A method for realizing ultra-wideband white noise

Abstract

The invention relates to a method for realizing ultra-wideband white noise. A seed generator is divided into four paths, which are respectively connected to two random number generating modules, the random number generating modules are composed of a multiplication congruential generator module and a Lag Fibonaicc generator module, the multiplication congruential generator is connected to the Lag Fibonaicc generator module to generate a uniformly distributed signal; the two random number generating modules are respectively connected to two function changing modules, and whitening of uniform noise is completed by an improved Box-Muller method, and the output ends of the two function changing modules are respectively connected to multi-path merging modules; the multi-path merging module realizes multi-path merging by an improved multi-phase parallel filtering method, and finally forms an ultra-wideband white noise signal; the invention solves the problem of selecting the first p numbers of a Lag Fibonaicc sequence, and adopts an HSM realization method to obtain the same accuracy with less storage resources; the multi-phase parallel filtering reduces the occupation of multiplier resources, and supports high-bandwidth and high-speed realization.

Description

Technical Field

[0001] The present invention provides an ultra-wideband white noise realization method, which can realize the generation of white noise with a bandwidth of hundreds of megabytes and can be widely used in application scenarios such as electronic countermeasures, interference simulators and electromagnetic environment simulation. Background Art

[0002] Common methods for white noise include m-sequence whitening and Box-Muller algorithm, both of which can produce white noise with quite good effect. However, when the white noise bandwidth is required to be very wide, it is difficult to implement high-speed multi-phase with Box-Muller and m-sequence whitening methods. Therefore, improvements are needed.

[0003] The Box-Muller deformation algorithm described in "A Gaussian White Noise Generator Based on FPGA" (Classification Number: H03B29 / 00(2006.01)I) is difficult to implement in parallel to generate ultra-wideband white noise.

[0004] "Digital Voice-Grade Gaussian White Noise Generator" (classification number: CN101907715A) uses m-sequence combined with WALLACE algorithm. Although m-sequence high-speed parallelization is simple to implement, WALLACE parallelization is difficult to implement, so it is also difficult to generate ultra-wideband white noise. Summary of the invention

[0005] The purpose of the present invention is to provide a method for realizing ultra-wideband white noise.

[0006] The present invention provides a method for realizing ultra-wideband white noise, which is implemented by an ultra-wideband white noise realization system, wherein the system is composed of a seed generator, a random number generation module, a function change module and a multi-channel merging module; wherein:

[0007] The seed generator is divided into four paths, each connected to two random number generation modules. The random number generation module consists of a multiplication congruential generator module and a Lag Fibonaicc generator module. The output end of the multiplication congruential generator is connected to the input end of the Lag Fibonaicc generator module to generate uniformly distributed signals of IQ (two paths each, a total of 4 paths);

[0008] The output ends of the two-way random number generation modules are respectively connected to the input ends of the two-way function change modules, and the uniform noise is whitened by the improved Box-Muller method. The output ends of the two-way function change modules are respectively connected to the multi-way merging modules;

[0009] The multi-channel merging module realizes multi-channel merging by means of improved multi-phase parallel filtering, and finally forms an ultra-wideband white noise signal; the specific steps of the implementation method are as follows:

[0010] (1) A seed generator randomly generates four random number seeds that can generate relatively good non-correlation and sends them to two random number generation modules as four seed inputs;

[0011] (2) After the two random number generation modules receive the four-way seeds, each random number generation module uses a combination of a multiplication congruential generator module and a Lag Fibonaicc generator module to generate four uniformly distributed random numbers;

[0012] (3) The two-way function transformation module generates two-way orthogonal IQ Gaussian data using the improved Box-Muller method according to the four-way random numbers received;

[0013] (4) The multi-channel merging module generates high-bandwidth white noise data based on the two received orthogonal Gaussian data using an improved four-phase parallel filtering structure.

[0014] In the present invention, the four seeds in step (1) are Seed0, Seed1, Seed2 and Seed3. The selection of the four seeds must meet the following conditions:

[0015] Seed0+Seed2=Seed1+Seed3=M (Formula 1)

[0016] Where: Seed0, Seed1, Seed2 and Seed3 are the four input seeds respectively, and M is the dividend in the random number generation module;

[0017] In the present invention, the random number generation module in step (2) generates uniformly distributed random numbers by combining a multiplication congruential generator and a Lag Fibonaicc generator;

[0018] When the multiplication congruential generator receives the seed, it generates the first p random numbers according to formula 2;

[0019] X i+1 =aX i Mod M,i≤p (Formula 2)

[0020] Where: X i is the i-th random number, X i+1 is the i+1th random number, a is a constant, M is the dividend, and p is the number of random numbers generated by the multiplication congruential generator;

[0021] Then these p numbers are sent to the Lag Fibonaicc generator, which uses formula 3 to calculate the following random numbers based on the first p numbers;

[0022] X i+1 =Xi-q +X i-p Mod M,i>p (Formula 3)

[0023] Where: X i-q is the iqth random number, X i-p is the random number of the ip, X i+1 is the i+1th random number, a is a constant, M is the dividend, p and q are X p +X q +1 is the primitive root, and p>q; the values ​​of p and q affect the quality of the generated random numbers.

[0024] In the present invention, the function in step (3) is implemented using the Box-Muller method;

[0025] For the two uniformly distributed random variables u1 and u2 generated in step (2), use formula 4 to calculate:

[0026]

[0027] Among them: u1 and u2 are two uniformly distributed random numbers, x I and x Q They are two channels of orthogonal Gaussianized data output by each function transformation module.

[0028] In the present invention, the multi-channel merging module in step (4) is implemented by using a parallel FIR filter;

[0029] The parallel filtering structure adopts a "divide and conquer" processing method, dividing the two sequences "to be convolved" into several subsequences of "the same number" according to the principle of cross data distribution, such as the two-phase decomposition shown below;

[0030] The input and output relationship of an FIR filter with N taps in the time domain is as follows:

[0031]

[0032] Where: x[n] is the input signal sequence, h[n] is the sequence of tap coefficients of the FIR filter, N is the number of taps, n is the sampling time sequence, and k is the current sampling time;

[0033] y[n] can be expressed in the z domain as:

[0034]

[0035] Where: H(z) is the z-domain transform of h[n], X(z) is the z-domain transform of x[n], Y(z) is the z-domain transform of y[n], N is the number of taps, and n is the sampling time sequence;

[0036] Decompose X(z) into two parts: odd part and even part, as shown below:

[0037]

[0038] Where: x[n] is the input signal sequence, X(z) is the z-domain transform of x[n], X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively;

[0039] Similarly, H(z) can also be decomposed into odd and even parts as follows:

[0040] H(z)=H0(z 2 )+z -1 H1(z 2 ) (Formula 8)

[0041] Where: H0(z 2 ) and H1(z 2 ) correspond to the z-domain transform of h[2k] and h[2k+1] respectively. 2 ) and H1(z 2 ) are all of length N / 2;

[0042] Using Formula 7 and Formula 8, Y(z) is recalculated as follows:

[0043]

[0044] Where: X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively. 2 ) and H1(z 2 ) correspond to the z-domain transformation of h[2k] and h[2k+1], respectively, and Y0(z 2 ) and Y1(z 2 ) are the z-transforms of y[2k] and y[2k+1] respectively;

[0045] Formula 9 is the polynomial decomposition representation of the parallel FIR filter. In each iteration, the filter operation can simultaneously process two inputs x[2k] and x[2k+1] and simultaneously generate outputs y[2k] and y[2k+1];

[0046] The implementation structure corresponding to Formula 9 requires 2N multiplications and 2(N-1) additions;

[0047] Rewrite Formula 9 as:

[0048]

[0049] Where: X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively. 2 ) and H1(z 2 ) correspond to the z-domain transformation of h[2k] and h[2k+1], respectively, and Y0(z 2 ) and Y1(z 2 ) are the z-transforms of y[2k] and y[2k+1] respectively;

[0050] In formula 10, Y0(z 2 ) and Y1(z 2 ) all appear in X0(z 2 )H0(z 2 ) and X1(z 2 )H1(z 2 ), which can be reused in hardware implementation. Such a structure uses 3N / 2 multipliers and 3(N / 2-1)+4 adders.

[0051] In the present invention, an improved structure of a 4-way parallel FIR filter is derived, assuming:

[0052]

[0053] Among them: X0, X1, X2, X3 correspond to the z-domain transformation of x[4k], x[4k+1], x[4k+2], x[4k+3] respectively, H0, H1, H2, H3 correspond to the z-domain transformation of h[4k], h[4k+1], h[4k+2], h[4k+3] respectively, Y0, Y1, Y2, Y3 correspond to the z-domain transformation of y[4k], y[4k+1], y[4k+2], y[4k+3] respectively, X0′, X1′ correspond to the z-domain transformation of x[4k]+x[4k+2], x[4k+1]+x[4k+3] respectively, H0′, H1′ correspond to the z-domain transformation of h[4k]+h[4k+2], h[4k+1]+h[4k+3] respectively;

[0054] Further deduction yields:

[0055]

[0056] Where: X0, X1, X2, X3 correspond to the z-domain transformation of x[4k], x[4k+1], x[4k+2], x[4k+3] respectively, H0, H1, H2, H3 correspond to the z-domain transformation of h[4k], h[4k+1], h[4k+2], h[4k+3] respectively, X0′, X1′ correspond to the z-domain transformation of x[4k]+x[4k+2], x[4k+1]+x[4k+3] respectively, H0′, H1′ correspond to the z-domain transformation of h[4k]+h[4k+2], h[4k+1]+h[4k+3] respectively;

[0057] Through the above derivation, a 4-way parallel FIR filter is obtained.

[0058] The beneficial effects of the present invention are:

[0059] (1) The random number generation part uses the multiplication congruential method to solve the problem of selecting the first p numbers in the Lag Fibonaicc sequence. At the same time, the high speed, long period, and high-dimensional uniformity of the Lag Fibonaicc sequence are used to solve the shortcomings of the multiplication congruential method such as short period and strong correlation, so that uniform random numbers with better quality can be obtained.

[0060] (2) Function transformation module Box-Muller algorithm The function uses the HSM implementation method to use less storage resources to achieve the same accuracy;

[0061] (3) The multi-channel parallel module uses improved multi-phase parallel filtering to reduce the multiplier resource usage and support high-bandwidth and high-speed implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is an implementation block diagram of the present invention;

[0063] Figure 2 yes The function graph is plotted and segmented in the interval (0,1]. It can be seen from the figure that the function is extremely nonlinear near 0 and 1. Therefore, the traditional lookup table method based on uniform address cannot be used for the calculation of this function, because for highly nonlinear areas, very small segments may be used to achieve the accuracy of the linear area;

[0064] Figure 3 It is obtained by simulation using the HSM method Function graphs;

[0065] Figure 4 This is the implementation structure diagram of the polyphase filter:

[0066] Figure 5 It is a two-way parallel FIR filter implementation structure;

[0067] Figure 6 It is an improved two-way parallel FIR filter implementation structure;

[0068] Figure 7 It is an improved structure of 4-way parallel filtering;

[0069] The numbers in the figure are: 1 is the seed generator, 2 is the multiplication congruential generator, 3 is the Lag Fibonaicc generator, 4 is the function change module, and 5 is the multi-item merging module. DETAILED DESCRIPTION

[0070] The present invention is further described below by way of embodiments in conjunction with the accompanying drawings.

[0071] Embodiment 1:

[0072] Figure 1 The block diagram of the present invention is a system composed of two random number generation modules, two function change modules and multiple merging modules. The random number generation module uses the Fabonicci algorithm to generate uniformly distributed signals of IQ (two channels each, a total of 4 channels). The function change module, by implementing Sine and cosine finally complete the whitening of uniform noise, and finally realize multi-channel merging through multi-phase parallel filtering to form an ultra-wideband white noise signal.

[0073] (1) The seed generator randomly generates four seeds (i.e., Seed0, Seed1, Seed2, and Seed3) and sends them to the four inputs of the two random number generation modules respectively; in order to make the generated random numbers have good non-correlation, the selection of the four seeds must meet the following conditions:

[0074] Seed0+Seed2=Seed1+Seed3=M (Formula 1)

[0075] Where: Seed0, Seed1, Seed2 and Seed3 are the four input seeds respectively, and M is the dividend in the random number generation module;

[0076] (2) The random number generation module uses a combination of a multiplicative congruential generator and a Lag Fibonaicc generator to generate uniformly distributed random numbers.

[0077] When the multiplication congruential generator receives the seed, it generates the first p random numbers according to formula 2.

[0078] X i+1 =aX i Mod M,i≤p (Formula 2)

[0079] Where: X i is the i-th random number, X i+1is the i+1th random number, a is a constant, M is the dividend, and p is the number of random numbers generated by the multiplication congruential generator;

[0080] Then these p numbers are sent to the Lag Fibonaicc generator. The Lag Fibonaicc generator generates the following random numbers based on the first p numbers using formula 3;

[0081] X i+1 =X i-q +X i-p Mod M,i>p (Formula 3)

[0082] Where: X i-q is the iqth random number, X i-p is the random number of the ip, X i+1 is the i+1th random number, a is a constant, M is the dividend, p and q are X p +X q +1 is the primitive root, and p>q; the values ​​of p and q affect the quality of the generated random numbers;

[0083] (3) The function transformation module is used to convert the uniformly distributed data obtained in step (2) into white noise. This is achieved using the Box-Muller method.

[0084] For the two uniformly distributed random variables u1 and u2 generated in step (2), use formula 4 to calculate:

[0085]

[0086] Among them: u1 and u2 are two uniformly distributed random numbers, x I and x Q They are two channels of orthogonal Gaussian data output by each function transformation module;

[0087] In the function change module, COS and SIN are well implemented by the CORDIC algorithm, mainly because The implementation of the operation. This function is a composite function, such as Figure 2 As shown, the function is extremely nonlinear near 0 and 1, so the traditional lookup table method based on uniform address cannot be used for the calculation of this function, because very small segments may be required to achieve the accuracy of the linear region in highly nonlinear regions. Composite functions can basically be decomposed into several basic functions for hierarchical calculation. However, this method will not only bring large delays and rounding errors when implemented in hardware, but may also make the calculation impossible;

[0088] Therefore, the following method is adopted: divide (0, 1] into two intervals: (0, 0.5) and [0.5, 1]. For (0, 0.5), use its midpoint to segment, and then use its midpoint to segment (0, 0.25). Do the same for [0.5, 1], such as Figure 2 As shown. In this way, in each interval, a straight line y=ax+b can be used to approximate, that is, each interval is replaced by two coefficients a and b. This can be implemented by a lookup table. The length of the lookup table is twice the number of bits of the input variable x, and each unit in the table is the sum of the number of bits required for a and b. The number of bits of x is 32, so the table length is 64 bits. From the simulation results, it can be calculated that a needs 33 bits to represent and b needs 31 bits to represent, as shown in Figure 3 shown. Figure 3 There are two important small modules in the system: the segment address module and the a,b coefficient lookup table module. The segment address module requires more resources when using the general addressing method, because it involves 32 1-bit additions, the rate is very low, and many adders are required. For 32-bit input, at least 4 pipelines are required. With direct addressing, no adders are required, and only 2 pipelines are required. For the a,b coefficient lookup table module, multiple calculations and simulations are required to check the correctness and accuracy of the results in order to determine the coefficients a,b for each small interval. After continuous simulation, the following is achieved. Figure 4 The effect shown;

[0089] (4) Multi-channel merging module, mainly implements parallel filtering algorithm: through the first two algorithm modules, ultra-wideband white noise has actually been obtained. If it is necessary to realize broadband noise within a certain wide frequency, the baseband white noise needs to be filtered. Since it is an ultra-wideband operation, parallel filtering is required. At the same time, due to the finite length impulse response characteristics of the FIR filter, a parallel FIR filter is used for implementation;

[0090] The parallel filtering structure adopts a "divide and conquer" processing method, dividing the two sequences "to be convolved" into several subsequences of "the same number" according to the principle of cross data distribution, such as the two-phase decomposition shown below;

[0091] The input and output relationship of an FIR filter with N taps in the time domain is as follows:

[0092]

[0093] Where: x[n] is the input signal sequence, h[n] is the sequence of tap coefficients of the FIR filter, N is the number of taps, n is the sampling time sequence, and k is the current sampling time;

[0094] y[n] can be expressed in the z domain as:

[0095]

[0096] Where: H(z) is the z-domain transform of h[n], X(z) is the z-domain transform of x[n], Y(z) is the z-domain transform of y[n], N is the number of taps, and n is the sampling time sequence;

[0097] X(z) can be decomposed into two parts: odd part and even part, as shown below:

[0098]

[0099] Where: x[n] is the input signal sequence, X(z) is the z-domain transform of x[n], X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively;

[0100] Similarly, H(z) can also be decomposed into odd and even parts as follows:

[0101] H(z)=H0(z 2 )+z -1 H1(z 2 ) (Formula 8)

[0102] Where: H0(z 2 ) and H1(z 2 ) correspond to the z-domain transform of h[2k] and h[2k+1] respectively. 2 ) and H1(z 2 ) are all of length N / 2;

[0103] Using Formula 7 and Formula 8, Y(z) is recalculated as follows:

[0104]

[0105] Where: X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively. 2 ) and H1(z 2 ) correspond to the z-domain transformation of h[2k] and h[2k+1], respectively, and Y0(z 2 ) and Y1(z 2 ) are the z-transforms of y[2k] and y[2k+1] respectively;

[0106] Formula 9 is the polynomial decomposition representation of the parallel FIR filter. In each iteration, the filter operation can simultaneously process two inputs x[2k] and x[2k+1] and simultaneously generate outputs y[2k] and y[2k+1];

[0107] Figure 5 The implementation structure corresponding to Formula 9 is given, which requires 2N multiplications and 2(N-1) additions;

[0108] Rewrite Formula 9 as:

[0109]

[0110] Where: X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively. 2 ) and H1(z 2 ) correspond to the z-domain transformation of h[2k] and h[2k+1] respectively. 2 ) and Y1(z 2 ) are the z-transforms of y[2k] and y[2k+1] respectively;

[0111] In formula 10, Y0(z 2 ) and Y1(z 2 ) all appear in X0(z 2 )H0(z 2 ) and X1(z 2 )H1(z 2 ), can be reused in hardware implementation, and its implementation structure is as follows Figure 6 As shown. Such a structure uses 3N / 2 multipliers and 3(N / 2-1)+4 adders;

[0112] Similarly, the improved structure of the 4-way parallel FIR filter is derived, assuming:

[0113]

[0114] Among them: X0, X1, X2, X3 correspond to the z-domain transformation of x[4k], x[4k+1], x[4k+2], x[4k+3] respectively, H0, H1, H2, H3 correspond to the z-domain transformation of h[4k], h[4k+1], h[4k+2], h[4k+3] respectively, Y0, Y1, Y2, Y3 correspond to

[0115] The z-domain transformation of y[4k],y[4k+1],y[4k+2],y[4k+3], X0′,X1′ respectively correspond to

[0116] The z-domain transformation of x[4k]+x[4k+2],x[4k+1]+x[4k+3], H0′,H1′ respectively correspond to

[0117] The z-domain transformation of h[4k]+h[4k+2],h[4k+1]+h[4k+3];

[0118] Further deduction yields:

[0119]

[0120] Among them: X0, X1, X2, X3 correspond to the z-domain transformation of x[4k], x[4k+1], x[4k+2], x[4k+3] respectively, H0, H1, H2, H3 correspond to the z-domain transformation of h[4k], h[4k+1], h[4k+2], h[4k+3] respectively, X0′, X1′ correspond to

[0121] The z-domain transformation of x[4k]+x[4k+2],x[4k+1]+x[4k+3], H0′,H1′ respectively correspond to

[0122] The z-domain transformation of h[4k]+h[4k+2],h[4k+1]+h[4k+3];

[0123] Through the above derivation, we can get the improved structure of 4-way parallel FIR filter as follows Figure 7 As shown;

[0124] like Figure 6 and Figure 7 As shown in the figure, the parallel filtering structure adopts a parallel structure of multi-phase decomposition, which greatly improves the throughput rate of the FIR filter. The input data is also decomposed by multi-phase, and its rate is consistent with the sampling rate of the final filter output. The data bandwidth can be 0.4 times the sampling rate, which solves the defect of limited bandwidth of the multi-phase filtering structure based on interpolation; but the parallel filtering structure also increases the overhead of FPGA resources. The two-way parallel filtering structure requires 2K multiplication and 2K addition operations, and the hardware resource overhead is twice that of the traditional digital FIR structure; the four-way parallel filtering structure requires 6K multiplication and 6K+8 addition operations, and the hardware resource overhead is 6 times that of the traditional digital FIR structure.

Claims

1. A method for realizing ultra-wideband white noise, wherein the method is realized by an ultra-wideband white noise realization system, wherein the system is composed of a seed generator, a random number generation module, a function transformation module and a multi-channel merging module; and the characteristics are as follows: The seed generator is divided into four paths, which are respectively connected to two random number generation modules. The random number generation module consists of a multiplication congruential generator module and a Lag Fibonaicc generator module. The output end of the multiplication congruential generator module is connected to the input end of the Lag Fibonaicc generator module to generate two IQ paths, a total of four paths of uniformly distributed signals; The output ends of the two-way random number generation modules are respectively connected to the input ends of the two-way function transformation modules, and the uniform noise is converted into white noise by the improved Box-Muller method. The output ends of the two-way function transformation modules are respectively connected to the multi-way merging modules. The multi-channel merging module realizes multi-channel merging through an improved multi-phase parallel filtering method, and finally forms an ultra-wideband white noise signal; The specific steps of the implementation method are as follows: (1) A seed generator randomly generates four random number seeds that can generate relatively good non-correlation and sends them to two random number generation modules as four seed inputs; (2) After the two random number generation modules receive the four-way seeds, each random number generation module generates four-way random numbers with uniform distribution by using the combination of the multiplication congruential generator module and the Lag Fibonaicc generator module; the random number generation module generates uniformly distributed random numbers by using the combination of the multiplication congruential generator module and the Lag Fibonaicc generator module; When the multiplication congruential generator module receives the seed, it generates the first p random numbers according to formula 2; X i+1 =aX i Mod M, i≤p (Formula 2) Where: X i is the i-th random number, X i+1 is the i+1th random number, a is a constant, M is the dividend, and p is the number of random numbers generated by the multiplication congruential generator module; Then these p numbers are sent to the Lag Fibonaicc generator module, which uses formula 3 to calculate the following random numbers based on the first p numbers. X i+1 =X i-q +X i-p Mod M, i>p (Formula 3) Where: X i-q is the iqth random number, X i-p is the random number of the ip, X i+1 is the i+1th random number, a is a constant, M is the dividend, p and q are X p +X q +1 primitive root, and p>q; the values ​​of p and q affect the quality of the generated random numbers; (3) The two-way function transformation module generates two-way orthogonal IQ Gaussian data using the improved Box-Muller method according to the four-way random numbers received; (4) The multi-channel merging module generates high-bandwidth white noise data based on the two received orthogonal Gaussian data using an improved four-phase parallel filtering structure.

2. The method for realizing ultra-wideband white noise according to claim 1, characterized in that The four seeds mentioned in step (1) are Seed0, Seed1, Seed2 and Seed3. The selection of the four seeds must meet the following conditions: Seed0+Seed2=Seed1+Seed3=M (Formula 1) Wherein: Seed0, Seed1, Seed2 and Seed3 are the four input seeds respectively, and M is the dividend in the random number generation module.

3. The method for realizing ultra-wideband white noise according to claim 1, characterized in that In the multi-channel merging module in step (4), a parallel FIR filter is used for implementation; The parallel filtering structure adopts a "divide and conquer" processing method, dividing the two sequences "to be convolved" into several subsequences of "the same number" according to the principle of cross data distribution, as shown in the two-phase decomposition below; The input and output relationship of an FIR filter with N taps in the time domain is as follows: Where: x[n] is the input signal sequence, h[n] is the sequence of tap coefficients of the FIR filter, N is the number of taps, n is the sampling time sequence, and k is the current sampling time; y[n] is expressed in the z domain as: Where: H(z) is the z-domain transform of h[n], X(z) is the z-domain transform of x[n], Y(z) is the z-domain transform of y[n], N is the number of taps, and n is the sampling time sequence; Decompose X(z) into two parts: odd part and even part, as shown below: Where: x[n] is the input signal sequence, X(z) is the z-domain transform of x[n], X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively; Similarly, H(z) can also be decomposed into odd and even parts as follows: H(z) = H0(z 2 ) + z -1 H1(z 2 ) (Equation 8) Where: H0(z 2 ) and H1(z 2 ) correspond to the z-domain transform of h[2k] and h[2k+1] respectively; sub-filter H0(z 2 ) and H1(z 2 ) are all of length N / 2; Using Formula 7 and Formula 8, Y(z) is recalculated as follows: Where: X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively; H0(z 2 ) and H1(z 2 ) correspond to the z-domain transformation of h[2k] and h[2k+1], respectively, and Y0(z 2 ) and Y1(z 2 ) are the z-transforms of y[2k] and y[2k+1] respectively; Formula 9 is the polynomial decomposition representation of the parallel FIR filter. In each iteration, the filter operation can process two inputs x[2k] and x[2k+1] simultaneously and generate outputs y[2k] and y[2k+1] simultaneously. The implementation structure corresponding to Formula 9 requires 2N multiplications and 2(N-1) additions; Rewrite Formula 9 as: Where: X0(z 2 ) and X1(z 2 ) correspond to the z-domain transformations of x[2k] and x[2k+1] respectively; H0(z 2 ) and H1(z 2 ) correspond to the z-domain transformation of h[2k] and h[2k+1], respectively, and Y0(z 2 ) and Y1(z 2 ) are the z-transforms of y[2k] and y[2k+1] respectively; In formula 10, Y0(z 2 ) and Y1(z 2 ) all appear in X0(z 2 )H0(z 2 ) and X1(z 2 )H1(z 2 ), which can be reused in hardware implementation. Such a structure uses 3N / 2 multipliers and 3(N / 2-1)+4 adders.

4. The method for realizing ultra-wideband white noise according to claim 3, characterized in that The improved structure of the 4-way parallel FIR filter is derived, assuming: Among them: X0, X1, X2, X3 correspond to the z-domain transformation of x[4k], x[4k+1], x[4k+2], x[4k+3] respectively, H0, H1, H2, H3 correspond to the z-domain transformation of h[4k], h[4k+1], h[4k+2], h[4k+3] respectively, Y0, Y1, Y2, Y3 correspond to the z-domain transformation of y[4k], y[4k+1], y[4k+2], y[4k+3] respectively, X0′, X1′ correspond to the z-domain transformation of x[4k]+x[4k+2], x[4k+1]+x[4k+3] respectively, H0′, H1′ correspond to the z-domain transformation of h[4k]+h[4k+2], h[4k+1]+h[4k+3] respectively; Further deduction yields: Where: X0, X1, X2, X3 correspond to the z-domain transformation of x[4k], x[4k+1], x[4k+2], x[4k+3] respectively, H0, H1, H2, H3 correspond to the z-domain transformation of h[4k], h[4k+1], h[4k+2], h[4k+3] respectively, X0′, X1′ correspond to the z-domain transformation of x[4k]+x[4k+2], x[4k+1]+x[4k+3] respectively, H0′, H1′ correspond to the z-domain transformation of h[4k]+h[4k+2], h[4k+1]+h[4k+3] respectively; Through the above derivation, a 4-way parallel FIR filter is obtained.

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