JPS62157967A - Method of processing fourier transformation data - Google Patents

Abstract

PURPOSE:To shorten time for operation by making operation only on data of positive frequency from a median and diverting negative frequency data linear symmetric or point symmetric to the arithmetic value of the positive frequency data. CONSTITUTION:Frequency data F1 and F2 are stored in RAM 11 and 12 through a central processing unit 10 and each of frequency data F1, F2 is sent to a multiplier 15, a divider 16, two complementers 17 and an adder 18 and arithmetic data obtained are stored in a RAM 13. Arithmetic data to be put in the RAM 13 are obtained by making specified arithmetic on all data stored in the RAM 11 and 12. Real part frequency data are linear symmetric basing on the median and imaginary part frequency data are point symmetric in reference to the median. Observing this, operation is made on only either of positive or negative frequency data, and actually obtained arithmetic data are diverted to other positive or negative frequency data.

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a method for processing Fourier transformed data, and more specifically, to obtain a cross power spectrum and a transfer function based on frequency data consisting of complex numbers obtained by Fourier transforming sampling data of two input signals. It relates to data processing methods applied to [Technical Background of the Invention] A cross power spectrum and a transfer function are obtained by first performing Fourier transform on two input signals to obtain two types of frequency data, and then multiplying or dividing these data. This Fourier transform (F F T) is usually
This is performed on 2° sampling data, and since the frequency data consists of complex numbers, it includes a real part and an imaginary part. Therefore, the number of data obtained by FFT is twice the number of sampling data (number of inputs), and it takes several tens of times more time to multiply or divide all the data than addition and subtraction, and improvements in this regard are desired. It was rare. [Purpose of the Invention] This invention was made in view of the above-mentioned conventional circumstances, and its purpose is to obtain frequency data consisting of complex numbers including real and imaginary parts when determining a cross power spectrum or a transfer function. An object of the present invention is to provide a method for processing Fourier transform data that requires calculations in approximately half the time required by conventional methods. [Summary of the invention] When a certain input signal is Fourier transformed, as mentioned above,
Frequency data consisting of complex numbers including a real part and an imaginary part is obtained. Now, if this data is plotted along the frequency axis, the real part frequency data will generally have a waveform as shown in Figure 6(a), while the imaginary part frequency data will have a waveform as shown in Figure 6(b), for example. The waveform will be as shown in . That is, as is clear from this waveform diagram, the center is DC co
H7) results in positive and negative frequencies, but in that case, the real part frequency data becomes line symmetrical with respect to the median value (OHz), and the imaginary part frequency data becomes linearly symmetrical with respect to the median value (OHz). It becomes a 180 degree rotationally symmetrical shape (point symmetrical shape). Such frequency data retains its properties as long as it is frequency data even if addition, subtraction, multiplication, and division operations are performed. This invention makes use of such characteristics of frequency data, and for example, calculates only positive frequency data from OL (z, and for negative frequency data, converts the calculated value of the positive frequency data to a line symmetry or a point. This invention is designed to shorten the calculation time by symmetrical application. [Examples] This invention will be explained in detail below with reference to the embodiments shown in the accompanying drawings. To implement, three random access memories (RAMs) 11, 12 are used as shown in FIG.
．． 13 is prepared. In this case, assuming that the number of sampling data of the human signal is 2',...512, each RAM 1.1, 1.2, 13 has 512 storage areas for storing real part frequency data and 512 storage areas for storing imaginary part frequency data. Similarly, 512 storage areas for frequency data storage are provided. That is, FIG. 2(a) shows the RAM II memory address format, and the Fourier-transformed first
The input signal frequency data of F, = An + 1 Bn (n = 1
~512), A1 to A5□2 are stored in the real part storage area of this RAMII, and B1 to A5□2 are stored in the imaginary part storage area.
F1st□ is stored. FIG. 2(b) shows the memory address format of the RAM 12, in which the frequency data of the second input signal that has been Fourier transformed is F2=Cn
11Dn (n=1-512), this RAM12
C1 to C9□2 are stored in the real part storage area, and D1 to D51□ are stored in the imaginary part storage area. Furthermore, FIG. 2(c) shows the memory address format of the RAM 13, in which the real part and imaginary part of the calculation data F, X F, or F1/F are respectively stored. . Incidentally, the real part of F+XF2, which is the multiplication value when calculating the cross power spectrum, is (AnCn-
BnDn), the imaginary part is (BnCrx+AnDn),
The real part of F1/F2, which is the division value when determining the transfer function, is (AnCn+BnDn)/(Cn2+Dn2), and the imaginary part is (BnCn-AnDn)/(Cn2+Dn'). RAM II and 12 have a central processing unit (CPU) 10
The above frequency data F1 and F2 are stored through the frequency data F1. F, are sent to the multiplier 15, the complementer 17 of the divider 16.2, and the adder/subtractor '18 according to the program written in the read-only memory (ROM) 14, and the resulting operation data is The data is stored in the RAM 13. The calculation data to be stored in the RAM 13 is obtained by performing a predetermined calculation on all the data stored in the RAMs 1l and 12, but in this invention, as mentioned above, the real local wave number data is the median value. (O
Hz), and the imaginary part frequency data is point symmetrical with respect to the median value, and we perform calculations only on either the positive or negative frequency axis data, For the other positive or negative frequency axis data, by reusing the actually obtained calculation data,
The calculation time is greatly reduced. That is, according to the present invention, for example, there are three subroutines I, n, and m, and when obtaining a cross power spectrum, subroutines I and ① are executed as shown in FIG. 3(a), while the transfer function is If you want to find it, use Figure 3 (b).
■ Like a subroutine. ■Execute. First, subroutine I will be explained with reference to flowchart 1- shown in FIG. 4(a). In this subroutine 11, if the address of memory address format 1- is set as variable P, it is first set to 1. Then, the real part frequency data Ap of address P of RAMII
and imaginary part frequency data Bp, and the real part frequency data Cp and imaginary part frequency data Dp at address P of the RAM 12 are sent to the multiplier 15, Apxcp 1BpXDp; Bp,
Multiply values xcp and ApXDp are obtained, and each of these multiplier values is transferred to the adder/subtractor 18 to obtain real part calculation data x,
p, that is, (APXCp-BPXDp), and imaginary part operation data Yp, that is, (B pXCp+APXDI+) are calculated, and each of these operation data X P t YP is stored in RAM1.
Store it at address P of 3. This is P=(n/2)+1
(=2n7). That is, according to this example, in the memory address format of RAMII and ]2, address 2n7 is the median value (OHz) on the frequency axis.
For example, the storage area from address 1 to address 2n6 corresponds to the negative frequency, and the storage area from address 2n8 to address 51
For example, if addresses up to 2 correspond to positive frequencies, execute this subroutine I.

[, than this,
In the memory address format l- of the RAM 13, the above real part calculation data xp and imaginary part calculation data yp are stored in addresses 1 to 2n6 corresponding to the negative frequency and addresses 2n7 corresponding to the median value (OHz), respectively. That will happen. Further, in subroutine (2), as shown in FIG. 4(b), the address of the memory address format is set to variable P, which is first set to 1, similarly to the above-mentioned sub-tower I. Then, address P of RAM11 and RA
The real part frequency data A, C and the imaginary part frequency data B, D are respectively called from address P of M12, and these data are calculated according to a predetermined program in the multiplier 15, the adder/subtractor 18, and the divider 6. , real part calculation data X
p (in this case, (Ap xcp×BpXDp)/(C
p2+I)p2)) and imaginary part calculation data Yp (in this case, (BpXCp-A', pXDp)/(Cp2+Dp)
2)), and each of these calculation data X P r Y P
is stored at address P in the RAM 13. Same as <P=
By performing the operations up to (n/2)+1 (=2n7), the above calculation data Xp and Yp are stored in the storage areas from address 1 to address 2n6 and address 2n7 of the RAM 13, respectively, as in the case of subroutine I above. It will be remembered. Then, in subroutine (2), the calculation data stored, for example, from address 2 to address 2n6 in the RAM 13 is transferred and stored in the unstored storage area from address 2n8 to address 512 in a predetermined order. That is, as shown in the flowchart of FIG. 4(c), first, 2 is set as a variable indicating the address of the storage area.
First, let Q be 2 and R be n, in this case 512. Then, the real part calculation data X at address Q of RAM 13 is stored in the real part storage area at address P. That is, in this embodiment, data equal to the real part calculation data x2 at address 2 is stored as xsi□ in the real part storage area at address 512, and data equal to the real part calculation data x2 at address 3 is stored as xsi□.
Data equal to 3 is entered as X51° at address 511, and thereafter X4 is entered at address 510, x5 is entered at address 509, and so on. At the same time, RAM13
The imaginary part calculation data Y at address Q is called, and after the sign of this imaginary part calculation data Y is inverted by the 2's complementer 17 and becomes -Y,
The above real part calculation data X. Similarly, it is stored in the imaginary part storage area at address R. This is used as a] cycle, and for each cycle, 1 is added to the variable Q, and 1 is subtracted from the variable R,
Convert this to Q = n / 2 (2n6), i.e. 2n
Repeat 5 times. Therefore, by executing this subroutine (2), the real part storage area of the RAM 13, for example, from address 2n8 to address 512, which corresponds to the positive frequency, can be stored line-symmetrically with the real part calculation data at the negative frequency without actually performing calculations. In the same way, the imaginary part storage area from address 2n8 to address 512 stores point-symmetric imaginary part calculation data whose sign is inverted. According to this method, the calculation time is about half that of the conventional method of calculating all data. In the above example, the 2n7 address is set to the median value (Or(z)
, but this may also be a 2n6 address. However, in this case, in the first step of subroutine ■, variable Q is set to 1, while variable Rtt
Let it be n-1. In addition, the memory address format l- of RAM11.12.13 is arranged sequentially from address 1 to address 512, and the border is (
OHz), and the frequency axis is such that negative frequencies and positive frequencies increase in the left and right directions, but as shown in Figure 5, for example, address 1 is used as the reference for OH7, and the positive frequency For , the frequency axis is taken from address 1 to address 2n6, and for the other negative frequency, it is 51.
The frequency axis may be taken from address 2 to address 2n7. [Effects] As is clear from the description of the embodiments described above, according to the present invention, when determining a cross power spectrum or a transfer relationship based on frequency data consisting of complex numbers obtained by Fourier transforming two input signals, It is only necessary to perform calculations on positive or negative frequencies, and therefore, the calculation time can be approximately halved compared to the conventional method, and the effect is remarkable.

[Brief explanation of drawings]

FIG. 1 is a schematic block diagram for implementing the data processing method according to the present invention, and FIGS.
An explanatory diagram for explaining the memory address format set in each RAM shown in the figure, FIG. 3(a),
4(b) is a flowchart showing the main routine for determining the cross power spectrum and transfer function according to the present invention, FIGS. 4(a), 4(b),
(C) is a flowchart of subroutines t, n, and m, respectively. FIG. 5 is an explanatory diagram showing a memory address format different from that in FIG. FIG. 3 is a waveform diagram showing partial frequency data and imaginary part frequency data. In the figure, 10 is the CPU, 11 to 13 are the RAM, and 14 is the RO.
M, 15 is a multiplier, 16 is a divider, 17 is a two's complementer,
18 is an adder/subtracter.

Claims (1)

[Claims] Data applied to find a cross power spectrum or a transfer function based on frequency data consisting of complex numbers obtained by Fourier transforming 2^n sampling data for each of two input signals. In this processing method, when storing the real part and imaginary part of complex number operation data obtained by multiplying or dividing each of the above frequency data in 2^n storage areas, the above operation is performed in a positive or negative manner. The calculation is performed only on one of the frequency axes, and the real and imaginary parts are stored in each storage area corresponding to that frequency axis, and the above calculation is not performed on the other positive or negative frequency axis, and the real part is , the same data as the real part data stored in the storage area is stored in the storage area corresponding to the other frequency axis in a predetermined order, and the imaginary part is stored in the storage area. 1. A method for processing Fourier transform data, comprising inverting the sign of imaginary part data and storing the imaginary part data in a predetermined order in a storage area corresponding to the other frequency axis.