Arithmetic device, radio wave interferometer, and arithmetic operation method

Abstract

According to the present invention, processing for extracting 2N-1 pieces of first data (at) which are contiguous in time-series order and generating a first N row x N column matrix (Am) constituted so that first data from the n-th to the (n + N - 1)th of the extracted 2N-1 pieces of first data (at) are aligned in time-series order as row data of the n-th row is executed once each time the 2N-1 pieces of first data (at) to be extracted is shifted N pieces in time-series order, for a total of M times. M pieces of first matrices (Am) are added to generate a first addition matrix (alpha). Processing for extracting N pieces of second data (b* t) which are contiguous in time-series order and generating an N row x 1 column second matrix (B* m) constituted so that the extracted N pieces of second data (b* t) are aligned in time-series order as column data is executed once each time the N pieces of second data (b* t) are shifted N pieces in time-series order, for a total of M times. M pieces of second matrices (B* m) are added to generate a second addition matrix (beta).

Description

Calculation device, radio wave interferometer, and calculation method

[0001] The present invention relates to a computing device, a radio interferometer, and a computing method.

[0002] A radio interferometer is a type of radio telescope (see, for example, Non-Patent Document 1), and is a device that investigates the radiation distribution from a celestial body by performing cross-correlation analysis on signals received by two antennas.

[0003] Since the received signal is obtained as a function of time, the time series data obtained by sampling one of the received signals at regular time intervals is expressed as a ０ , a １ , a ２ , ..., and the other received signal is sampled at the same timing to obtain time series data as b ０ , b １ , b ２ , ..., the cross-correlation function is defined as follows: Here, N is a natural number equal to or greater than 2. Since j takes values ​​from 0 to N-1, the cross-correlation vector (c ０ , c １ , c ２ , ..., c Ｎ－１ ) is obtained. * indicates the complex conjugate.

[0004] In radio interferometry, the time when the signals from the celestial body are received by the two antennas is different, so the time series data b ｉ is the time series data a ｉ (where i is any natural number). ｊ indicates the time difference (delay time) between when a signal emitted from a celestial body is received by two antennas.

[0005] Usually, each cross-correlation function c of the cross-correlation vector ｊ Since the cross-correlation vector consists of N elements, it takes N multiplications to calculate the cross-correlation vector. ２ times multiplication is required.

[0006] Furthermore, in radio interferometry, the cross-correlation vector is N２ The data to be output is not output after every multiplication, but after being averaged or added M times in the time direction. ｊ Then, γ ｊ Each time M×N is output ２ times.

[0007] Hidehiko Agata et al., "Dictionary of Astronomy," [online], published September 2017, Astronomical Society of Japan, [searched June 12, 2024], Internet: <https: / / astro-dic.jp / radio-interferometer / >

[0008] In radio interferometry, the cross-correlation vector (c ０ , c １ , c ２ , ..., c Ｎ－１ ) is Fourier transformed to obtain spectroscopic data (cross-correlation spectrum). To investigate the motion of celestial bodies in detail, it is necessary to increase the frequency resolution of the cross-correlation spectrum, while also requiring a wider frequency band. To simultaneously satisfy these requirements, it is necessary to dramatically increase the number of channels N in the Fourier transform. When the number of channels N is increased, the amount of calculation required to obtain the cross-correlation vector increases by N. ２ increases in proportion to

[0009] The present invention has been made in light of the above-mentioned circumstances, and an object of the present invention is to provide a calculation device, a radio wave interferometer, and a calculation method that can reduce the amount of calculation.

[0010] In order to achieve the above object, a calculation device according to a first aspect of the present invention includes: a first matrix generation unit that extracts 2N-1 pieces of first data that are consecutive in chronological order from first data obtained by sampling a first input signal at regular time intervals, and generates a first matrix with N rows and N columns such that the nth to (n+N-1)th first data of the extracted 2N-1 pieces of first data are arranged in chronological order as row data in the nth row, M times in total, where M and N are natural numbers of 2 or more and n is an integer between 0 and N-1; a first adder that adds up the M first matrices generated by the first matrix generation unit; The digital signal processing device includes a second matrix generation unit that extracts N pieces of second data that are consecutive in chronological order from second data obtained by sampling a second input signal at the same timing as the first input signal, and generates a second matrix with N rows and 1 column configured so that the extracted N pieces of second data are arranged in chronological order as column data, the process being performed M times in total, once each time the extracted N pieces of second data are shifted by N pieces in chronological order; and a second addition unit that adds up the M pieces of second matrices generated by the second matrix generation unit to generate a second addition matrix.

[0011] The digital signal processing device may further include a cross-correlation calculation unit that generates a cross-correlation vector having elements that are cross-correlation functions between the first data and the second data by multiplying the first summation matrix and the second summation matrix.

[0012] The apparatus may further include a fast Fourier transform unit that performs a fast Fourier transform on the cross-correlation vector calculated by the cross-correlation calculation unit to obtain a cross-correlation spectrum.

[0013] A radio interferometer according to a second aspect of the present invention comprises: the arithmetic device according to the first aspect of the present invention; a first antenna that inputs a signal corresponding to a received radio wave as a first input signal to the arithmetic device; and a second antenna that inputs a signal corresponding to a radio wave received at a position different from that of the first antenna as a second input signal to the arithmetic device.

[0014] A computing method according to a third aspect of the present invention is a computing method executed by a computing device, comprising: a first matrix generation step of extracting 2N-1 pieces of first data that are consecutive in chronological order from first data obtained by sampling a first input signal at regular time intervals, and generating a first matrix with N rows and N columns such that the nth to (n+N-1th) first data pieces of the extracted 2N-1 pieces of first data are arranged in chronological order as row data in the nth row, the first matrix being executed M times, once every time the extracted 2N-1 pieces of first data are shifted by N pieces in chronological order; and a first addition step of generating a first sum matrix by adding up the M first matrices generated in the first matrix generation step. The method includes a second matrix generation step of extracting N pieces of second data that are consecutive in chronological order from second data obtained by sampling a second input signal at the same timing as the first input signal, and generating a second matrix with N rows and 1 column configured so that the extracted N pieces of second data are arranged in chronological order as column data, the process being performed M times in total, once each time the extracted N pieces of second data are shifted N pieces in chronological order; and a second addition step of adding up the M pieces of second matrices generated in the second matrix generation step to generate a second addition matrix.

[0015] The calculation device, radio interferometer, and calculation method according to the present invention can reduce the amount of calculation.

[0016] 1 is a block diagram showing the configuration of a radio interferometer according to an embodiment of the present invention. FIG. 2 is a block diagram showing the configuration of the integrating circuit of FIG. 1. FIG. 3 is a schematic diagram showing the processing of a first matrix generating unit of FIG. 2. FIG. 4 is a schematic diagram showing the processing of a second matrix generating unit of FIG. 2. FIG. 5 is a schematic diagram showing the flow of integration and cross-correlation calculations and the number of multiplications in the arithmetic device of FIG. 1. FIG. 6 is a flowchart showing the arithmetic processing executed by the arithmetic device of FIG. 1. FIG. 7 is a graph showing an example of a first input signal and a second input signal. FIG. 8 is a graph showing an example of a cross-correlation vector. FIG. 9 is a graph showing an example of a cross-correlation spectrum (cross spectrum). FIG. 10 is a graph showing the absolute value of a cross-correlation vector, the absolute value and phase of a cross-correlation spectrum obtained by a arithmetic device according to an embodiment (number of accumulations M=2). FIG. 11 is a graph showing the absolute value of a cross-correlation vector, the absolute value and phase of a cross-correlation spectrum obtained by a arithmetic device according to an embodiment (number of accumulations M=4). FIG. 12 is a graph showing the absolute value of a cross-correlation vector, the absolute value and phase of a cross-correlation spectrum obtained by a arithmetic device according to an embodiment (number of accumulations M=8). 1 is a graph showing the absolute values ​​of cross-correlation vectors and the absolute values ​​and phases of cross-correlation spectra obtained by a calculation device according to the present embodiment (number of accumulations M=16); FIG. 2 is a graph showing the absolute values ​​of cross-correlation vectors and the absolute values ​​and phases of cross-correlation spectra obtained by a calculation device according to the present embodiment (number of accumulations M=32); FIG. 3 is a graph showing the relationship between the number of accumulations and the signal-to-noise ratio; and FIG. 4 is a graph showing the absolute values ​​of cross-correlation vectors and the absolute values ​​and phases of cross-correlation spectra obtained by a conventional calculation device (number of accumulations M=8).

[0017] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In each drawing, the same or equivalent parts are denoted by the same reference numerals. In the following embodiments, expressions such as "have," "include," or "contain" also include the meaning of "consisting of" or "consisting of." In the present embodiments, N and M are natural numbers of 2 or more, n is an integer from 0 to N-1, and m is an integer from 0 to M-1.

[0018] 1, a radio wave interferometer 1 includes two antennas 1A and 1B and a computing device 100. The antennas 1A and 1B input signals corresponding to received radio waves to the computing device 100. The signal output from the antenna 1A as the first antenna is sampled at regular time intervals and converted from analog to digital to generate first digital received data a ｔ (a ０ , a １ , a ２ , ...) is input to the arithmetic unit 100. The signal output from the antenna 1B as the second antenna is the first input signal a ｔ The second digital received data b is sampled at the same timing as the first digital received data b and is analog-to-digital converted. ｔ (b ０ , b １ , b ２ , . . . ) are input to the arithmetic unit 100.

[0019] The sampling time interval is determined based on the frequency resolution of the desired fast Fourier transform. ｔ , b ｔ The data are sampled at the same timing. The sampling circuit and the analog-to-digital conversion circuit may be incorporated into the arithmetic unit 100.

[0020] [Calculation Device] As shown in FIG. 1, the calculation device 100 includes a complex transform circuit 2, an integration circuit 3, a cross-correlation calculation circuit 4 as a cross-correlation calculation section, and a fast Fourier transform circuit 5 as a fast Fourier transform section.

[0021] [Complex Number Transformation Circuit] The complex number transformation circuit 2 transforms the first digital received data a ｔ (a ０ , a １ , a ２ , ...) are input, and the data are converted into first complex data a ｔ Furthermore, the complex number conversion circuit 2 converts the second digital received data b ｔ (b ０ , b １ , b ２, ...), and converts the data into second complex data b ＊ ｔ Convert it to and output it.

[0022] [Integration Circuit] The integration circuit 3 receives the first complex data a ｔ The integration circuit 3 integrates the second complex number data b ＊ ｔ The calculation process for α and β will be described below.

[0023] As shown in FIG. 2, the integration circuit 3 includes a first matrix generation unit 10A, a first adder unit 11A, a second matrix generation unit 10B, and a second adder unit 11B.

[0024] [First Matrix Generation Unit] The first matrix generation unit 10A generates the first complex number data a ｔ (a ０ , a １ , a ２ , ...) is input to the first matrix generation unit 10A. ｔ The memory device 100 includes a buffer (not shown) for temporarily storing the data.

[0025] Here, for example, N=4 and M=4. As shown in FIG. ｔ As a ０ , a １ , a ２ , a ３ , a ４ , a ５ , a ６ , a ７ , a ８ , a ９ , a １０ , a １１ , a １２ , a １３ , a １４ , a １５ , a １６ , a １７ , a １８ are stored in the buffer. The first matrix generation unit 10A generates the first complex number data a ０ ~a １８The first complex data a ０ ~a ６ Furthermore, the first matrix generation unit 10A extracts the extracted first complex number data a ０ ~a ６ Based on this, a first matrix A with N rows and N columns, i.e., 4 rows and 4 columns, ０ Specifically, the first matrix generation unit 10A generates the first matrix data a ０ , a １ , a ２ , a ３ The row data in the second row is the second to fifth first complex data a １ , a ２ , a ３ , a ４ The row data in the third row is the third to sixth first complex data a ２ , a ３ , a ４ , a ５ and the fourth to seventh first complex data a ３ , a ４ , a ５ , a ６ The first matrix A is ０ Generate.

[0026] In this way, the first matrix generation unit 10A generates the first complex number data a ０ ~a １８ 2N-1 pieces of first complex data a ０ ~a ６ The extracted 2N-1 first complex data a ０ ~a ６ Among them, the first complex data a from nth to n+N-1th ｎ ~a ｎ＋Ｎ－１ The first matrix A of N rows and N columns is arranged in chronological order as the row data of the nth row. ０ Execute the process to generate

[0027] Furthermore, the first matrix generation unit 10A generates the first complex number data a ｎ The position where the first complex number data a is extracted is shifted by N. ０ ~a １８2N-1 pieces of first complex data a ４ ~a １０ The extracted 2N-1 first complex data a ４ ~a １０ Among them, the first complex data a from nth to n+N-1th ｎ ~a ｎ＋Ｎ－１ The first matrix A of N rows and N columns is arranged in chronological order as the row data of the nth row. １ Execute the process to generate

[0028] Furthermore, the first matrix generation unit 10A generates the first complex number data a ｎ The position where the first complex number data a is extracted is shifted by N. ０ ~a １８ 2N-1 pieces of first complex data a ８ ~a １４ The extracted 2N-1 first complex data a ８ ~a １４ Among them, the first complex data a from nth to n+N-1th ｎ ~a ｎ＋Ｎ－１ The first matrix A of N rows and N columns is arranged in chronological order as the row data of the nth row. ２ Execute the process to generate

[0029] Furthermore, the first matrix generation unit 10A generates the first complex number data a ｎ The position where the first complex number data a is extracted is shifted by N. ０ ~a １８ 2N-1 pieces of first complex data a １２ ~a １８ The extracted 2N-1 first complex data a １２ ~a １８ Among them, the first complex data a from nth to n+N-1th ｎ ~a ｎ＋Ｎ－１ The first matrix A of N rows and N columns is arranged in chronological order as the row data of the nth row. ３ Execute the process to generate

[0030] In this way, the first matrix generation unit 10A generates the first complex number data aｔ 2N-1 pieces of first complex data a ｔ The extracted 2N-1 complex data a ｔ A first matrix A having N rows and N columns is configured so that the first complex data from the nth to the n+N-1th are arranged in chronological order as row data in the nth row. ｍ (m=0 to M−1) is extracted from the 2N−1 pieces of first complex number data a ｔ is executed once for every N shifts in chronological order, for a total of M times.

[0031] [First Addition Unit] The first addition unit 11A adds M first matrices A ｍ (m=0 to M−1) to generate the first addition matrix α. In the example shown in FIG. ０ , A １ , A ２ , A ３ The matrix to which is added becomes the first addition matrix α.

[0032] [Second Matrix Generation Unit] Returning to FIG. 2, the second matrix generation unit 10B generates the second complex number data b ＊ ｔ (b ＊ ０ , b ＊ １ , b ＊ ２ , ...) is input to the second matrix generation unit 10B. ＊ ｔ The memory device 100 includes a buffer (not shown) for temporarily storing the data.

[0033] Here, as in the example shown in Fig. 3, for example, N = 4 and M = 4. As shown in Fig. 4, the second complex number data b ＊ ｔ As, b ＊ ０ , b ＊ １ , b ＊ ２ , b ＊ ３ , b ＊ ４ , b ＊ ５ , b＊ ６ , b ＊ ７ , b ＊ ８ , b ＊ ９ , b ＊ １０ , b ＊ １１ , b ＊ １２ , b ＊ １３ , b ＊ １４ , b ＊ １５ The second matrix generation unit 10B generates the second complex number data b ＊ ０ ~b ＊ １５ N pieces of second complex number data b ＊ ０ ~b ＊ ３ Furthermore, the second matrix generation unit 10B extracts the extracted N pieces of second complex number data b ＊ ０ ~b ＊ ３ The second matrix B has N rows and 1 column and is configured so that the data are arranged in chronological order as column data. ＊ ０ Generate.

[0034] Furthermore, the second matrix generation unit 10B generates the second complex number data b ＊ ｎ The position where the second complex number data b is extracted is shifted by N. ＊ ０ ~b ＊ １５ N pieces of second complex number data b ＊ ４ ~b ＊ ７ The extracted N pieces of second complex data b ＊ ４ ~b ＊ ７ The second matrix B has N rows and 1 column and is configured so that the data are arranged in chronological order as column data. ＊ １Furthermore, the second matrix generation unit 10B generates the second complex number data b ＊ ｎ The position where the second complex number data b is extracted is shifted by N. ＊ ０ ~b ＊ １５ N pieces of second complex number data b ＊ ８ ~b ＊ １１ The extracted N pieces of second complex data b ＊ ８ ~b ＊ １１ The second matrix B has N rows and 1 column and is configured so that the data are arranged in chronological order as column data. ＊ ２ Furthermore, the second matrix generation unit 10B generates the second complex number data b ＊ ｎ The position where the second complex number data b is extracted is shifted by N. ＊ ０ ~b ＊ １５ N pieces of second complex number data b ＊ １２ ~b ＊ １５ The extracted N pieces of second complex data b ＊ １２ ~b ＊ １５ The second matrix B has N rows and 1 column and is configured so that the data are arranged in chronological order as column data. ＊ ３ Generate.

[0035] In this way, the second matrix generation unit 10B generates the second complex number data b ＊ ｔ N pieces of second complex number data b ＊ ｔ The extracted N pieces of second complex data b ＊ ｔ The second matrix B has N rows and 1 column and is configured so that the data are arranged in chronological order as column data. ＊ ｍ(m=0 to M−1) is extracted as N pieces of second complex number data b ＊ ｔ is executed once every N shifts in chronological order, a total of M times. ＊ ０ , b ＊ １ , b ＊ ２ , b ＊ ３ The second matrix B ＊ ０ and b ＊ ４ , b ＊ ５ , b ＊ ６ , b ＊ ７ The second matrix B ＊ １ and b ＊ ８ , b ＊ ９ , b ＊ １０ , b ＊ １１ The second matrix B ＊ ２ and b ＊ １２ , b ＊ １３ , b ＊ １４ , b ＊ １５ The second matrix B ＊ ３ and are generated.

[0036] [Second Addition Unit] The second addition unit 11B adds M second matrices B ＊ ｍ (m=0 to M−1) to generate the second addition matrix β. In the example shown in FIG. ＊ ０ and the second matrix B ＊ １ and the second matrix B ＊ ２ and the second matrix B ＊ ３ and are added together to generate a second addition matrix β.

[0037] [Cross-correlation Calculation Circuit] As shown in FIG. 1, the cross-correlation calculation circuit 4 multiplies the first addition matrix α by the second addition matrix β to obtain the first complex data a ｔ and the second complex data b ＊ ｔ Generate a cross-correlation vector γ with

[0038] As described above, the integrating circuit 3 receives the first complex data a ｔ The first matrix A based on ｍ (m=0 to M−1) to form a first summation matrix α, and a second complex number data b ＊ ｔ The second matrix B based on ＊ ｍ (m=0 to M−1) to generate a second addition matrix β, and the cross-correlation calculation circuit 4 outputs the multiplication result γ of the first addition matrix α and the second addition matrix β.

[0039] The product of the first addition matrix α and the second addition matrix β is as follows: γ = αβ = (A ０ +A １ +A ２ +...+A Ｎ－１ ) (B ＊ ０ +B ＊ １ +B ＊ ２ +...+B ＊ Ｎ－１ ) = A ０ B ＊ ０ +A １ B ＊ １ +A ２ B ＊ ２ +...+A Ｎ－１ B ＊ Ｎ－１ + (A ０ B ＊ １ +A ０ B ＊ ２ + ...) In this way, αβ contains A, which has cross-correlation functions as elements. ｍ B ＊ ｍ A component that is not ０ B＊ １ +A ０ B ＊ ２ +...) is included. However, A ０ and B ＊ ０ While it is correlated with ０ and B ＊ １ Matrices with mismatched subscript signs, such as γ, are not correlated and can be considered to have a value of 0. Therefore, γ is calculated by multiplying the first complex data a ｔ and the second complex data b ＊ ｔ It can be defined as a vector whose elements are the cross-correlation function between

[0040] As shown in FIG. 5, γ is calculated by the above formula, ０ B ＊ ０ And, A １ B ＊ １ And, A ２ B ＊ ２ However, the integrating circuit 3 of the arithmetic device 100 according to this embodiment first calculates A ０ +A １ +A ２ +...+A Ｎ－１ , i.e., the first matrix A ｍ (m=0 to M−1) is added to obtain the first addition matrix α.

[0041] Furthermore, the integrator circuit 3 ＊ ０ +B ＊ １ +B ＊ ２ +...+B ＊ Ｎ－１ , i.e., the second matrix B ＊ ｍ (m=0 to M−1) is added to obtain the second addition matrix β.

[0042] Furthermore, the cross-correlation calculation circuit 4 calculates αβ to obtain γ. In this way, the number of multiplications until γ is calculated is reduced to M×N ２ From the first time, N ２ The number of times can be reduced to just 1. Multiplication requires a much larger number of digital operations than addition, so reducing the number of multiplications can significantly reduce the number of digital operations required to calculate γ. The larger M is, the greater the effect of reducing the number of multiplications. Note that the calculation process in which integration is performed first and then a cross-correlation calculation is performed, as in this embodiment, is referred to as a "pre-integration type," while the calculation process in which cross-correlation calculation is performed first and then integration is referred to as a "post-integration type," as in the conventional case.

[0043] 1, the fast Fourier transform circuit 5 obtains a cross-correlation spectrum by performing a fast Fourier transform (FFT) on the cross-correlation vector γ calculated by the cross-correlation calculation circuit 4. The number of sampling points (number of channels) of the fast Fourier transform is N.

[0044] At least a portion of the hardware of the arithmetic device 100 can be configured with a digital signal processing circuit such as an FPGA (Field Programmable Gate Array). For example, the complex transform circuit 2, integrator circuit 3, cross-correlation calculation circuit 4, and fast Fourier transform circuit 5 can be configured with digital signal processing circuits. The complex transform circuit 2, integrator circuit 3, cross-correlation calculation circuit 4, and fast Fourier transform circuit 5 may be configured with multiple digital signal processing circuits. The complex transform circuit 2, integrator circuit 3, cross-correlation calculation circuit 4, and fast Fourier transform circuit 5 may each be configured with a separate digital signal processing circuit.

[0045] Furthermore, at least a portion of the hardware of the arithmetic device 100 may be implemented by a computer including a CPU (Central Processing Unit) and memory. When the CPU executes a program stored in the memory, at least some of the functions performed by the complex transform circuit 2, the integrator circuit 3, the cross-correlation calculation circuit 4, and the fast Fourier transform circuit 5 may be implemented by an information processing device in which software and hardware (computer) work together. For example, the complex transform circuit 2, the integrator circuit 3, and the cross-correlation calculation circuit 4 may be configured as FPGAs, and the fast Fourier transform may be performed by the information processing device. In this way, by implementing at least some of the functions of the arithmetic device 100 by a computer, it is possible to reduce the manufacturing costs of the arithmetic device 100.

[0046] Next, the operation of the arithmetic device 100 according to this embodiment, that is, the arithmetic method executed by the arithmetic device 100, will be described.

[0047] As shown in FIG. 6, first, the arithmetic unit 100 receives the first digital received data a ｔ and the second digital received data b input from the antenna 1B. ｔ The system waits for the input of the first digital received data a (Step S1; No). ｔ , second digital received data b ｔ When newly inputted (step S1; Yes), the calculation device 100 calculates 2N-1 pieces of first digital received data a that have not yet been used in the calculation. ｔ and N pieces of second digital received data b ｔ The first digital received data a is stored in the buffer, and it is determined whether it can be acquired (step S2). If it cannot be acquired (step S2; No), the calculation device 100 again ｔ , second digital received data b ｔ The system waits for input (Step S1; No).

[0048] On the other hand, if it is possible to acquire it (step S2; Yes), the complex number transformation circuit 2 acquires 2N-1 pieces of the first digital received data a that are not used in the calculation. ｔand N pieces of second digital received data b ｔ and the first complex data a ｔ and the second complex data b ＊ ｔ and are converted into complex numbers (step S3).

[0049] Next, as shown in FIG. 3, the first matrix generation unit 10A generates first complex data a as first data obtained by sampling the first input signal received by the antenna 1A at regular time intervals. ｔ 2N-1 pieces of first complex data a ｔ The extracted 2N-1 first complex data a ｔ Among them, the first complex data a from nth to n+N-1th ｔ The first matrix A of N rows and N columns is arranged in chronological order as the row data of the nth row. ｍ (m=0 to M−1) is extracted as 2N−1 pieces of first complex number data a ｔ is executed once for every N shifts in chronological order, a total of M times (step S4; first matrix generation step).

[0050] Next, as shown in FIG. 5, the first adder 11A adds the M first matrices A ｍ (m=0 to M−1) to generate a first addition matrix α (step S5; first addition step).

[0051] As shown in FIG. 4, the second matrix generation unit 10B generates second complex data b ＊ ｔ N pieces of second complex number data b ＊ ｔ The extracted N pieces of second complex data b ＊ ｔ The second matrix B has N rows and 1 column and is configured so that the data are arranged in chronological order as column data. ｍ (m=1 to M−1) is extracted as N pieces of second complex number data b ＊ ｔis executed once for every N shifts in chronological order, a total of M times (step S6; second matrix generation step).

[0052] Next, as shown in FIG. 5, the second adder 11B adds the M second matrices B ＊ ｍ (m=0 to M−1) to generate a second addition matrix β (step S7; second addition step).

[0053] Next, as shown in FIG. 5, the cross-correlation calculation circuit 4 multiplies the first addition matrix α by the second addition matrix β to obtain the first input signal (first complex number data) a ｔ and the second input signal (second complex data) b ＊ ｔ A cross-correlation vector γ is generated, the elements of which are the cross-correlation functions of the first input signal a and the second input signal a (step S8; cross-correlation calculation step). ｔ (see FIG. 7A) and the second input signal b ｔ (see FIG. 7A) and a cross-correlation vector (see FIG. 7B) indicating the time difference delay between the two signals.

[0054] Next, the fast Fourier transform circuit 5 performs a fast Fourier transform on the cross-correlation vector γ calculated by the cross-correlation calculation circuit 4 to obtain a cross-correlation spectrum (step S9; fast Fourier transform step). By executing this fast Fourier transform step, the cross-correlation spectrum (cross spectrum) shown in Fig. 7C is obtained. The cross spectrum is spectroscopic data indicating the frequency components included in the cross-correlation vector.

[0055] After step S9 is completed, the calculation device 100 again receives the first digital received data a ｔ , second digital received data b ｔ The system waits for input (Step S1; No).

[0056] 6, steps S4 and S6 may be performed simultaneously or in reverse order. Steps S5 and S7 may be performed after step S4 and step S6, respectively, and the order in which the two steps are performed may be simultaneously or in reverse order. ｔ and the second digital received data b ｔ If the data is already complex number data, the complex number conversion circuit 2 shown in Fig. 1 is not necessary. In this case, step S3 is omitted in the calculation process of Fig. 6.

[0057] [Numerical Simulation] Numerical simulation was performed on the operation of the arithmetic unit 100 of the radio interferometer 1 according to this embodiment.

[0058] 8, 9, 10, 11 and 12 show the results of a simulation of the arithmetic processing executed by the radio interferometer 1 according to this embodiment. In this simulation, the number of sampling points (number of channels) N, which is the unit for performing the fast Fourier transform, is set to 1000. Also, the first input signal a ｔ and the second input signal b ｔ The time difference delay is set to 3 clocks, and a signal is input that will produce 500 channels of line spectrum in the cross spectrum. However, in reality, signals from celestial bodies contain continuous wave components and line components. A random number is generated with an intensity 10 times stronger than the line component and added as a continuous wave component.

[0059] 8, 9, 10, 11, and 12 show the results of simulations where the number of integrations is M=2, 4, 8, 16, and 32, respectively. In FIGS. 8 to 12, the upper graphs show the absolute values ​​of the cross-correlation vector γ obtained by this simulation. The middle graphs show the absolute values ​​of the cross-spectrum obtained by performing a fast Fourier transform on the cross-correlation vector. The lower graphs show the phase.

[0060] As shown in Figures 8, 9, 10, 11, and 12, regardless of whether M = 2, 4, 8, 16, or 32, the absolute value of the cross-correlation vector γ calculated by the pre-integration arithmetic unit 100 according to this embodiment peaks at the 3-clock position, and the time difference delay is detected from the position of this peak (top graph). Furthermore, as shown in the middle graphs in Figures 8 to 12, the absolute value and phase of the cross spectrum also have nearly identical waveforms. As can be seen by comparing Figures 8, 9, 10, 11, and 12 with Figure 14, these waveforms are nearly identical to those obtained by conventional post-integration arithmetic processing (M = 8).

[0061] 13, the signal-to-noise ratio increases as the number of integrations M increases. Even if the number of integrations M increases, as described above, the arithmetic device 100 reduces the number of multiplications, and therefore, it is possible to suppress an increase in the amount of calculation.

[0062] As described above in detail, the arithmetic device 100 according to the present embodiment can reduce the number of multiplications to M×N ２ From N ２ This reduces the amount of calculation, and therefore the processing speed can be increased.

[0063] The frequency resolution Δν of the cross spectrum (spectroscopic data) can be expressed by the following equation: Δν = BW / N, where BW is the bandwidth (sampling rate) in the fast Fourier transform. In order to increase the frequency resolution (reduce Δν), it is necessary to increase the bandwidth BW or the number of sampling points N. Furthermore, in order to increase the frequency resolution and widen the frequency band to obtain a spectrum up to a high frequency band, it is necessary to increase the number of sampling points N. According to the arithmetic device 100 of this embodiment, even if the number of sampling points N is increased, the number of multiplications can be reduced and an increase in the amount of calculation can be suppressed, thereby making it possible to widen the frequency band while improving the frequency resolution.

[0064] Furthermore, according to this embodiment, the number of multiplication circuits that perform multiplication can be reduced, and therefore the arithmetic device 100 can be made lighter.

[0065] In the above embodiment, the explanation is mainly given assuming N = 4 and M = 4. However, N and M can be changed as appropriate, and N and M may be different. N is determined based on the required frequency resolution, and can be, for example, about 1000 or more, as described above.

[0066] Furthermore, the radio interferometer 1 according to this embodiment includes two antennas 1A and 1B. However, the radio interferometer 1 may include three or more antennas. For example, when three antennas 1A, 1B, and 1C are included, γ is calculated between antenna 1A and antenna 1B, γ is calculated between antenna 1B and antenna 1C, and γ is calculated between antenna 1C and antenna 1A. If the number of antennas is K, the number of multiplication operations is K(K-1) / 2 times that of the case where there are two antennas. Even in this case, the number of multiplications in the cross-correlation operation of the signals of the two antennas is MN. ２ From N ２ In this case, a calculation device 100 may be provided for each antenna combination, or the same calculation device 100 may be configured to perform calculations for all antenna combinations.

[0067] In the above embodiment, the arithmetic device 100 is described as performing integration processing, cross-correlation calculation processing, and fast Fourier transform on complex data. However, the arithmetic device 100 may be a device that performs integration processing, cross-correlation calculation processing, and fast Fourier transform on real data.

[0068] Although the present embodiment has been described with reference to a radio interferometer 1, the present invention is not limited to this. The present invention is applicable to any device that performs frequency conversion on a digital signal converted from an analog signal. In other words, the arithmetic device 100 according to the present embodiment is applicable to various fields as long as it performs cross-correlation calculations on two signals.

[0069] This invention allows various embodiments and modifications without departing from the broad spirit and scope of this invention. Furthermore, the above-described embodiments are intended to explain this invention and do not limit the scope of this invention. That is, the scope of this invention is defined by the claims, not the embodiments. Various modifications made within the scope of the claims and the meaning of the invention equivalent thereto are considered to be within the scope of this invention.

[0070] In addition, this application claims priority based on Japanese Patent Application No. 2024-98420 filed on June 19, 2024, and the specification, claims, and drawings of Japanese Patent Application No. 2024-98420 are incorporated herein by reference.

[0071] The present invention can be applied to the cross-correlation calculation of two time series data.

[0072] REFERENCE SIGNS LIST 1 Radio wave interferometer, 1A, 1B Antenna, 2 Complex number transformation circuit, 3 Integration circuit, 4 Cross-correlation calculation circuit (cross-correlation calculation unit), 5 Fast Fourier transform circuit (fast Fourier transform unit), 10A First matrix generation unit, 10B Second matrix generation unit, 11A First addition unit, 11B Second addition unit, 100 Calculation device

Claims

1. A first matrix generation unit that extracts 2N-1 pieces of first data that are consecutive in chronological order from first data obtained by sampling a first input signal at regular time intervals, and generates a first matrix with N rows and N columns configured so that the nth to (n+N-1)th first data of the extracted 2N-1 pieces of first data are arranged in chronological order as row data in the nth row, where M and N are natural numbers of 2 or more and n is an integer between 0 and N-1; and a first addition unit that adds up the M first matrices generated by the first matrix generation unit to generate a first sum matrix. a second matrix generation unit that extracts N pieces of second data that are consecutive in chronological order from second data obtained by sampling a second input signal at the same timing as the first input signal, and generates a second matrix with N rows and 1 column configured so that the extracted N pieces of second data are arranged in chronological order as column data, the process being performed M times, once each time the extracted N pieces of second data are shifted N pieces in chronological order; and a second addition unit that adds up the M second matrices generated by the second matrix generation unit to generate a second addition matrix.

2. The arithmetic device according to claim 1, further comprising a cross-correlation calculation unit that generates a cross-correlation vector having elements that are cross-correlation functions between the first data and the second data by multiplying the first addition matrix and the second addition matrix.

3. The calculation device according to claim 2, further comprising a fast Fourier transform unit that performs a fast Fourier transform on the cross-correlation vector calculated by the cross-correlation calculation unit to obtain a cross-correlation spectrum.

4. A radio wave interferometer comprising: a calculation device according to any one of claims 1 to 3; a first antenna that inputs a signal corresponding to a received radio wave as a first input signal to said calculation device; and a second antenna that inputs a signal corresponding to a radio wave received at a position different from that of said first antenna as a second input signal to said calculation device.

5. A calculation method executed by a calculation device, comprising: a first matrix generation step of extracting 2N-1 consecutive first data items in chronological order from first data obtained by sampling a first input signal at regular time intervals, and generating a first matrix with N rows and N columns such that the nth to (n+N-1)th first data items of the extracted 2N-1 first data items are arranged in chronological order as row data in the nth row, the first matrix being executed M times, once each time the extracted 2N-1 first data items are shifted by N positions in chronological order; and a first addition step of generating a first sum matrix by adding up the M first matrices generated in the first matrix generation step. a second matrix generation step of extracting N pieces of second data that are consecutive in chronological order from second data obtained by sampling a second input signal at the same timing as the first input signal, and generating a second matrix with N rows and 1 column configured so that the extracted N pieces of second data are arranged in chronological order as column data, the process being performed M times, once each time the extracted N pieces of second data are shifted N pieces in chronological order; and a second addition step of adding up the M pieces of second matrices generated in the second matrix generation step to generate a second addition matrix.

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