FIR filter based on error-free probability calculation
阅读说明：本技术 基于无误差概率计算的fir滤波器 (FIR filter based on error-free probability calculation ) 是由 卢有亮 张恒源 王浩 赵成 卢鹏宇 陈瑜 唐豪 任伟 于 2019-09-25 设计创作，主要内容包括：本发明公开了一种基于无误差概率计算的FIR滤波器,该滤波器包括前向转换模块、无误差概率乘法器、无误差概率加法器和后向转化模块。本发明将输入的信号值转化到概率域上,然后利用概率计算方法对信号进行处理,最后对得到的概率域上的序列进行计数转换回二进制下得到最终的输出信号值,大大降低了滤波器所消耗的硬件资源,具有无误差、容错性能更好等优点。(The invention discloses an FIR filter based on error-free probability calculation, which comprises a forward conversion module, an error-free probability multiplier, an error-free probability adder and a backward conversion module. The invention converts the input signal value to the probability domain, then processes the signal by using the probability calculation method, and finally counts the sequence on the probability domain and converts the sequence back to the binary system to obtain the final output signal value, thereby greatly reducing the hardware resource consumed by the filter and having the advantages of no error, better fault-tolerant performance and the like.)
1. An FIR filter based on error-free probability calculation is characterized by comprising a forward conversion module, an error-free probability multiplier, an error-free probability adder and a backward conversion module;
the forward conversion module is used for normalizing the input signal and the filter coefficient, respectively converting the normalized input signal and the normalized filter coefficient into a concentrated distribution sequence and a uniform distribution sequence, and transmitting the concentrated distribution sequence and the uniform distribution sequence to the error-free probability multiplier;
the error-free probability multiplier is used for carrying out an AND operation on the concentrated distribution sequence and the uniform distribution sequence to obtain an error-free probability multiplication result and transmitting the error-free probability multiplication result to the error-free probability adder;
the error-free probability adder is used for adding the sequence of the error-free probability multiplication result to obtain an error-free probability addition result and transmitting the error-free probability addition result to the backward conversion module;
and the backward conversion module is used for converting the probability sequence of the filtering result into a binary number value to obtain the filtering result.
2. The FIR filter based on error-free probability computation of claim 1, wherein the forward conversion module comprises a concentrated sequence generation unit for converting the input signal into a concentrated distribution sequence and a uniform sequence generation unit for converting the filter coefficients into a uniform distribution sequence.
3. The FIR filter based on calculation without error probability as claimed in claim 2, wherein the lumped sequence generation unit converts the input data into 1 lumped at the head of the sequence and 0 lumped at the tail of the sequence and having a length of 2n1*2n1The concentration of (2) is distributed to 0,1 sequences.
4. The FIR filter based on calculation without error probability according to claim 2, wherein the uniform sequence generating unit applies the filter coefficients according to binary value c x 2n2Is generated with a corresponding total length of 2n2*2n2Uniformly distributed 0,1 sequences.
5. An FIR filter based on error-free probability computation according to claim 3 or 4, characterized in that said error-free probability adder performs a phase OR operation on two random sequences to obtain an error result, and performs a phase AND operation to obtain an error compensation, and the sum of the results of the two operations to obtain the result of the error-free probability addition computation.
6. The FIR filter based on error-free probability calculation of claim 5, characterized in that it specifically comprises 1 centralized sequence generating unit, n-1 registers, n uniform sequence generating units, n error-free probability multipliers, n-1 error-free probability adders and 1 backward transformation module; the centralized sequence generating unit and the register are sequentially arranged, and the corresponding error-free probability multiplier and the corresponding error-free probability adder are respectively sequentially arranged in parallel at the connecting end; the input end of the error-free probability multiplier is connected with the corresponding uniform sequence generation unit, and the tail end of the error-free probability adder is connected with the backward conversion module.
Technical Field
The invention belongs to the technical field of digital signal processing, and particularly relates to an FIR filter based on error-free probability calculation.
Background
The digital filter is a device commonly used in the field of digital signal processing, and is also an indispensable component in modern communication systems, wherein a Finite Impulse Response (FIR) filter is one of the most commonly used and important filters in digital signal processing systems because the FIR filter can be designed to have any amplitude-frequency characteristic, and simultaneously, the FIR filter ensures accurate and strict linear phase characteristics, and the unit sampling Response of the FIR filter is Finite in length, so that the FIR filter is a stable system. The main goal of implementing an FIR digital filter on a digital chip is to not only obtain filter coefficients that meet performance criteria, but also reduce the hardware resources consumed as much as possible.
Probability calculation is a brand-new numerical value representation system, and a group of randomly coded pulse sequences are used for representing numerical values with the value range of [0, 1 ]. The addition and multiplication in the probability domain can be realized by a simple logic gate structure. Compared with the traditional calculation method, the probability calculation has the advantages of low circuit complexity, strong fault-tolerant capability, less resource consumption and the like.
Disclosure of Invention
The invention mainly aims to provide an FIR filter based on error-free probability calculation, which uses a probability adder and a probability multiplier to realize the addition and multiplication operations under the traditional binary system after a filter coefficient and an input signal pass through a probability sequence conversion unit, and finally finishes the output of filter data through a backward conversion unit from a probability sequence to a binary value.
In order to achieve the above object, the present invention provides an FIR filter based on error-free probability calculation, which comprises a forward conversion module, an error-free probability multiplier, an error-free probability adder and a backward conversion module;
the forward conversion module is used for normalizing the input signal and the filter coefficient, respectively converting the normalized input signal and the normalized filter coefficient into a concentrated distribution sequence and a uniform distribution sequence, and transmitting the concentrated distribution sequence and the uniform distribution sequence to the error-free probability multiplier;
the error-free probability multiplier is used for carrying out an AND operation on the concentrated distribution sequence and the uniform distribution sequence to obtain an error-free probability multiplication result and transmitting the error-free probability multiplication result to the error-free probability adder;
the error-free probability adder is used for adding the sequence of the error-free probability multiplication result to obtain an error-free probability addition result and transmitting the error-free probability addition result to the backward conversion module;
and the backward conversion module is used for converting the probability sequence of the filtering result into a binary number value to obtain the filtering result.
Further, the forward conversion module includes a concentrated sequence generation unit and a uniform sequence generation unit, the concentrated sequence generation unit is configured to convert the input signal into a concentrated distribution sequence, and the uniform sequence generation unit is configured to convert the filter coefficient into a uniform distribution sequence.
Further, the concentrated sequence generating unit converts the input data into 1 concentrated at the head of the sequence and 0 concentrated at the tail of the sequence, and the length of the 1 concentrated at the tail of the sequence is 2n1*2n1The concentration of (2) is distributed to 0,1 sequences.
Further, the uniform sequence generation unit applies the filter coefficients according to a
Further, the error-free probability adder performs phase or operation on the two random sequences to obtain an error result, performs phase and operation calculation to obtain error compensation, and obtains the result of the error-free probability addition calculation by the sum of the results of the two operations.
Further, the system specifically comprises 1 centralized sequence generating unit, n-1 registers, n uniform sequence generating units, n error-free probability multipliers, n-1 error-free probability adders and 1 backward conversion module; the centralized sequence generating unit and the register are sequentially arranged, and the corresponding error-free probability multiplier and the corresponding error-free probability adder are respectively sequentially arranged in parallel at the connecting end; the input end of the error-free probability multiplier is connected with the corresponding uniform sequence generation unit, and the tail end of the error-free probability adder is connected with the backward conversion module.
The invention has the beneficial effects that: the invention converts the filter coefficient and the input data to the corresponding probability domain, then respectively converts the filter coefficient and the input data to the uniform distribution sequence and the concentrated distribution sequence, replaces the multiplier and the adder under the traditional binary system by using the probability multiplier and the probability adder, and finally outputs the final filter result by the finally calculated sequence through the backward conversion unit, thereby greatly reducing the hardware resource consumed by the filter and having the advantages of no error, better fault-tolerant performance and the like.
Drawings
FIG. 1 is a schematic diagram of the FIR filter structure based on error-free probability calculation of the present invention;
FIG. 2 is a schematic diagram of a uniform sequence generation unit in the present invention;
FIG. 3 is a schematic diagram of a centralized sequence generation unit in the present invention;
FIG. 4 is a schematic diagram of an error-free probability multiplier of the present invention;
FIG. 5 is a schematic diagram of an error-free probability adder according to the present invention;
FIG. 6 is a schematic diagram of a back conversion module in the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The main solution of the embodiment of the invention is as follows:
as shown in fig. 1, an FIR filter based on error-free probability calculation includes a forward conversion module, an error-free probability multiplier, an error-free probability adder and a backward conversion module;
the forward conversion module is used for normalizing the input signal and the filter coefficient, respectively converting the normalized input signal and the normalized filter coefficient into a concentrated distribution sequence and a uniform distribution sequence, and transmitting the concentrated distribution sequence and the uniform distribution sequence to the error-free probability multiplier;
the error-free probability multiplier is used for carrying out an AND operation on the concentrated distribution sequence and the uniform distribution sequence to obtain an error-free probability multiplication result and transmitting the error-free probability multiplication result to the error-free probability adder;
the error-free probability adder is used for adding the sequence of the error-free probability multiplication result to obtain an error-free probability addition result and transmitting the error-free probability addition result to the backward conversion module;
and the backward conversion module is used for converting the probability sequence of the filtering result into a binary number value to obtain the filtering result.
The forward conversion module of the invention mainly realizes the conversion of the input signal value from binary system to probability domain, namely the filter coefficient ciProbability value Pc for converting to the same bit width as the input data xiAnd PxiSpecifically, input data x (x < 2)n1) And a filter coefficient c (c < 2)n2) Normalized and converted into probability values Px, Pc (Px: x/2)n1，Pc＝c/2n1N1 > n2), and then changing Px, Pc to Px ═ 2 (x ═ 2)n1)/(2n1*2n1)，Pc＝(c*2n1)/(2n1*2n1)。
In addition, the forward conversion module further includes a concentrated sequence generation unit for converting the input signal into a concentrated distribution sequence and a uniform sequence generation unit for converting the filter coefficients into a uniform distribution sequence.
As shown in FIG. 2, the concentrated sequence generating unit inputs n-bit input data Xn-1Xn-2...X1X0The
As shown in FIG. 3, the uniform sequence generating unit inputs n-bit input data Xn-1Xn-2...X1X0For input data X thereini，XiGenerating a corresponding sequence for 1，XiIf the sequence is O, the sequence is all O, and 1 is circularly shifted to the right by 2n-i-1-1 bit, outputting the final uniformly distributed sequence, thereby implementing the filtering coefficient according to
Through the conversion of the forward conversion module, the proportion of 1 in the uniformly distributed sequence and the centrally distributed sequence generated in this way is determined without error.
Take an FIR filter with 12 bits of input data as an example, where the maximum value of the filter coefficient is cmax(cmax＜2n) If n < 12, the filter coefficients are all converted into probability values under 12-bit width, and if n > 12, all the filter coefficients are converted into probability values under n-bit width, which will be described later by taking n < 12 as an example. Converting probability value of input data into Px ═ x/212＝(x*212)/(212*212) Conversion of probability values of filter coefficients into Pci＝ci/212＝(ci*212)/(212*212) Then Px and Pc are respectively addediGenerating length of 2 by centralized distribution sequence generating unit and uniform distribution sequence generating unit24Concentrated distribution sequence PX and uniform distribution sequence PCi。
As shown in fig. 4, the error-free probability multiplier of the present invention is used for concentrating the distribution sequence PX and the uniform distribution sequence PC generated by the aforementioned forward conversion moduleiAnd carrying out AND operation to obtain a probability multiplication result without error.
As shown in fig. 5, the error-free probability adder of the present invention is used to perform addition operation on the sequences calculated by the error-free probability multiplier, calculate the final filtering result, perform phase or operation on two random sequences, calculate the error result, perform the phase and operation, calculate the error compensation, and the sum of the two operation results is the result of the error-free probability addition calculation.
As shown in fig. 6, the backward transformation module of the present invention is used to obtain a final sequence through error-free probability calculation, and then calculate 1 in the sequence through an accumulator to obtain an output result in binary system.
The specific structure of the FIR filter based on error-free probability calculation of the present invention is described in further detail below.
As shown in fig. 1, the FIR filter based on error-free probability calculation of the present invention specifically includes an n-order structure composed of 1 centralized sequence generating unit, n-1 registers D, n uniform sequence generating units, n error-free probability multipliers, n-1 error-free probability adders and 1 backward transformation module; the concentrated sequence generating unit and the register are sequentially connected in series, and the corresponding error-free probability multiplier and the corresponding error-free probability adder are sequentially connected in parallel at the connecting ends between the concentrated sequence generating unit and the register D and between the register D and the register D respectively; the input end of each error-free probability multiplier is connected with the corresponding uniform sequence generation unit, the output end of the 1 st-order error-free probability multiplier is directly connected with the second-order error-free probability adder, and the nth-order error-free probability adder at the tail end is connected with the backward conversion module.
The generated input data centralized distribution sequence PX and the filter coefficient uniform distribution sequence PC areiThe AND operation completes the input data x and the filter coefficient ciAnd (4) multiplying.
The input data after each order of delay register is concentrated with a distribution sequence PX and a corresponding filter coefficient uniform distribution sequence PCiAfter multiplication, all the products are added through an adding operation to complete the convolution accumulation operation.
The product value after each factorial operation is subjected to OR gate operation to obtain an addition value under the traditional probability adder, and the error compensation value can be obtained by performing AND gate operation once again, wherein the combination of the two values is the probability sum without errors.
After all the multiply-accumulate operations, the final filtering output can be converted from the probability domain to the binary value system through a probability sequence to binary value backward conversion unit to obtain the final filtering result.
The backward unit from the probability domain to the binary numerical system is an accumulator, the number of 1 in the probability sequence is accumulated, and the obtained final value is the corresponding value of the probability sequence under the corresponding binary numerical system.
The invention converts the filter coefficient and the input data into the corresponding probability domain, then respectively converts the filter coefficient and the input data into the uniform distribution sequence and the concentrated distribution sequence, replaces the multiplier and the adder under the traditional binary system by using the probability multiplier and the probability adder, and finally outputs the final filter result to the backward conversion unit by the finally calculated sequence.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
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