 0, and its absolute value is all less than 2 ^kwhen-1, wherein k is nonnegative integer; Described first acquisition module 12 is s=a ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ c ', described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', wherein a ' be a opposite number, the opposite number that b ' is b, the opposite number that c ' is c, the opposite number that d ' is d, the first reference value w that described first computing module 13 calculates ₁=st=a ' b ' 2 ^4k+2+ (a ' d '+b ' c ') 2 ^2k+1+ c ' d '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, during c < 0, b>=0, d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a2 according to the first transformed value that the first complex signal obtains ^2k+1+ c ', described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d ', wherein c ' be c opposite number, the opposite number that d ' is d, the described first reference value w that described first computing module 13 calculates ₁=st=ab2 ^4k+2+ (ad '+bc ') 2 ^2k+1+ c ' d '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th be the value of cd to the nonnegative integer of the formation of the value of 2k-1 bit; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and when a < 0, c>=0, b < 0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ c, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d, wherein a ' be a opposite number, the opposite number that b ' is b, the described first reference value w that described first computing module 13 calculates ₁=st=a ' b ' 2 ^4k+2+ (a ' d+b ' c) 2 ^2k+1+ cd; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, c>=0, during b < 0, d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a2 according to the first transformed value that the first complex signal obtains ^2k+1+ c, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', wherein b ' be b opposite number, the opposite number that d ' is d, the described first reference value w that described first computing module 13 calculates ₁=st=ab ' 2 ^4k+2+ (ad '+b ' c) 2 ^2k+1+ cd '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab; The opposite number obtaining the value of (-ab)-(-cd) is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and when a < 0, c < 0, b>=0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ c ', described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d, wherein a ' be a opposite number, the opposite number that c ' is c, the first reference value w that described first computing module 13 calculates ₁=st=a ' b2 ^4k+2+ (a ' d+bc ') 2 ^2k+1+ c ' d; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the imaginary part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab; The opposite number obtaining the value of (-ab)-(-cd) is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, when c < 0, b < 0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a2 according to the first transformed value that the first complex signal obtains ^2k+1+ c ', described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d, wherein c ' be c opposite number, the opposite number that b ' is b, the first reference value w that described first computing module 13 calculates ₁=st=ab ' 2 ^4k+2+ (ad+b ' c ') 2 ^2k+1+ c ' d; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab; The opposite number obtaining the value of x=(-ab)-(-cd) is as the real part of the product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and during a < 0, c>=0, b>=0, d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d ', wherein a ' be a opposite number, the opposite number that d ' is d, the first reference value w that described first computing module 13 calculates ₁=st=a ' b2 ^4k+2+ (a ' d '+bc) 2 ^2k+1+ cd '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-cd; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the imaginary part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ab; The opposite number obtaining the value of (-ab)-(-cd) is as the real part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, c>=0, b>=0, during d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a2 according to the first transformed value that the first complex signal obtains ^2k+1+ c, described the second transformed value t=d ' 2 obtained according to the second complex signal ^2k+1+ b, wherein d ' be d opposite number, the first reference value w that described first computing module 13 calculates ₁=st=ad ' 2 ^4k+2+ (ab+cd ') 2 ^2k+1+ bc; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of bc; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ad; The opposite number obtaining the value of (-ad)-(bc) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, during c < 0, b>=0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=c ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ a, described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d, wherein c ' be c opposite number, the first reference value w that described first computing module 13 calculates ₁=st=bc ' 2 ^4k+2+ (ab+c ' d) 2 ^2k+1+ ad; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of ad; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-bc; The opposite number obtaining the value of (-bc)-(ad) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, c>=0, during b < 0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a2 according to the first transformed value that the first complex signal obtains ^2k+1+ c, described the second transformed value t=d2 obtained according to the second complex signal ^2k+1+ b ', wherein b ' be b opposite number, the first reference value w that described first computing module 13 calculates ₁=st=ad2 ^4k+2+ (ab '+cd) 2 ^2k+1+ b ' c; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-bc; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ad; The value obtaining (ad)-(-bc) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and during a < 0, c>=0, b>=0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=c2 according to the first transformed value that the first complex signal obtains ^2k+1+ a ', described the second transformed value t=b2 obtained according to the second complex signal ^2k+1+ d, wherein a ' be a opposite number, the first reference value w that described first computing module 13 calculates ₁=st=ad2 ^4k+2+ (ab '+cd) 2 ^2k+1+ b ' c; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-ad; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of bc; The value obtaining (bc)-(-ad) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and during a < 0, c < 0, b>=0, d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ c ', described the second transformed value t=d ' 2 obtained according to the second complex signal ^2k+1+ b, wherein a ' be a opposite number, the opposite number that c ' is c, the opposite number that d ' is d, the first reference value w that described first computing module 13 calculates ₁=st=a ' d ' 2 ^4k+2+ (a ' b+c ' d ') 2 ^2k+1+ bc '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-bc; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of ad; The value obtaining (ad)-(-bc) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, during c < 0, b < 0, d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=c ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ a, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', wherein b ' be b opposite number, the opposite number that c ' is c, the opposite number that d ' is d, the first reference value w that described first computing module 13 calculates ₁=st=b ' c ' 2 ^4k+2+ (ab '+c ' d ') 2 ^2k+1+ ad '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of-ad; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit, the opposite number obtaining described nonnegative integer is as the real part of the product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of bc; The value obtaining (bc)-(-ad) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and during a < 0, c < 0, b < 0, d>=0, wherein k is nonnegative integer; Described first acquisition module 12 is s=a ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ c ', described the second transformed value t=d2 obtained according to the second complex signal ^2k+1+ b ', wherein a ' be a opposite number, the opposite number that b ' is b, the opposite number that c ' is c, the first reference value w that described first computing module 13 calculates ₁=st=a ' d2 ^4k+2+ (a ' b '+c ' d) 2 ^2k+1+ b ' c '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of bc; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-ad; The opposite number obtaining the value of (-ad)-(bc) is as the imaginary part of product of described first plural number and the second plural number;

Or the first real part a, the first imaginary part c of the first complex signal that receive at described first receiver module 11, the absolute value of the second real part b of the second complex signal and the second imaginary part d are all less than 2 ^k-1, and a>=0, during c < 0, b < 0, d < 0, wherein k is nonnegative integer; Described first acquisition module 12 is s=c ' 2 according to the first transformed value that the first complex signal obtains ^2k+1+ a, described the second transformed value t=b ' 2 obtained according to the second complex signal ^2k+1+ d ', wherein b ' be b opposite number, the opposite number that c ' is c, the opposite number that d ' is d, the first reference value w that described first computing module 13 calculates ₁=st=b ' c ' 2 ^4k+2+ (ab '+c ' d ') 2 _2k+1+ ad '; Described second acquisition module 14 is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of ad; Obtain w ₁the nonnegative integer that forms of the value of 2k+1 to 4k+1 bit as the real part of product of described first plural number and the second plural number; Obtain w ₁4k+2 to 6k+1 bit value form nonnegative integer be the value of-bc; The opposite number obtaining the value of (-bc)-(ad) is as the imaginary part of product of described first plural number and the second plural number.

One of ordinary skill in the art will appreciate that: all or part of step realizing said method embodiment can have been come by the hardware that programmed instruction is relevant, aforesaid program can be stored in a computer read/write memory medium, this program, when performing, performs the step comprising said method embodiment; And aforesaid storage medium comprises: ROM, RAM, magnetic disc or CD etc. various can be program code stored medium.

Last it is noted that above embodiment is only in order to illustrate technical scheme of the present invention, be not intended to limit; Although with reference to previous embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that: it still can be modified to the technical scheme described in foregoing embodiments, or carries out equivalent replacement to wherein portion of techniques feature; And these amendments or replacement, do not make the essence of appropriate technical solution depart from the scope of various embodiments of the present invention technical scheme.

Claims (12)

1. use a multiplier to realize a method for complex multiplication, it is characterized in that, comprising:

Receive the first complex signal a+ci and the second complex signal b+di, described first complex signal and the second complex signal are all the digital signals that communicates;

Carry out shifting processing according to the first real part a of described first complex signal and the first imaginary part c and obtain the first transformed value s, and carry out shifting processing according to the second real part b of described second complex signal and the second imaginary part d and obtain the second transformed value t;

According to described first transformed value s and described second transformed value t, multiplier is utilized to carry out calculating acquisition first reference value w ₁=st;

According to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number.

2. use according to claim 1 multiplier realizes the method for complex multiplication, it is characterized in that, first real part a of described first complex signal and the first imaginary part c, and the second real part b of described second complex signal and the absolute value of the second imaginary part d are all less than or equal to 2 ^k-1-1, wherein k is positive integer; Described the first transformed value s=a2 obtained according to the first complex signal ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d; And described first reference value w ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd.

3. use according to claim 2 multiplier realizes the method for complex multiplication, it is characterized in that, according to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number comprises:

According to described first reference value w ₁obtain the second reference value with the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}};$

According to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part:

At w ₁+ (2 ^2k-1-1), when>=0, w is obtained ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of cd;

At w ₁+ (2 ^2k-1-1) during < 0, acquisition-[w ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of cd;

According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number:

At w ₂+ (2 ^2k-1-1), when>=0, w is obtained ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the imaginary part of value as the product of described first plural number and the second plural number of ad+bc;

At w ₂+ (2 ^2k-1-1) during < 0, acquisition-[w ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the imaginary part of value as the product of described first plural number and the second plural number of ad+bc;

According to described 3rd reference value w ₃obtain the product ab of the first real part and the second real part:

At w ₃+ (2 ^2k-1-1), when>=0, w is obtained ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of ab;

At w ₃+ (2 ^2k-1-1) during < 0, acquisition-[w ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of ab;

The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

4. use according to claim 2 multiplier realizes the method for complex multiplication, it is characterized in that, according to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of the first plural number and the second plural number comprises:

The second reference value is obtained according to described first reference value w1 with the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}};$

According to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part:

Obtain w ₁+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of cd, wherein K _ifor positive integer, and w1+ (2 ^2k-1-1)+K _i2 ^2k>=0;

According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number:

Obtain w ₂+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 as the imaginary part of the product of described first plural number and the second plural number, wherein K _ifor positive integer, and w ₂+ (2 ^2k-1-1)+K _i2 ^2k>=0;

According to described 3rd reference value w ₃obtain the product ab of the first real part and the second real part:

Obtain w ₃+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of ab, wherein K _ifor positive integer, and w ₃+ (2 ^2k-1-1)+K _i2 ^2k>=0;

The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

5. use according to claim 2 multiplier realizes the method for complex multiplication, it is characterized in that, according to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number comprises:

According to described first reference value w ₁obtain the second reference value

According to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part:

Obtain w ₁the signed integer that the value of low 2k bit is formed is the value of cd;

According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number:

Obtain w ₂the signed integer that the value of low 2k bit is formed as the imaginary part of the product of described first plural number and the second plural number, and wherein at w ₁the value of 2k-1 bit when being 0, w ₂value equal w ₁2k to the value of 6k-1 bit; At w ₁the value of 2k-1 bit be 1, w ₂value equal w ₁2k add 1 to the value of 6k-1 bit;

According to described second reference value w ₂obtain the product ab of the first real part and the second real part:

At w ₂the value of 2k-1 bit when being 0, obtain w ₂2k to 4k-1 bit value form signed integer be the value of ab, at w ₂the value of 2k-1 bit when being 0, obtain w ₂2k to 4k-1 bit value form signed integer add that 1 signed integer obtained is the value of ab; Wherein, described w ₂value equal w when the value of the 2k-1 bit of w1 is 0 ₁2k to the value of 6k-1 bit, at w ₁the value of 2k-1 bit be 1, w ₂value equal w ₁2k add 1 to the value of 6k-1 bit;

The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

6. use according to claim 1 multiplier realizes the method for complex multiplication, it is characterized in that, is is more than or equal to 0 and is less than or equal in the value of the first real part a, the first imaginary part c, the second real part b and the second imaginary part d integer time, described according to first complex signal obtain the first transformed value s=a2 ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d; And described first reference value w ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd, wherein k is positive integer;

According to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number comprises:

Obtain w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd;

Obtain w ₁the nonnegative integer that forms of the value of 2k to 4k-1 bit as the imaginary part of product of described first plural number and the second plural number;

Obtain w ₁4k to 6k-1 bit value form nonnegative integer be the value of ab;

The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

7. use a multiplier to realize a device for complex multiplication, it is characterized in that, comprising:

First receiver module, for receiving the first complex signal a+ci and the second complex signal b+di, described first complex signal and the second complex signal are all the digital signals that communicates;

First acquisition module, obtain the first transformed value s for carrying out shifting processing according to the first real part a of described first complex signal and the first imaginary part c, and carry out shifting processing according to the second real part b of described second complex signal and the second imaginary part d and obtain the second transformed value t;

First computing module, for according to described first transformed value s and described second transformed value t, utilizes multiplier to carry out calculating acquisition first reference value w ₁=st;

Second acquisition module, for according to described first reference value w ₁obtain the real part of the product of described first plural number and the second plural number, and the imaginary part of the product of described first plural number and the second plural number.

8. use according to claim 7 multiplier realizes the device of complex multiplication, it is characterized in that, first real part a and the first imaginary part c of the first complex signal that described first receiver module receives, and the second real part b of described second complex signal and the absolute value of the second imaginary part d are all less than or equal to 2 ^k-1-1, wherein k is positive integer; The first transformed value s=a2 that described first acquisition module obtains according to the first complex signal ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d; The first reference value w that described first computing module calculates ₁=st=ab2 ^4k+ (ad+bc) 2 ^2k+ cd.

9. use according to claim 8 multiplier realizes the device of complex multiplication, it is characterized in that, described second acquisition module comprises:

First reference value acquiring unit, for according to described first reference value w ₁obtain the second reference value $w_2=\frac{(w_1-\mathrm{cd})}{2^{2k}}$ With the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}};$

First coefficient acquiring unit, for according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part, namely at w ₁+ (2 ^2k-1-1), when>=0, w is obtained ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of cd, at w ₁+ (2 ^2k-1-1) during < 0, acquisition-[w ₁+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of cd; According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number, namely at w ₂+ (2 ^2k-1-1), when>=0, w is obtained ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 as the imaginary part of the product of described first plural number and the second plural number, at w ₂+ (2 ^2k-1-1) during < 0, acquisition-[w ₂+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is as the imaginary part of the product of described first plural number and the second plural number; According to described 3rd reference value w ₃obtain the product ab of the first real part and the second real part, namely at w ₃+ (2 ^2k-1-1), when>=0, w is obtained ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit is formed deducts 2 ^2k-1the value of-1 is the value of ab, at w ₃+ (2 ^2k-1-1) during < 0, acquisition-[w ₃+ (2 ^2k-1-1) nonnegative number that the value of low 2k bit] is formed deducts 2 ^2k-1the opposite number of the value of+1 is the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

10. use according to claim 8 multiplier realizes the device of complex multiplication, it is characterized in that, described second acquisition module comprises:

First reference value acquiring unit, for according to described first reference value w ₁obtain the second reference value $w_2=\frac{(w_1-\mathrm{cd})}{2^{2k}}$ With the 3rd reference value $w_3=\frac{(w_2-(\mathrm{ad}+\mathrm{bc}))}{2^{2k}};$

Second coefficient acquiring unit, for according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part, namely obtain w ₁+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of cd, wherein K _ifor positive integer, and w ₁+ (2 ^2k-1-1)+K _i2 ^2k>=0; Obtain the product of the first real part and the second imaginary part according to described second reference value, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number, namely obtains w ₂+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 as the imaginary part of the product of described first plural number and the second plural number, wherein K _ifor positive integer, and w ₂+ (2 ^2k-1-1)+K _i2 ^2k>=0; And the product ab of the first real part and the second real part is obtained according to described 3rd reference value, namely obtain w ₃+ (2 ^2k-1-1)+K _i2 ^2klow 2k bit value form nonnegative number deduct 2 ^2k-1the value of-1 is the value of ab, wherein K _ifor positive integer, and w ₃+ (2 ^2k-1-1)+K _i2 ^2k>=0; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

11. uses according to claim 8 multiplier realizes the device of complex multiplication, and it is characterized in that, described second acquisition module comprises:

Second reference value acquiring unit, for according to described first reference value w ₁obtain the second reference value $w_2=\frac{(w_1-\mathrm{cd})}{2^{2k}};$

3rd coefficient acquiring unit, for according to described first reference value w ₁obtain the product cd of the first imaginary part and the second imaginary part, namely obtain w ₁the signed integer that the value of low 2k bit is formed is the value of cd; According to described second reference value w ₂obtain the product of the first real part and the second imaginary part, and the sum of products ad+bc of the first imaginary part and the second real part is plural as described first and the imaginary part of the product of the second plural number, namely obtains w ₂the signed integer that the value of low 2k bit is formed as the imaginary part of the product of described first plural number and the second plural number, and wherein at w ₁the value of 2k-1 bit when being 0, w ₂value equal w ₁2k to the value of 6k-1 bit; At w ₁the value of 2k-1 bit be 1, w ₂value equal w ₁2k add 1 to the value of 6k-1 bit; According to described second reference value w ₂obtain the product ab of the first real part and the second real part, namely at w ₂the value of 2k-1 bit when being 0, obtain w ₂2k to 4k-1 bit value form signed integer be the value of ab, at w ₂the value of 2k-1 bit when being 0, obtain w ₂2k to 4k-1 bit value form signed integer add that 1 signed integer obtained is the value of ab; Wherein, described w ₂value at w ₁the value of 2k-1 bit equal w when being 0 ₁2k to the value of 6k-1 bit, at w ₁the value of 2k-1 bit be 1, w ₂value equal w ₁2k add 1 to the value of 6k-1 bit; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.

12. uses according to claim 7 multiplier realizes the device of complex multiplication, it is characterized in that, first real part a, the first imaginary part c of the first complex signal that described first receiver module receives, the second real part b of the second complex signal and the value of the second imaginary part d are the integer being more than or equal to 0, the first transformed value s=a2 that described first acquisition module obtains according to the first complex signal ^2k+ c, described the second transformed value t=b2 obtained according to the second complex signal ^2k+ d, and the first reference value w that described first computing module calculates ₁=st=ab2 ^4k+ (ab+bc) 2 ^2k+ cd, wherein k is positive integer;

Described second acquisition module is specifically for obtaining w ₁the 0th nonnegative integer formed to the value of 2k-1 bit be the value of cd, obtain w ₁the nonnegative integer that forms of the value of 2k to 4k-1 bit as the imaginary part of product of described first plural number and the second plural number, acquisition w ₁4k to 6k-1 bit value form nonnegative integer be the value of ab; The value obtaining ab-cd is as the real part of product of described first plural number and the second plural number.