Graphic data processor

A graphic data processor for processing two-dimensional signals or one-dimensional signals such as observed graphic data. One graphic data processor includes circuitry for effecting two-dimensional Fourier conversion of the observed graphic data signals such that components occur with respect to first through fourth image limits on the resultant two-dimensional Fourier plane; circuitry for forming processed graphic data including circuitry for nullifying all but one of the components from the first through fourth image limits and circuitry for effecting two-dimensional inverse Fourier conversion on the one component to derive the processed graphic data; circuitry for determining the phase component of the processed graphic data; and circuitry for determining the local gradient of said phase component. Another graphic data processor includes circuitry for effecting one-dimensional Fourier conversion of the observed graphic data signals; circuitry for forming processed graphic data including circuitry for nullifying negative components, leaving positive components and circuitry for effecting one-dimensional inverse Fourier conversion on one component to drive the processed graphic data; circuitry for determining the phase component of the processed graphic data; and circuitry for determining the instantaneous frequency.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention is directed to a graphic data processor for processing 
observed graphic data (hereafter graphic data signals). In particular, it 
is directed to a technique for the quantitative detection of the 
composition and grains in observed graphic data. 
2. Description of the Prior Art 
In the past, Fourier conversion has been generally applied in frequency 
analysis. For example, distribution of the frequency components may be 
determined by the following equation: 
##EQU1## 
where one-dimensional signal x(n), (n=0.apprxeq.N-1), is obtained by AD 
conversion at a sampling frequency of Fs(Hz) over a period of T sec, where 
T=N/Fs, and j=the imaginary number. 
In this method, however, signals are processed as a whole, and what is 
determined is the sum of the frequencies over the entire signal range. To 
obtain partial frequency distribution in this method, a signal has to be 
divided into a number of ranges, external Fourier conversion applied to 
each of these ranges, and a frequency distribution obtained for each. It 
is, however, not possible to calculate in this method the frequency every 
sampling period Ts(ACC)=1/Fs (momentary frequency of the signals) because 
of the following relation between the span Ta of the ranges and frequency 
resolution Fr. 
EQU Fr=1/Ta . . . (2) 
The two-dimensional Fourier conversion shown in equation (3) is applied 
also to analyze spatial frequencies of images: 
##EQU2## 
However, this method of analysis also applies to images as a whole so that 
the spatial frequency distribution obtained here is the sum of the 
frequencies for the entire image. Thus, to apply the method to an image in 
order to determine the local spatial frequency distribution in it, the 
image must be divided into a number of small areas, two-dimensional 
Fourier conversion applied to each to these areas, and a spatial frequency 
distribution for the areas obtained. As in the case of one-dimensional 
signals, the more an area is reduced in size, the more does the frequency 
resolution deteriorate making it impossible to determine local spatial 
frequency for each picture element. 
OBJECTS OF THE INVENTION 
A primary object of this invention is to provide an image processor for 
processing observed signals and also to provide the technology for 
quantitative detection of the local composition and dot pattern 
corresponding to the observed signals. Another object of the invention is 
to provide, in a device for processing two-dimensional signals like 
graphic data signals, a technology for the determination of local 
frequency graphic data by obtaining, respectively, two-dimensional 
analytical signals from two-dimensional observed signals and local spatial 
graphic data frequencies from local gradients of the phase of 
two-dimensional analytical signals. 
Still another object of the invention is to provide, in a device for 
processing observed signals on one-dimensional basis, a technology for the 
determination of instantaneous frequency graphic data by obtaining, 
respectively, one-dimensional analytical signals from observed signals and 
instantaneous data frequencies, in which is accomplished a differential 
operation of the phase of one-dimensional analytical signals which are 
obtained from observed signals. 
These objects of the invention and specific characteristics of the 
invention are detailed in the description and drawing provided hereunder. 
SUMMARY OF THE INVENTION 
The following is a summary of the representative items constituting the 
invention described above. 
In a graphic data processor which processes twodimensional graphic data 
signals, two-dimensional Fourier conversion is applied to observed 
signals, nullifying all except one of the four components on the 
corresponding two-dimensional Fourier plane from the first to the fourth 
image limits, creating graphic data by two-dimensional inverse Fourier 
conversion, obtaining the phase component of the above graphic data 
signal, and quantitativity determining the local dot pattern of the 
picture data or the phase corresponding to change in the concentration 
value. Furthermore, calculating local gradients from the phase components 
and obtaining local graphic data frequency from the local gradients of the 
phase, the local dot pattern of the picture data or the frequency 
corresponding to change in the concentration value is quantitatively 
determined. 
Furthermore, in a graphic date processor which processes observed signals, 
one-dimensional Fourier conversion is applied to the observed signals, 
nullifying only the negative frequency components, obtaining 
one-dimensional analytical signals by inverse one-dimensional Fourier 
conversion, determining the instantaneous frequencies by accomplishing a 
differential operation of the phase components of the one-dimensional 
analytical signals, obtaining the graphic data from the instantaneous 
frequencies, and quatitatively determining the local composition and data 
pattern corresponding to the observed signals. 
PRINCIPLE OF THE INVENTION 
It is known that the real and imaginary parts of the Fourier conversion of 
causality signals are in Hilbert conversion relation with respect to each 
other. Also, the real part can be made equal to the observed signal by 
nullifying the negative frequency component of the Fourier conversion of 
the observed signals (this being definedas causality on the frequency 
axis), thereby obtaining a complex number signal of which the imaginary 
part is the Hilbert conversion of the observed signal. In general, this is 
referred to as an analytical signal, the properties of which satisfy the 
analysis function. From the analytical signal thus determined, it is 
possible to obtain the instantaneous amplitude (envelope) and 
instantaneous phase of the observed signal, and, furthermore, the 
instantaneous frequency from a time differential of the phase. This method 
of analysis can be extended and applied to two-dimensional signals also, 
determining local spatial frequency of the graphic data and from it 
obtaining the graphic data. 
Hilbert conversion for the observed signal x(t) is given by equation (4): 
##EQU3## 
where the * represents the convolution. Fourier conversion of relation (4) 
gives relation (5) 
##EQU4## 
where X(.omega.) is a Fourier conversion of x(t) and X(.omega.) is a 
Fourier conversion of x(t). 
Furthermore, sgn.omega. is a sign function given by the following: 
##EQU5## 
Here causality conforms to Fourier conversion X(.omega.) of the observed 
signal x(t). In other words, the positive frequency component of 
X(.omega.) is doubled. 
Represented by X(.omega.), this is expressed by equation (7) 
##EQU6## 
Considering equation (5), this may be expressed as follows: 
##EQU7## 
Inverse Fourier conversion of either side of the above equation gives 
equation (9): 
##EQU8## 
In other words x(t) is the inverse Fourier conversion of x(.omega.). In 
x(t), which is a complex number signal, the real and the imaginary parts 
are related according to the Hilbert conversion. A signal of this type is 
generally referred to as an analytical signal. It is believed that 
analytical signal x(t) is a complex vector expression of observed signal 
x(t), so that x(t) may be expressed by equation (10). 
##EQU9## 
Here r(t) represents instantaneous amplitude (envelope) and .theta.(t) 
instantaneous phase. Analytical signal x(t) does not include a negative 
frequency component so that .theta.(t) is a monotonically increasing 
function. The time differential of .theta.(t) indicates instantaneous 
frequency f(t) and is given by equation (13). 
##EQU10## 
As a result, from the observed signal x(t), analytical signal x(t) can be 
obtained and the instantaneous amplitude, phase, and frequency thereof 
calculated. Furthermore, an analytical signal with a negative frequency 
component, if obtained, will be a complex conjugate of the analytical 
signal obtained from the positive frequency component, each having a phase 
opposite in sign to that of the other but having an equal local amplitude. 
As a result, the local frequency obtained from the two will be equal in 
their absolute values, differing only in sign. The observed signal 
represented by equation(14) was used as an example for analysis to clearly 
indicate that relation between the observed signal and analytical signal. 
EQU X(t)=1/2(1+sin(2.pi.t)). sin(20.pi.t) . . . (14) 
where 0.ltoreq.t.ltoreq.1. The result of processing the above appears in 
FIG. 1. 
This is a signal represented by a sine wave of frequency 10 Hz the 
amplitude of which gradually increases and decreases. Evidently from FIG. 
1, r(t) represents the envelope of the signal, and .theta.(t) is a linear 
function that gives a constant frequency for the signal. Accordingly, f(t) 
has a constant value agreeing with the frequency of the signal. 
Next, equation (15) represents a signal the frequency of which increases 
with time. The result of processing this signal appears in FIG. 2. 
EQU x(t)=1/2(1+sin(2.pi.t)).sin (40.pi.t) . . . (15) 
Here .theta.(t) is proportional to the square of time and f(t) proportional 
to time, allowing the instantaneous frequency of the signal to be 
determined correctly. In this way, by obtaining the analytical signal for 
an irregular signal, it is possible to isolate the amplitude and 
frequencies corresponding to every successive point of time. For example, 
where the observed signal is obtained as a product of the envelope signal 
undergoing a smooth change and having only a positive value and the 
carrier signal with both a positive and negative value and changing 
comparatively faster, the technology offered by this invention will allow 
the envelope signal and the carrier signal to be isolated from each other 
and determined from the observed signal. Furthermore, where the frequency 
of the carrier signal changes with time, the frequency of the carrier 
signal can be determined for any point of time. 
However, the conventional difference treatment allows only the differential 
signal to be determined for the observed signal itself so that in this 
approach it is not possible to directly determine the frequency of the 
carrier signal. 
Next, a causality is applied to Fourier conversion D(x,y) of the 
two-dimensional signal d(x,y) as is common with graphic data. In other 
words, the first image limit of the two-dimensional Fourier plane is 
multiplied four-fold, nullifying the rest of the image limits. If this is 
expressed as D(.omega.x,.omega.y), then this is expressed as shown in 
equation (16). 
EQU D(.omega.x,.omega.y)=(1+sgn.omega.x) (1+sgn.omega.y) D(.omega.x,.omega.y) . 
. . (16) 
Equation (17) is obtained through an inverse Fourier conversion of the 
above: 
EQU d(x,y)=d(x,y)-d x y(x,y)+j (d x (x,y)-d y(x,y)) . . . (17) 
where, 
##EQU11## 
Here d(x,y) is a complex number signal, the real and imaginary parts of 
which will be related through Hilbert conversion if a secondary Hilbert 
conversion is defined by equation (21). Accordingly, a two-dimensional 
analysis function is defined for d(x,y). 
##EQU12## 
Since d(x,y) does not have any component except the first image limit on 
the two-dimensional Fourier plane, it is a signal with its phase extending 
along the positive directions of, respectively, the x and y axes. In other 
words, this corresponds to isolating, from among signals with their phases 
extending in different directions, a signal with its phases extending in, 
respectively, the x and y direction. Equation (22) expresses the complex 
vector of the two-dimensional analytical signal. 
##EQU13## 
Here, r(x,y) and .theta.(x,y) are apparently expressions for, 
respectively, local amplitude and local phase of the graphic data. Thus, 
local frequency f(x,y) is obtained for the graphic data on the basis of 
the local gradient of the phases determined corresponding to the optimum 
fitness of four neighboring picture elements. In other words, if, 
respectively, .theta.(i,j), .theta.(i+1,j), .theta.(i,j+1), and 
.theta.(i+1,j+1) represent the phases of the four neighboring picture 
elements, equations (23), (24), and (25) will give the coefficients of the 
optimum plane z=ax+by+c for which the sum of the squares of error is 
minimum. 
##EQU14## 
Accordingly, local frequency f(x,y), is given by equation (26) as the 
magnitude of the gradients of this plane. The contour lines in FIG. 3 are 
an expression of the graphic data built on the basis of the results of 
calculation. In FIG. 3, d represents the concentration (luminance) while 
the firm and the dotted lines represent, respectively, bright convex and 
dark concave areas. 
FIG. 4 represents the graphic data corresponding to the local frequencies. 
Furthermore, there are apparently four two-dimensional analytical signals 
depending upon which image limit on the two-dimensional Fourier plane is 
to be projected for each of which two-dimensional complex signals may be 
obtained with their respective phases in mutually different directions. 
These, however, are not independent of each other, all having equal local 
amplitude, differing only in phase. However, since the phases also are in 
a specific dependency relation so that the size of the local gradient of a 
phase will always have the same value whichever two-dimensional analytical 
function it is obtained from.

DESCRIPTION OF THE PREFERRED EMBODIMENT I 
FIGS. 5 and 6 explain the graphic data processor in embodiment I of this 
invention, concerning therapeutic graphic data like tomographs, CT data, 
etc. FIG. 5 is a block diagram showing the entire configuration of said 
graphic data processors while FIG. 6 is a block diagram showing the 
details of the gradient calculator shown in FIG. 5. 
In FIG. 5, 1 represents an observed signal detector like a light detector 
for the TV cameras, radiation detectors for the dose of radiation relating 
to x-ray pictures, or ultrasonic devices for the ultrasonic graphic data. 
In this figure, 2 represents an analog/digital converter, which converts 
the observed signals into digital signals and 3 represents an auxiliary 
storage device such as a magnetic disk or a magnetic tape device. 
Secondary memories are represented by, respectively, 4, 6, 8, 11 and 13, 
while 5 and 7 are respectively, first and the second arithmetic 
processors. A divider 9 and inverse tangent table 10 are also provided. A 
gradient calculator 12 may comprise, as shown in FIG. 6, an 
adder-subtracter 12a, a first register 12b, multiplier 12c, a second 
register 12d, an adder 12e, and a square root table 12f. An output device 
14 may correspond to a TV monitor, a film lighting device, a printer, etc. 
Controllers used for the above devices are based on the usual methods, and 
therefore, details thereof are omitted from this description. 
The following is a description of the graphic data processor in example I, 
based on the application of the principles underlying this invention to 
ultrasonic tomography. 
Thus, it is assumed here, that ultrasonic graphic data is subjected to 
two-dimensional Fourier analysis nullifying all by one of the components 
from the first to the fourth image limits on the Fourier plane, followed 
by two-dimensional inverse Fourier conversion. 
In FIGS. 5 and 6, ultrasonic tomographs are detected by the ultrasonic 
tomographic device corresponding to observed signal detector 1. In other 
words, an ultrasonic pulse beam having directivity is radiated on the body 
under examination, receiving the signals given back as response from areas 
differing in audio impedance, specifying the position within the body 
under examination on the basis of the time elapsing between radiations of 
the ultrasonic pulses and reception of signals emitted in response and 
also the direction of ultrasonic pulse radiation, obtaining the 
correspondence between the size of reflected signals and the 
concentration, converting into graphic data the change in audio impedance 
from place to place in the body under examination, and thereby, obtaining 
the ultrasonic tomographic images. 
FIG. 11 is a block diagram illustrating connections of circuit components 
for obtaining observed graphic data. Pulse signals generated from an 
oscillator 21 are inputted through a driver 22 to a US probe 23 in which 
analog switches 24 and piezoelectric transducer (PZT) array 25 are 
included. An ultrasonic pulse beam is radiated from the US probe 23 in 
response to a control signal from a controller 26 into a body under 
examination 27. Upon radiation, the PZT array 25 receives an echo signal 
indicating a level of audio impedance and the depth of the body where the 
beam is reflected. The echo signals thus obtained are fet through an 
amplifier 28 to an analog/digital (A/D) converter 29 which corresponds in 
FIG. 5 to the one designated by reference numeral 2. 
The following describes the operations involved in determining the local 
frequencies of, respectively, the two-dimensional analytical signals and 
the graphic data. The above ultrasonic reflected signals are converted 
into digital signals by analog/digital (A/D) converter 2 and fed to 
two-dimensional memory 4. Observed signals stored in two-dimensional 
memory 4 are subjected to two-dimensional Fourier conversion of 
two-dimensional signals in first arithmetic processor 5, and further the 
values obtained by the arithmetic processor 5 are stored in 
two-dimensional memory 6. Contents of two-dimensional memory 6 stored 
after Fourier conversion re read out in such a way as to nullify the 
negative frequencty components, leaving only the positive frequency 
components which are then subjected to inverse Fourier conversion in 
second arithmetic processor 7 to obtain the value given by equation (17) 
which is then stored in two-dimensional memory 8. 
Next, the value in two-dimensional memory 8 is read and, using divider 9, 
##EQU15## 
is determined, this being then sent to inverse tangent table 10 to obtain 
##EQU16## 
This value is stored in two-dimensional memory 11. The value of 
.theta.(x,y) stored in memory 11 represents local phase, FIG. 6 describes 
in detail the operation involved in obtaining local frequency f(x,y) by 
gradient calculator 12 from local phase .theta.(x,y). 
To begin with, first register 12b is zero-cleared, the four picture 
elements .theta.(i,j), .theta.(i+1,j), .theta.(i,j+1), and 
.theta.(i+1,j+1) neighboring on local frequency .theta.(x,y) are read 
successively from two-dimensional memory 1, values of these four picture 
elements are added to or subtracted from the contents in first register 
12B by using adder-subtracter 12A, determining a in (23). Immediately 
hereafter, multiplier 12C is used to obtain from this result, value 
a.sup.2, this being stored in second register 12D. 
Next, using the same procedure, equation (24) is executed in order to 
obtain the value b in first register 12B, obtaining b.sup.2 by using 
multiplier 12C. The value b.sup.2 is fed into adder 12E. Using adder 12E, 
contents a.sup.2 and b.sup.2 of second register 12D are added and the 
value of the gradient f(x,y) worked out by using square root table 12F. In 
this way, gradient calculator 12 is used to determine the value of local 
frequency f(x,y) in equation (26), storing the results in two-dimensional 
memory 13. The value of local frequency f(x,y) stored in two-dimensional 
memory 13 is displayed by output device 14. 
According to embodiment I, the two-dimensional analytical signal can be 
determined from ultrasonic tomographic sgnals, determining from the local 
gradient of the phase thereof the local spatial frequency of the graphic 
data and thereby the local frequency graphic data whereby it is possible 
to determine the local composition of the body under examination, offering 
a new parameter for diagnosis. 
It is possible, for example, to carry out quantitative diagnosis vased on 
differential diagnostic criteria (in particular, refer to FIG. 7) of a 
mammary gland tumor as referred to under section 5 (sampling tissue 
characteristics), page 210 to 211, in Graphic Data Engineering in 
Therapeutics, contained in the collection of reports of the Thirteenth 
Radiographic Symposium (Nov. 5-6, 1981), these reports being incorporated 
herein by reference. Conventionally, malignant and benign tumors are 
distinguished one from the other on the basis of experience, referring to 
the echoes from the periphery, interior, and anterior parts of the tumors. 
This invention improves the probability of correctness of a diagnosis 
making quantitative diagnosis of tissues possible on the basis of local 
frequency graphic data corresponding to specific locations. 
DESCRIPTION OF THE PREFERRED EMBODIMENT II 
FIG. 7 is a block diagram of the graphic data processor in embodiment II of 
this invention. 
In the graphic data processor of embodiment II, functions of 
two-dimensional memories 4, 6, 8, 11 and 13 of the graphic data processor 
in embodiment I are combined into a common two-dimensional memory 15. 
Operations of the graphic data processor in embodiment II are identical to 
those of the graphic data processor in embodiment I and are, therefor, 
omitted from the description. 
DESCRIPTION OF THE PREFERRED EMBODIMENT III 
FIGS. 8 to 10 are flow charts describing the operation of the graphic data 
processor in embodiment III of this invention. FIG. 8 is a flow chart of 
the two-dimensional Fourier conversion (determining only the positive 
frequency component) in this embodiment. FIG. 9 is a flow chart of the 
inverse two-dimensional Fourier conversion and FIG. 10, a flow chart of 
the calculations involved in the determination of local amplitude, local 
phase, and local frequency, Furthermore, the * indicates the direction of 
single dimensional Fourier conversion or that of single dimensional 
inverse Fourier conversion. 
In the graphic data processor of embodiment III, all the operations of 
two-dimensional memory 4 and the following components in embodiment I are 
preformed by a computer. 
The following describes the operation of the graphic data processor in 
embodiment III. This operation is implemented in the same manner as is 
done in embodiments I or III. 
(A) Operations of the Two-dimensional Fourier Converter. 
In FIG. 8, the observed signals (original graphic data) n=0, 1, 2, . . . , 
N-1 in computer memory of block (1) are subjected to Fourier conversion. 
##EQU17## 
repeating this N times at (2). 
Here, k=0, 1, 2, . . . , N-1, taking one dimensional Fourier conversion 
D.sub.1 (k,n)=0 for k=N/2, . . . , N-1. Also, j in the above equation 
represents the imaginary number. 
As shown by the transverse dotted lines in blocks (3) and (4), operations 
(2) makes it possible to obtain, respectively, the values of the real and 
the imaginary parts on the left side of the one-dimensional Fourier 
conversion plane in the m direction of the observed signal. 
Next, one-dimensional Fourier conversion 
##EQU18## 
is carried out at (5) N/2 times for observed signals k=0, 1, 2, . . . , 
N-1. 
Here one-dimensional Fourier conversion D(k,l)=0 is performed for l=N/2, . 
. . , N-1. In the above, j represents the imaginary number. 
Longitudinal dotted lines in blocks (6) and (7) show operation (5) makes it 
possible to obtain the values of, respectively, the real and the imaginary 
parts of the observed signal on the one-dimensional Fourier conversion 
plane in the n direction at 1/4 the distance from the left (this 
corresponding to the positive frequency components). The source code of 
the above-described operataion is shown below. 
______________________________________ 
A(I,J) = d(I,J) 
B(I,J) = 0.0 
Integer*4 MM, M, NN, K, FUGO, ICON 
Real*4 A(M,M), B(M,M) 
NN = 2 
FUGO = 1 
CALL FFT(A,B,MM,NN,FUGO,ICON) 
K = M/2 
DO 100 J = 2, K 
DO 100 I = 2, K 
A(I,J) = 2*A(I,J) 
B(I,J) = 2*B(I,J) 
100 CONTINUE 
DO 200 J = K+1, M 
DO 200 I = 1, M 
A(I,J) = 0.0 
B(I,J) = 0.0 
200 CONTINUE 
DO 300 J = 1, K 
DO 300 I = K+1, M 
A(I,J) = 0.0 
B(I,J) = 0.0 
300 CONTINUE 
FUGO = -1 
CALL FFT(A,B,MM,NN,FUGO,ICON) 
d(I,J) = A(I,J) + jB(I,J) 
______________________________________ 
In the above source code listing of the program, 
FFT: a subroutine of fast Fourier transform 
d(I,J): an analytical signal data argument of the subroutine of FFT 
A: Real Part 
B: Imaginary Part 
NM: the size of dimension 
NN: Dimensionality 
FUGO: 1; Fourier conversion -1; inverse Fourier conversion 
ICON: status when subroutine is operated 
(B) Operations involved in Inverse Fourier Conversion. 
The system in FIG. 9 performs n successive N/2 inverse one-dimensional 
Fourier conversion (8) 
##EQU19## 
on the real and imaginary parts of the two-dimensional Fourier conversion 
value in said blocks (6) and (7) (K=0, 1, 2, . . . , N/2-1). In the above 
equation, j represents the imaginary number. 
As the longitudinal dotted line in blocks (9) and (10) indicate, operation 
(8) makes it possible to obtain the values of, respectively, the real and 
the imaginary parts for the top half and n direction of the inverse 
one-dimensional Fourier conversion plane corresponding to the observed 
signals. 
This is followed by N inverse one-dimensional Fourier conversions 
(operation 11) on the above inverse one-dimensional Fourier conversion 
plane blocks (8) and (10) for n=0, 1, 2, . . . , N-1. 
##EQU20## 
Operation (11) makes it possible to obtain the values of real part 
Re(d(m,n)), imaginary part Im(d(m,n)) of the two-dimensional analytical 
signal for blocks (12) and (13). 
(C) Operations involved in the Determination of Local Amplitude, Local 
Phase and Local Frequency. 
In FIG. 10, operations (14) and (15) are performed to obtain, from the 
values of, respectively, the real part Re (d(m,n)) and imaginary part Im 
(d(m,n)) of the two-dimensional analytical signal in blocks 12 and 13, 
local amplitude 
##EQU21## 
and local phase 
##EQU22## 
Operation (18) is used to determine the local frequency f(m,n) from the 
local gradient of local phases .theta.(m,n) in block (17) of the above 
results. In other words, local frequency is determined by carrying out 
operatoins of equations (23), (24), (25) and (26). 
DESCRIPTION OF THE PREFERRED EMBODIMENT IV 
FIGS. 12 through 14 illustrate the graphic data processor in embodiment IV 
of this invention, concerning therapeutic graphic data like tomographs, CT 
data, etc. 
FIG. 12 is a block diagram showing the entire configuration of the graphic 
data processor while FIGS. 13 and 14 are flow charts in which all the 
operations of two-dimensional memory 34 and the flowing components in Fig. 
12 are performed by a computer. And furthermore, FIG. 13 is a flow chart 
of one-dimensional Fourier conversion (determining only the positive 
frequency components) and the inverse one-dimensional Fourier conversion. 
FIG. 14 is a flow chart of calculating instantaneous amplitude, 
instantaneous phase, and instantaneous frequency. 
In FIG. 12, an ultrasonic pulse beam having directivity is radiated on the 
body under examination, receiving the signals given back as response from 
areas differnig in audio impedance, and specifying the position within the 
body under examination on tha basis of the time elapsing between 
radiations of the ultrasonic pulses and reception of signals emitted in 
response and also the direction of ultrasonic pulse radiation. The 
received signals are fed to an analog/digital (A/D) converter 32, and are 
stored in two-dimensional memory 34 according to the direction and an 
elapsing time of pulse radiation. 
The following describes the operation involved in determining the 
one-dimensional analytical signals and the instataneous frequencies. In 
the first arithmetic processor 35, one-dimensional Fourier conversion on 
time with respect to a predetermined direction of a pulse beam is applied 
to the observed signals stored in two-dimensional memory 34. And the 
resultant values are memorized, in order, in two-dimensional memory 36 
according to the direction of pulse radiation. Contents of two-dimensional 
memory 36 stored after one-dimensional Fourier conversion are read out in 
such a way as to nullify the negative frequency components, leaving only 
the positive frequency components which are then subjected to inverse 
one-dimensional Fourier conversion with respect to a predetermined 
direction of a pulse beam in the second arithmetic processor 37 to obtain 
one-dimensional analyticadl signals. The one-dimensional analytical 
signals are memorized in two-dimensional memory 38. Next, the value in 
two-dimensional memory 38 is read out and, using divider 39. 
##EQU23## 
is determined. Here, n is a number of a direction of a pulse beam, and t 
is a elapsing time of the pulse beam with respect to each direction of the 
pulse beams. This is then sent to inverse tangent table 40 to obtain 
##EQU24## 
This value is stored in two-dimensional memory 41. The value of 
.theta.(n,t) stored in memory 41 represents instantaneous phase. 
Each of the two adjacent elements of the instantaneous phases with respect 
to time-axis is inputted, in order, to a differential calculator 42, 
thereby obtaining an instantaneous frequency f(n,t) shown by the following 
equation in the differential calculator 42. 
##EQU25## 
The value of the instantaneous frequency f(n,t) is memorized in 
two-dimensional memory 43, and is displayed by output device 44. 
EFFECTS OF THE INVENTION 
The following are the effects of the invention described above: 
(1) Quantitative detection of local composition or dot pattern for the 
observed signals in a graphic data processor by performing two-dimensional 
Fourier conversion of observed signal, nullifying all but one of the 
components from the first to the fourth of the image limits on the 
corresponding two-dimensional Fourier plane, followed by generating 
graphic data through two-dimensional inverse Fourier conversion, said 
graphic data being used for the determination of the phase component of 
said graphic data signal, determining local gradient from said phase 
component, and obtaining local frequency of graphic data from local 
gradient of said phase. 
(2) Determining, from (1) above, characteristic local fluctuations, in the 
CT value of the body examined or the frequency component of different 
system noises appearing in x-ray CT graphic data on the body being 
examined. 
(3) Obtaining, from (1) above, local frequencies in ultrasonic tomographs, 
thereby quantitatively determining local differences in the densities of 
scatterings on the body under examination, 
(4) Improving the precision of diagnosis and examinations through (1) to 
(3) above. 
The above invention is obviously not limited to the scope of the 
embodiments described above but may be modified in different ways as long 
as the underlying principles are not violated. 
For example, even though the examples cited above relate to applications of 
this invention to medical fields, the invention may be applied to 
examination of the uniformity for granular status on the surface of the 
graphic data obtained on materials or examination of the stage of mixing 
of two or more materials.