Direct aiming weapon target scoring system and method based on fire concentration shooting

Abstract

The invention discloses a direct aiming weapon target scoring system and method based on concentrated fire shooting, and belongs to the technical field of data processing. In the system, an image sensor is used for acquiring image information of N artillery striking targets and transmitting the image information to a second data processor; the second data processor comprises an image processing module and an intelligent target scoring module, and the image processing module preprocesses image information to obtain a sequence first landing area image of a target hit by a shell and corresponding sequence first landing time; in the intelligent target scoring module, an estimation module estimates the second landing time of the N cannonballs according to the ejection data of the cannonballs emitted by the N artillery, the distance between the muzzle of the artillery and the target and the environmental data; and the calculation module calculates a landing area image of a shell launched by the # imgabs4 # artillery according to the following formula: # imgabs0 #: # imgabs1 #, and a first landing area # imgabs3 # corresponding to the time # imgabs2 #, wherein the first landing area # imgabs3 # is deduced as the landing area image of the shell launched by the # imgabs4 # artillery. According to the invention, the shooting hit condition of each artillery during fire concentration shooting can be distinguished.

Description

Technical Field

[0001] The invention relates to a target reporting system and method based on concentrated fire shooting and direct aiming weapons, belonging to the technical field of data processing. Background Art

[0002] At present, in the process of conducting firepower strike damage-related test subjects, cameras, high-altitude drones or target area detectors are usually used to collect the damage status of the target area, such as the Chinese invention patent application with publication number CN116258983A, but there is a lack of necessary data information collection for various firepower equipment on the battlefield, and a lack of qualitative data analysis of the shooting training results of artillery equipment. From the test training results, it can be seen that more of the range damage of firepower damage is reflected, and the shooting hits of various artillery equipment are difficult to distinguish, and it is difficult to directly link the shooting party with the hit target. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the purpose of the present invention is to provide a target reporting system and method based on concentrated fire and direct-aiming weapons, which can distinguish the shooting hits of each artillery.

[0004] To achieve the above-mentioned purpose, one aspect of the present invention provides a target reporting system based on concentrated fire and direct aiming weapons, which includes a data control device and a recording device connected via a network, wherein the data control device includes a sensor array, a data receiving module, a data acquisition module, a first data processor and a first communication module, wherein the sensor array respectively obtains the distance from the muzzle of N artillery guns to the target and the firing data of the shells fired by the N artillery guns, the data receiving module receives the data obtained by the sensor array; the data acquisition module is used to obtain environmental data; the first data processor is used to process the firing data of the shells fired by the N artillery guns, the firing data of the shells fired by the N artillery guns, and the firing data of the shells fired by the N artillery guns. The distance to the target and environmental data are processed respectively and then sent to the recording device through the first communication module. The environmental data are such as wind speed and wind direction. The recording device includes a second communication module, a second data processor and an image sensor, wherein the second communication module receives data sent by the data control device; the image sensor is used to obtain image information of the target hit by the shells fired by N artillery pieces, and transmit the image information to the second data processor; the second data processor includes an image processing module and an intelligent target reporting module, and the image processing module pre-processes the image information to obtain the first landing area image of the sequence of the target being hit by the shells and the corresponding sequence first landing time The intelligent target reporting module includes an estimation module and a calculation module. The estimation module estimates the second landing time of the shells fired by N artillery according to the ejection data of the shells fired by N artillery, the distances from the muzzles of N artillery to the target and the environmental data. ; The calculation module calculates according to the following formula : , First landing time Corresponding first landing area image Inferred to be The image of the landing area of ​​the shell fired by the artillery, wherein N is a positive integer greater than or equal to 2.

[0005] To achieve the above-mentioned purpose, another aspect of the present invention provides a method for reporting a target based on concentrated fire and direct aiming weapons, which comprises the following steps: Step 1: The distances from the muzzles of N guns to the target and the firing data of the shells fired by the N guns are respectively acquired through the sensor array of the data control device, and the environmental data is acquired through the data acquisition module of the data control device; Step 2: The first data processor of the data control device processes the firing data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data, and then sends them to the recording device through the first communication module of the data control device; Step 3: receiving data sent by the data control device through the second communication module of the recording device; Step 4: acquiring image information of the target struck by the shells fired by the N artillery pieces through an image sensor of the recording device, and transmitting the image information to a second data processor of the recording device; Step 5: Preprocess the image information through the image processing module of the second data processor to obtain the first landing area image of the sequence where the target is hit by the shell and the corresponding sequence first landing time ; Step 6: The estimation module of the intelligent target reporting module of the second data processor estimates the second landing time of the N shells according to the ejection data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data. ; Step 7: The intelligent target reporting module calculation module of the second data processor calculates according to the following formula : , First landing time Corresponding first landing area image Inferred to be The image of the landing area of ​​the shell fired by the artillery, wherein N is a positive integer greater than or equal to 2.

[0006] Compared with the prior art, the target reporting system and method based on concentrated fire and direct aiming weapons provided by the present invention pre-processes image information through an image processing module to obtain the first landing area image and the first landing time of the sequence of targets hit by shells; estimates N second landing times of shells fired by N artillery pieces according to the firing data of shells fired by N artillery pieces, the distances from the muzzles of N artillery pieces to the targets and environmental data through an estimation module; obtains the second landing time with the smallest difference with a certain first landing time from the N second landing times through a calculation module, and the image of the landing area corresponding to the certain first landing time is inferred as the landing area image of the shells fired by the artillery piece with the second landing time with the smallest difference, thereby being able to distinguish the shooting hit situation of each artillery piece. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 It is a block diagram of the target reporting system based on concentrated fire and direct-aiming weapons provided by this invention.

[0008] Figure 2 It is a block diagram of the image processing module provided by the present invention. DETAILED DESCRIPTION

[0009] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0010] Figure 1 This is a block diagram of the target reporting system based on concentrated fire and direct aiming weapons provided by this invention, such as Figure 1 As shown, a data control device and a recording device are connected through a network based on a concentrated fire shooting direct aiming weapon target reporting system, wherein the data control device includes a sensor array, a data receiving module, a data acquisition module, a first data processor and a first communication module, wherein the sensor array respectively acquires the distances from the muzzles of N artillery pieces to the target and the firing data of the shells fired by the N artillery pieces, and the data receiving module receives the data acquired by the sensor array; the data acquisition module is used to acquire environmental data; the first data processor is used to process the firing data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the target and the environmental data, and then send them to the recording device through the first communication module; the recording device includes a second communication module, a second data processor and an image sensor, wherein the second communication module receives the data sent by the data control device; the image sensor is used to acquire image information of the target hit by the shells fired by the N artillery pieces, and transmit the image information to the second data processor; the second data processor includes an image processing module and an intelligent target reporting module, and the image processing module pre-processes the image information to acquire the first landing area image of the sequence where the target is hit and the corresponding sequence first landing time The intelligent target reporting module includes an estimation module and a calculation module. The estimation module estimates the second landing time of the shells fired by N artillery according to the ejection data of the shells fired by N artillery, the distances from the muzzles of N artillery to the target and the environmental data. ; The calculation module calculates according to the following formula : , First landing time Corresponding first landing area image Inferred to be The image of the landing area of ​​the shell fired by the artillery, wherein N is a positive integer greater than or equal to 2.

[0011] The firing data includes the firing time, firing speed, tilt angle, etc. of the projectile.

[0012] The recording device also includes an input and output unit, which includes a keyboard, a display, a printing interface, etc.

[0013] The present invention uses an image processing module to pre-process image information to obtain the first landing area and the first landing time of the sequence when the target is hit; uses an estimation module to estimate N second landing times of the shells fired by N artillery according to the firing data of the shells fired by N artillery, the distances from the muzzles of the N artillery to the target and environmental data; uses a calculation module to obtain the second landing time with the smallest difference from a certain first landing time from the N second landing times, and the landing area image corresponding to the certain first landing time is inferred as the landing area image of the shells fired by the artillery with the second landing time with the smallest difference, so that the shooting hit situation of each artillery can be distinguished.

[0014] Figure 2 This is the block diagram of the image processing module provided by the present invention, such as Figure 2 As shown, the image processing module includes a segmentation unit, a first calculation unit, a second calculation unit and an extraction unit, wherein the segmentation unit divides a frame of image into Regions, , , where K is the number of pixels in a row of the pixel window, J is the number of pixels in a column of the pixel window, C is the number of pixels in a row of a frame image, and D is the number of pixels in a column of a frame image. represents a floor function; the first calculation unit calculates the first value of the pixel window at the ath row and the bth column according to the following formula: , In the formula, , The center pixel of the pixel window at row a and column b The value of Pixel , a=1,…,A, b=1,…,B; The second calculation unit calculates the second value of the pixel window at the ath row and the bth column according to the following formula: ; Extraction unit comparison and ,when When , the pixel value in the pixel window of the ath row and the bth column is set to 1, otherwise it is set to 0, so as to obtain the first landing area image of the target hit by the shell from a frame of image obtained by the image sensor.

[0015] The present invention takes into account the brightness changes in the local area of ​​the image through the above technical solution, and can segment the image more accurately, so as to more accurately extract the image of the area where the target is hit by the shell from a frame of image.

[0016] In the present invention, the sensor array includes sensor 1, sensor 2, ..., sensor N, each sensor includes at least a vibration sensor and a speed sensor, the N vibration sensors respectively obtain the firing time of the shells sent by the N artillery; the N speed sensors respectively obtain the firing speed of the shells sent by the N artillery. The artillery is, for example, artillery 1, artillery 2, ..., artillery N.

[0017] In the present invention, the first data processor is used to process the ejection data of the shells fired by N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data, specifically including: S4-1: Convert the ejection data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data into binary digits to generate a binary string, and divide the binary string into multiple groups, each group including 2 M bit code, M is greater than or equal to 3; S4-2: 2 M The bit codes are arranged in reverse order to obtain the first-order digital signal, and the first-order digital signal is divided into 2 M-1 group, and then input to the first level of M-level modulation iteration; the i-th level modulation iteration includes 2 M-i The i-th modulation butterfly unit includes 2 i input terminals and 2 i Output terminals; S4-3: The outputs of the two i-1-shaped modulation butterfly units of the i-1-th modulation iteration are used as the inputs of the i-th shaped modulation butterfly unit of the i-th modulation iteration.

[0018] In the present invention, the second i-1-shaped modulation butterfly unit of the two i-1-shaped modulation butterfly units i-1 The outputs are respectively related to the rotation factors Multiply and then add the 2 of the first i-1 modulation butterfly unit of the two i-1 modulation butterfly units. i-1 The output is 2 of the i-th modulation butterfly unit i-1 Output, 2 i-1 modulation butterfly units, 2 i-1 modulation butterfly units i-1 The outputs are respectively related to the rotation factors The output of the first i-1 modulation butterfly unit of the i-1 modulation butterfly unit is added to obtain the other two i-1 modulation butterfly units. i-1 outputs.

[0019] In the present invention, the two M-th butterfly units of the M-th stage M The outputs are transmitted as modulated signals in sequence through the first communication module to the second communication module of the recording device. The first communication module is a first point-to-point data transmission unit, and the second communication module is a second point-to-point data transmission unit.

[0020] The present invention can transmit 2 M bit code, which improves the efficiency of transmitting information.

[0021] The second data processor receives the 2 M The modulated signals are processed as follows to restore the firing data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data sent by the transmitting end. The specific process includes: S6-1: 2 M The modulation signals are arranged in reverse order of the code bits to obtain the second-order modulation signal, and the second-order modulation signal is divided into 2 M-1 The group is then input to the first stage of the M-stage demodulation iteration; the i-th stage demodulation iteration includes 2 M-i The i-th demodulation butterfly unit includes 2 i input terminals and 2 i Output terminals; S6-2: The outputs of the two i-1-shaped demodulation butterfly units of the i-1-th level demodulation iteration are used as the inputs of an i-th-shaped demodulation butterfly unit of the i-th level demodulation iteration.

[0022] In the present invention, the second i-1-shaped demodulation butterfly unit of the two i-1-shaped demodulation butterfly units i-1 The outputs are respectively related to the rotation factors Multiply and then add the 2 of the first i-1 demodulation butterfly unit of the two i-1 demodulation butterfly units. i-1 The output is 2 of the i-th demodulation butterfly unit i-1 outputs; 2 i-1-shaped demodulation butterfly units; 2 i-1-shaped demodulation butterfly units of the second i-1 The outputs are respectively related to the rotation factors After multiplication and inversion, the output of the first i-1-shaped demodulation butterfly unit of the two i-1-shaped demodulation butterfly units is added to obtain the other two i-shaped demodulation butterfly units. i-1 outputs.

[0023] In the present invention, the two M-th demodulation butterfly units of the M-th stage M The output is 2 sent by the data control device M Bit code.

[0024] The present invention can demodulate 2 M modulated signal to improve the demodulation efficiency.

[0025] The present invention also provides a method for reporting a target based on concentrated fire and direct aiming weapons, which comprises the following steps: Step 1: The distances from the muzzles of N guns to the targets and the firing data of the shells fired by the N guns are respectively acquired through the sensor array of the data control device, and the environmental data is acquired through the data acquisition module of the data control device; Step 2: The first data processor of the data control device processes the firing data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data, and then sends them to the recording device through the first communication module of the data control device; Step 3: receiving data sent by the data control device through the second communication module of the recording device; Step 4: acquiring image information of the targets struck by the N artillery pieces through an image sensor of the recording device, and transmitting the image information to a second data processor of the recording device; Step 5: Preprocess the image information through the image processing module of the second data processor to obtain the first landing area image of the sequence where the target is hit and the corresponding sequence first landing time ; Step 6: The estimation module of the intelligent target reporting module of the second data processor estimates the second landing time of the N shells according to the output data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets and the environmental data. ,The firing data of the projectile includes the firing time, the firing speed of the projectile, and the tilt angle; Step 7: The intelligent target reporting module calculation module of the second data processor calculates according to the following formula : , First landing time Corresponding first landing area Inferred to be The landing area image of the artillery, wherein N is a positive integer greater than or equal to 2.

[0026] The present invention also provides a computer program product, which includes computer program codes, and the computer program codes can be called by a processor to execute the method implemented by each module in the first data processor and the second data processor.

[0027] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined. The meaning of "several" is one or more, unless otherwise clearly and specifically defined.

[0028] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A target reporting system based on concentrated fire and direct aiming weapons, characterized in that: A data control device and a recording device connected via a network, wherein the data control device comprises a sensor array, a data receiving module, a data acquisition module, a first data processor and a first communication module, wherein the sensor array respectively acquires the distances from the muzzles of N artillery pieces to the target and the ejection data of the shells fired by the N artillery pieces, and the data receiving module receives the data acquired by the sensor array; the data acquisition module is used to acquire environmental data; the first data processor is used to process the ejection data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the target and the environmental data, and then send them to the recording device via the first communication module; the recording device comprises a second communication module, a second data processor and an image sensor, wherein the second communication module receives the data sent by the data control device; the image sensor is used to acquire image information of the shells fired by the N artillery pieces hitting the target, and transmit the image information to the second data processor; the second data processor comprises an image processing module and an intelligent target reporting module, and the image processing module pre-processes the image information to acquire the first landing area image of the sequence in which the target is hit by the shells and the corresponding sequence first landing time The intelligent target reporting module includes an estimation module and a calculation module. The estimation module estimates the second landing time of N shells according to the ejection data of the shells fired by N artillery pieces, the distances from the muzzles of N artillery pieces to the target and the environmental data. ; The calculation module calculates according to the following formula : ， First landing time Corresponding first landing area image Inferred to be An image of the landing area of ​​a shell fired by a cannon, wherein N is a positive integer greater than or equal to 2.

2. The target reporting system based on concentrated fire and direct aiming weapons according to claim 1 is characterized in that The image processing module includes a segmentation unit, a first calculation unit, a second calculation unit and an extraction unit, wherein the segmentation unit divides a frame of image acquired by the image sensor into Regions, , , where K is the number of pixels in a row of the pixel window, J is the number of pixels in a column of the pixel window, C is the number of pixels in a row of a frame image, and D is the number of pixels in a column of a frame image. represents a floor function; the first calculation unit calculates the first value of the pixel window at the ath row and the bth column according to the following formula: ， In the formula, , The center pixel of the pixel window at row a and column b The value of Pixel , a=1,…,A, b=1,…,B; The second calculation unit calculates the second value of the pixel window at the ath row and the bth column according to the following formula: ； Extraction unit comparison and ,when When , the pixel value in the pixel window of the ath row and the bth column is set to 1, otherwise it is set to 0, so as to obtain the first landing area image of the target hit by the shell from a frame of image obtained by the image sensor.

3. The target reporting system based on concentrated fire and direct aiming weapons according to claim 2 is characterized in that: The sensor array includes at least N vibration sensors and N velocity sensors, the N vibration sensors respectively acquire the ejection time of the shells fired by the N artillery pieces, and the N velocity sensors respectively acquire the ejection speed of the shells fired by the N artillery pieces.

4. The target reporting system based on concentrated fire and direct aiming weapons according to claim 3 is characterized in that: The first data processor is used to process the ejection data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data, specifically including: S4-1: Convert the ejection data of the shells fired by N artillery pieces, the distances from the muzzles of N artillery pieces to the targets, and the environmental data into binary numbers to generate a binary string, and divide the binary string into multiple groups, each of which includes 2 M bit code, M is greater than or equal to 3; S4-2: 2 M The bit codes are arranged in reverse order to obtain the first-order digital signal, and the first-order digital signal is divided into 2 M-1 group, and then input to the first level of M-level modulation iteration; the i-th level modulation iteration includes 2 M-i The i-th modulation butterfly unit includes 2 i input terminals and 2 i Output terminals; S4-3: The outputs of the two i-1-shaped modulation butterfly units of the i-1-th modulation iteration are used as the inputs of the i-th shaped modulation butterfly unit of the i-th modulation iteration.

5. The target reporting system based on concentrated fire and direct aiming weapons according to claim 4 is characterized in that: 2 i-1 modulation butterfly units 2 i-1 modulation butterfly units i-1 The outputs are respectively related to the rotation factors Multiply and then add the 2 of the first i-1 modulation butterfly unit of the two i-1 modulation butterfly units. i-1 The output is 2 of the i-th modulation butterfly unit i-1 outputs; 2 i-1 modulation butterfly units; 2 outputs of the second i-1 modulation butterfly unit i-1 The outputs are respectively related to the rotation factors The outputs of the first i-1-shaped modulation butterfly unit are added to obtain the other two outputs of the i-th-shaped modulation butterfly unit. i-1 outputs.

6. A method for reporting targets based on concentrated fire and direct aiming weapons, characterized in that: The steps include: Step 1: The distances from the muzzles of N guns to the target and the firing data of the shells fired by the N guns are respectively acquired through the sensor array of the data control device, and the environmental data is acquired through the data acquisition module of the data control device; Step 2: The first data processor of the data control device processes the firing data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data, and then sends them to the recording device through the first communication module of the data control device; Step 3: receiving data sent by the data control device through the second communication module of the recording device; Step 4: acquiring image information of the artillery shells fired by the N artillery pieces hitting the target through the image sensor of the recording device, and transmitting the image information to the second data processor of the recording device; Step 5: Preprocess the image information through the image processing module of the second data processor to obtain the first landing area image of the sequence where the target is hit by the shell and the corresponding sequence first landing time ; Step 6: The estimation module of the intelligent target reporting module of the second data processor estimates the second landing time of the shells fired by the N artillery pieces according to the ejection data of the shells fired by the N artillery pieces, the distances from the muzzles of the N artillery pieces to the targets, and the environmental data. ; Step 7: The calculation module of the intelligent target reporting module of the second data processor calculates according to the following formula : ， First landing time Corresponding first landing area image Inferred to be An image of the landing area of ​​a shell fired by a cannon, wherein N is a positive integer greater than or equal to 2.

7. The method for reporting a target based on concentrated fire and direct aiming weapons according to claim 6 is characterized in that , further comprising the following steps: S5-1: The segmentation unit of the image processing module segments a frame of image acquired by the image sensor into Regions, , , where K is the number of pixels in a row of the pixel window, J is the number of pixels in a column of the pixel window, C is the number of pixels in a row of a frame image, and D is the number of pixels in a column of a frame image. represents the floor function; S5-2: The first calculation unit of the image processing module calculates the first value of the pixel window at the ath row and the bth column according to the following formula: , In the formula, , The center pixel of the pixel window at row a and column b The value of Pixel , a=1,…,A, b=1,…,B; S5-3: The second value of the pixel window at the ath row and the bth column is calculated by the second calculation unit of the image processing module according to the following formula: ； S5-4: Extraction unit comparison by image processing module and ,when When , the pixel value in the pixel window of the ath row and the bth column is set to 1, otherwise it is set to 0, so as to obtain the first landing area image of the target hit by the shell from a frame of image obtained by the image sensor.

8. The method for reporting targets based on concentrated fire and direct aiming weapons according to claim 7 is characterized in that: The sensor array includes at least N vibration sensors and N speed sensors. The N vibration sensors respectively obtain the firing time of the shells fired by the N artillery pieces; and the N speed sensors respectively obtain the firing speed of the shells fired by the N artillery pieces.

9. The method for reporting targets based on concentrated fire and direct aiming weapons according to claim 8, characterized in that: Processing the firing data of the N artillery shells fired by the first data processor, the distance to the target and the environmental data specifically includes: S4-1: Convert the firing data of the shells fired by N artillery pieces, the distances from the muzzles of N artillery pieces to the targets, and the environmental data into binary digits, thereby generating a binary string, and divide the binary string into multiple groups, each of which includes 2 M bit code, M is greater than or equal to 3; S4-2: 2 M The bit codes are arranged in reverse order to obtain the first-order digital signal, and the first-order digital signal is divided into 2 M-1 group, and then input to the first level of M-level modulation iteration; the i-th level modulation iteration includes 2 M-i The i-th modulation butterfly unit includes 2 i input terminals and 2 i Output terminals; S4-3: The outputs of the two i-1-shaped modulation butterfly units of the i-1-th modulation iteration are used as the inputs of the i-th shaped modulation butterfly unit of the i-th modulation iteration.

10. The method for reporting targets based on concentrated fire and direct aiming weapons according to claim 9, characterized in that: 2 i-1 modulation butterfly units 2 i-1 modulation butterfly units i-1 The outputs are respectively related to the rotation factors Multiply and then add the 2 of the first i-1 modulation butterfly unit of the two i-1 modulation butterfly units. i-1 The output is 2 of the i-th modulation butterfly unit i-1 outputs; 2 i-1 modulation butterfly units; 2 outputs of the second i-1 modulation butterfly unit i-1 The outputs are respectively related to the rotation factors The output of the first i-1 modulation butterfly unit of the i-1 modulation butterfly unit is added to obtain the other two i-1 modulation butterfly units. i-1 outputs.

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