JPS6243774A - Data processor - Google Patents

Abstract

PURPOSE:To obtain a filter for an optional frequency characteristic by providing the first memory for storing a gain GK of every K-th harmonic in the Fourier transformation of an original data and the second memory for accumulating a cosine value and a sine value which divide one period into N equal parts and executing a specified operation based on a parameter K. CONSTITUTION:The titled processor is provided with the first memory for storing the gain GK at every K-th harmonic when an original data is Fourier transformed and the second memory for accumulating a cosine value cos(2pii/N), and a sine value sin(2pii/N) which divide one period into N equal parts, by setting a data number of the original data as (i)=0, 1, ..., N-1. Also, this processor is provided with a read-out control means for reading out cos(2pi.Ki/N) or sin(2pi.Ki/N) from the second memory by reading out and designating at every other (K-1) pieces the cosine value or the sine value divided into N equal parts, based on a data number (i) and a parameter K which is updated whenever the number (i) reaches N-1, and an operating means for inputting the output of the first and the second memories, executing the operation of an expression at every data number (i), and executing an inverse Fourier transformation. In this way, a filter to an optional frequency characteristic is obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to a data processing device that performs inverse Fourier transform.

[Technical background of the invention and its problems 1] Conventionally, the concept of applying a filter has been considered almost synonymous with performing convolution.

That is, when filter coefficient sequence 1 (l=-N to N) is given. A so-called stationary filter is obtained by calculating the following equation (1).

As a result of performing the Fourier transform, a frequency transfer characteristic F (Wk>) is given.

However, this type of convolution method has limitations. In other words, the filter processing for the frequency characteristics of the original data shown in FIG. However, in order to obtain a characteristic with such a steep change, it is necessary to increase \ in equation (1), which is considered unfeasible. .

[Object of the Invention] The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a data processing device that can perform an inverse Fourier transform with a relatively simple configuration. This makes it possible to realize a filter not only for changing characteristics but also for arbitrary frequency characteristics.

[Summary of the Invention] The outline of the present invention for achieving the above object is as follows: a first memory that stores the gain Gk for each harmonic when the original data is Fourier transformed; = o,
1.2. ..., where N-1 is the cosine value cos (2πi/N), which is obtained by dividing one period into N equal parts, and the sine value sin (2πi/
N), and the cosine or sine value divided into N equal parts is calculated based on the data number i and the parameter k that is updated every time this number i reaches N-1.
By specifying read every k-1> items, the second
cos(2π・ki/N) or sin(2
readout control means for reading out π-k i/N);
．． Input the output of the second memory and calculate Qi = ΣGl<-cos(2π・ki/N> or Qi'=ΣkGk・sin(2π−ki/N) for each data number i. and arithmetic means for performing inverse Fourier transform.

[Embodiments of the invention] First, the principle of the present invention will be explained.

The general formula for inverse Fourier transform is shown in equations (3) and (4) below. Here, Gk is the gain of the first harmonic when the original data is Fourier transformed, and i is the data number of the original data. r=o, 1. ..., N-1. Further, N is the total number of original data.

By the way, the cosine value cos(2π・2i/
N> is the second harmonic, and is generally cos(2π・ki/
N> is the first harmonic. Note that this also applies to the sine value.

Here, the relationship between the fundamental frequency of cosine cos(2πi/N> and the second harmonic C03(2π・2i/N) will be explained with reference to FIG. 1. In the same figure, the fundamental frequency cos(2πi/N)
/N) Each point above indicates a cosine value plotted by dividing one period into N equal parts. And the second harmonic c in the same figure
Each point on os(2π・2i/N> is the fundamental frequency co
The relationship is such that every other cosine value on s(2πi/N> is taken out.

The above relationship also applies to the 3rd harmonic, 4th harmonic, etc.
Generally, the cosine value of the harmonic is the cosine value of the fundamental frequency (k-
1> It is constructed by taking out every other piece. This also holds true for the relationship between the sine fundamental frequency sin(2xi/N) and the sine harmonic sin(2w-ki/N).

Therefore, in the present invention, when performing inverse Fourier transform on data that requires Fourier transform, the gain Gk for each harmonic when Fourier transform is performed on the original data is stored in the first memory, and one cycle is divided into N equal parts. Cosine value C03 (2yr i /
N) and a sine value sin(2xi/N) are stored in the second memory.

When multiplying the gain Gk by the cosine value or sine value of the fundamental frequency, the second memory sequentially outputs the cosine value and sine value corresponding to the data number i, and the cosine value or sine value of the harmonic is output in sequence. When multiplying sine values, control is performed so that every (k-1) cosine value or sine value in the second memory is read out. And this first one. Based on the output of the second memory, Equation (3) or Equation (4) is calculated to perform inverse Fourier transform.

Here, a filter creation device and a filtering device to which the present invention is applied will be briefly described.

FIG. 2(a) shows the original data series Di, and FIG. 2(b) shows the gain characteristics for each frequency when the original data series Di is Fourier transformed.

By storing all of this gain Gk in the first memory and performing the processing described above, inverse Fourier transform can be performed, which is significant in itself, but the device of the present invention also realizes a filter. It is also possible to do so. That is, when it is desired to remove the frequency gain in the shaded area from the original data in FIG. 2(b), the frequency gain Gk' to be removed is stored in the first memory as shown in FIG. 2(C). Then, Qi obtained by performing inverse Fourier transform based on this frequency gain Gk' (Fig. 2 (e
) can be used as a filter characteristic.

Therefore, after this, from the original data Di, this filter characteristic Q
By subtracting i, the original data Di can be filtered.

In addition to implementing the above filter, it is also possible to filter the original data Di in the device of the present invention. That is, among the frequency gains Gk in FIG. 2(b), the frequency gains Gk other than the shaded portion (gains to be removed from the original data)
' Qi obtained by performing inverse Fourier transform based on
This is nothing but the filtered version of the original data Di.

Next, an embodiment of the present invention based on the above principle will be described with reference to the drawings.

FIG. 3 is a block diagram of the apparatus of this embodiment.

In the figure, the first memory stores original data [)i (l
-〇, 1. . . , N-1> is stored in the Fourier transform, and first, the harmonic gain is stored as Gk. Then, as described later, the corresponding gain Qk is
It is designed to output .

The second memory 2 stores one period of the fundamental frequency shown in FIG.
The equally divided cosine value C03 (2πi/N) is accumulated, and a similar sine value sin (2πi/N) is accumulated.

The second memory 2 stores the cosine and sine values in association with the address 1 having the same number as the number i of the cosine and sine values divided into N equal parts.

That is, the cosine values are as shown in Table 1 below.

[ [ Also, the sine values are shown in Table 2 below.

The read control means 3 is composed of a host controller 4 and a memory address controller 5. The host controller 4 receives the data number i.

The parameter k and the total number of data N are output. Then, the host controller 4 sequentially outputs the number i from O to Nl, and the number i is N-
When the number reaches 1, the operation of updating the parameter k by one and outputting the number i again is repeated. Note that the value of the parameter is updated from O to at least N/2.

Note that the parameters from the host controller 4 are output to the first memory 1, and among the gains Qk in the first memory 1, the gain corresponding to the parameter k is read out and controlled. Further, the number i, parameter k, and total number of data N from the host controller 4 are output to the memory address controller 5, where they are used for address specification.

The memory address controller 5 receives the number @1 from the host controller 4. The parameter k is input and the address for the second memory 2 is determined. This memory address controller 5 determines the address (mod[k-i/N]-j) by performing the calculation of (5). Note that 1 is k-i/N
means the surplus integer of . By specifying this address l, the corresponding cosine value cos(2w −k
i/N> or the sine value sin(2π·ki/N) is read out from the second memory 2.

The calculation means 6 includes a multiplier 7. It consists of an adder 8 and a line register 9. The multiplier 7 has a first . The gain Gk from the second memories 1 and 2 is multiplied by the cosine value or sine value of the first harmonic. That is, Gk-CO8(2π・k
i/N> or Gk-sin(2x-ki/N) and outputs it to the adder 8. The adder 8 and line register 9 cumulatively add the output from the multiplier 7 to =o- to =N/2 for each data number i. That is, the arithmetic means 6 composed of the multiplier 7, the adder 8, and the line register calculates the above formula (3),
(4) is calculated.

The operation of the embodiment apparatus configured as described above will be explained with reference to FIG. 3.

First, the inverse Fourier transform regarding cosine will be explained.

The host controller 4 outputs the data number i as a parameter at the timing shown in FIG. The parameters change at least from O to N/2, and the data number i is O while each parameter k is being output.
~N-1 and output. In other words, each time the data number i reaches N-1, the parameter k is updated by one, and the process is repeated until the parameter k becomes N/2.

The parameters from this host controller 4 include the first
Among the gains Gk in the first memory 1, the gains Go, G1, . . . , GN/2 corresponding to the parameter k are sequentially output. Note that each gain Gk continues to output the same gain Gk unless the parameter K is updated, that is, until the data number becomes 0-N-1.

On the other hand, data number i from the host controller 4,
The parameter k and the total number of data N are output to the memory address controller 5, where they are used to determine the read address of the second memory 2.

The memory address controller 5 determines the address p by executing the calculation of equation (5) described above. Based on this address p, the cosine value c divided into N and stored in the second memory 2 is calculated according to the relationship shown in Table 1 described above.
os(2πi/N) will be read.

The relationship between data number i, address, and the output of the second memory 2 for each parameter is shown in the table below. Note that when k=o, cos O is output.

(Left below) When k・], ! In the case of s-2, (blank below) k-, in the case of \2'2 (an example where N is an even number), as you can see from the table above, the second memory is specified by the address. When k=1, the cosine 1 in the second key 2 is read out consecutively, and the cosine 1 is read out from k
= 2 is read every other time, and when k = 3, it is read every 2 times, that is, from the second memory 2 according to the parameter k, every (k-1>) The cosine (tar) is read out to give cos(2π·ki/N), which is the lean pull value of the cosine value of the first harmonic.

Next, in the calculation means 6, the first. Second memory 1.
Based on the output from 2, the calculation of equation (3) is performed for each data number i. And the data number! For each expression (3
) By multiplying Qi by 1, the inverse Fourier transform regarding the cosine is completed.

Incidentally, since the inverse Fourier transform regarding sine can be performed in the same manner as the above-mentioned operation, its explanation will be omitted.

In this manner, the device of the above embodiment has a relatively simple configuration, and can easily perform inverse Fourier transform. Moreover, by executing the calculation of the above formula (5) in the memory address controller 5 to determine the address l, the control for reading every (kl) cosine or sine values from the second memory 2 is simple and reliable. can be done.

Next, the operation when the device of the embodiment is used as the filter creation device or filtering device described above will be explained. When used in both devices, the only difference from the above-described embodiment is the content stored in the first memory 1.

When used as a filter creation device, the original data D
: Of each frequency dyne Gk when Fourier transformed,
Gains other than the frequency gain to be removed from the original data are set to zero and stored in the first memory 1. That is, the gain Gk' shown in FIG. 2(C) is stored in the first memory 1.

The meaning of Qi and Qi' obtained by performing inverse Fourier transform using the above embodiment device based on this gain Gk' is the waveform obtained by mapping the frequency space of FIG. 2(C) onto the real space, that is, , which means nothing but the existence of a filter. Therefore, this output Qi.

The original data can be filtered by subtracting Qi' from the original data Di.

On the other hand, when used as a filtering device, each frequency gain (3
Among these, the frequency gain to be removed from the original data is set to zero and stored in the first memory 1. That is, Fig. 2 (
A gain (3k) shown in means nothing but a waveform obtained by mapping the frequency space in Figure 2 (d>) onto the real space, that is, data obtained by filtering the original data. Therefore, in this case, subtraction processing must be performed on the waveform after the original data is filtered. Instead, the filtered data can be used as the output of the device of the above embodiment.

Note that the present invention is not limited to the above embodiments, and various modifications can be made within the scope of the gist of the present invention. For example, the configuration of the readout control means 3 is not limited to one in which the address is determined by the operation n of equation (3), and it is possible to read every (k-1) cosine value or sine value from the second memory 2. A variety of configurations can be adopted.

Furthermore, the present invention is capable of performing the above-mentioned inverse Fourier transform on two-dimensional data, and it is also possible to perform image filtering using the above-mentioned filtering operation. For example, Fourier transform is performed on a subtracted image of a blood vessel etc. obtained by subtracting images before and after injection of a contrast agent, a part of the frequency gain corresponding to the blood vessel image is increased, and this is stored in the first memory 1. It is also possible to perform filtering processing by storing and performing inverse Fourier transform. In this case, a clear image with an enhanced blood vessel image can be obtained.

[Advantageous Effects of the Invention 1 (Details above)] As described above, according to the present invention, it is possible to provide a data processing device that can perform inverse Fourier transform despite having a relatively simple configuration, and moreover, A filter for any frequency characteristic can be realized by using only the characteristic having , and it can also be used as a filtering device.

[Brief explanation of the drawing]

Figure 1 is a schematic explanatory diagram explaining the relationship between the fundamental frequency and the second harmonic, Figure 2 (a) is a characteristic diagram of the original data D1, and Figure 2 <b> is the result of Fourier transformation of the original data Di. Figure 2 (C) is the frequency characteristic diagram of the part that should be removed from the original data, Figure 2 (d) is the frequency characteristic diagram of the part that should be left as data, and Figure 2 (e) is the frequency characteristic diagram of the part that should be left as data. A characteristic diagram obtained by performing inverse Fourier transform based on the gain in Fig. 2 (C),
FIG. 3 is a block diagram of an apparatus according to an embodiment of the present invention, FIG. 4 is a timing chart showing the output timing of data number i and parameters, and FIG. 5 (a). (b) and (c) are schematic explanatory diagrams for explaining filter operations. 1... first memory, 2... second memory, 3...
- Reading control means, 6... calculation means. Agent Patent Attorney Tadashi Misawa Yoshitou 2

Claims (4)

[Claims] (1) A first memory that stores the gain Gk for each k-th harmonic when the original data is Fourier transformed, and the data number of the original data as i = 0, 1, 2, ..., N-1. , cosine value cos(2πi/N) obtained by dividing one period into N equal parts, sine value s
in(2πi/N), and the cosine value or sine divided into N equal parts based on the data number i and a parameter k that is updated every time this number i reaches N-1. By reading and specifying every (k-1) value, cos(2π·ki/N) is obtained from the second memory.
or a read control means for reading out sin(2π·ki/N) and the outputs of the first and second memories, Qi=Σ_kGk·cos(2π·ki/N) or Qi′=Σ_kGk·sin 1. A data processing device comprising: arithmetic means for performing an inverse Fourier transform by performing an arithmetic operation of (2π·ki/N) for each data number i. (2) The second memory stores the cosine value cos(2π
i/N), sine value sin(2πi/N), and the cosine value and sine value are stored in association with the address l having the same number as the number i of the sine value sin(2πi/N), and the readout control means stores the cosine value and the sine value mod(k・i/N).
2. The data processing device according to claim 1, wherein the data processing device specifies the read address l by executing an operation of /N)=l (l means a remainder integer of k·i/N). (3) The first memory stores each frequency gain Gk of the original data.
The data according to claim 1 or 2, wherein a gain corresponding to a frequency to be removed from the original data is stored as zero, and filtered data is created by calculation by the calculation means. Processing equipment. (4) The first memory stores each frequency gain Gk of the original data.
The data according to claim 1 or 2, wherein gains other than the gain corresponding to the frequency to be removed from the original data are stored as zero, and the filter characteristics are obtained by calculation by the calculation means. Processing equipment.