## Abstrict A flow meter for detecting a flow speed in such a manner that an
ultrasonic pulsed continuous wave is repeatedly transmitted toward
an object at predetermined intervals T, a phase vector indicative
of the phase of a reception signal due to the reflected wave is
produced at the predetermined intervals, the phase difference between
the present phase vector and the preceding phase vector is detected,
and a Doppler frequency is calculated from the average value of
a plurality of phase difference values to obtain the speed of the
object. The phase difference values are classified into a first
group consisting of position phase difference values and a second
group consisting of negative phase difference values, the cosine
and sine values of the central angle of the positive phase difference
values and the cosine and sine values of the central angle of the
negative phase difference values are calculated, and the argument
of a vector indicated by the weighted sum of cosine values and the
weighted sum of sine values is calculated to be used as an average
phase angle.
## Claims We claim:
1. An ultrasonic Doppler flow meter comprising:
transmitter-receiver means for transmitting an ultrasonic pulsed
continuous wave repeatedly toward an object at predetermined intervals,
receiving a reflected wave from the object, and generating a reception
signal from the received reflected wave;
phase detecting means for generating a phase vector indicative
of a phase of the reception signal each time the reception signal
is generated;
phase difference classifying means for generating a phase difference
value representing a phase difference between a present phase vector
and a preceding phase vector each time the phase vector is generated;
phase difference detecting means for classifying a plurality of
phase difference values outputted from the phase difference detecting
means into a first group consisting of positive phase difference
values and a second group consisting of negative phase difference
values;
means for calculating a first average angle from the phase difference
values belonging to the first group and obtaining a cosine value
and a sine value of the first average angle;
means for calculating a second average angle from the phase difference
values belonging to the second group and obtaining a cosine value
and a sine value of the second average angle;
means for calculating a weighted sum of the cosine values of the
first and second average angles by adding a first product to a second
product, the first product being a product of the cosine value of
the first average angle and a first weighting coefficient corresponding
to the number of phase difference values belonging to the first
group, the second product being a product of the cosine value of
the second average angle and a second weighting coefficient corresponding
to the number of phase difference values belonging to the second
group;
means for calculating a weighted sum of the sine values of the
first and second average angles by adding a third product to a fourth
product, the third product being a product of the sine value of
the first average angle and the first weighting coefficient, the
fourth product being a product of the sine value of the second average
angle and the second weighting coefficient;
means for calculating an argument of a vector from real and imaginary
parts of the vector which are equal to the weighted sum of the cosine
values and the weighted sum of the sine values, respectively, the
argument being a first total average value of the phase difference
values outputted from the phase difference detecting means; and
means for transforming the first total average value into a flow
speed.
2. An ultrasonic Doppler flow meter according to claim 1 further
comprising:
means for transforming the phase difference values outputted from
the phase difference detecting means into angles in a new polar
coordinate system in which a direction of the first total average
value serves as a reference axis;
means for adding and averaging the angles in the new polar coordinate
system; and
means for transforming an output of the adding and averaging means
into a value in an original polar coordinate system of the phase
difference values outputted from the phase difference detecting
means, the value in the original polar coordinate system being a
second total average value of the phase difference values outputted
from the phase difference detecting means;
wherein the means for transforming transforms at least one of the
first total average value and the second total average value into
a flow speed.
3. An ultrasonic Doppler flow meter comprising:
transmitter-receiver means for transmitting an ultrasonic pulsed
continuous wave repeatedly toward an object at predetermined intervals,
receiving a reflected wave from the object, and generating a reception
signal from the received reflected wave;
phase detecting means for generating a phase vector indicative
of a phase of the reception signal each time the reception signal
is generated;
phase difference detecting means for generating a phase difference
value representing a phase difference between a present phase vector
and a preceding phase vector each time the phase vector is generated;
first averaging means for calculating a first average value of
a plurality of phase difference values outputted from the phase
difference detecting means by classifying the phase difference values
into a first group consisting of positive phase difference values
and a second group consisting of negative phase difference values,
calculating a first average angle from the phase difference values
belong to the first group and decomposing the first average angle
into a cosine component and a sine component, calculating a second
average angle from the phase difference values belonging to the
second group and decomposing the second average angle into a cosine
component and a sine component, calculating a weighted sum of the
cosine components and a weighted sum of the sine components, and
calculating an argument of a vector having a real part equal to
the weighted sum of the cosine components and an imaginary part
equal to the weighted sum of the since components, the argument
being the first average value;
means for obtaining a second average value of the phase difference
values outputted from the phase difference detecting means by transforming
the phase difference values outputted from the phase difference
detecting means into values in a new polar coordinate system in
which a direction indicated by the first average value serves as
a reference axis, adding and averaging the values in the new polar
coordinate system, and transforming the added and averaged values
into a value in an original polar coordinate system of the phase
difference values outputted from the phase difference detecting
means, the value in the original polar coordinate system being the
second average value; and
means for transforming at least one of the first average value
and the second average value into a flow speed.
4. An ultrasonic pulse Doppler flow meter according to claim 3
further comprising a data processor for correcting an error in the
second average value by calculating a plurality of presumed average
values including fold back errors from the second average value,
calculating a plurality of differences between a sum of the phase
difference values outputted from the phase difference detecting
means and a plurality of sum data based on the plurality of presumed
average values each time a phase difference value is outputted from
the phase difference detecting means, evaluating the plurality of
differences to select one of the plurality of presumed average values
most closely representing an actual value of the second average
value, and correcting the second average value based on the selected
presumed average value.
5. An ultrasonic pulse Doppler flow meter according to claim 3
further comprising means for selecting one of the first average
value and the second average value and outputting the selected average
value to the means for transforming.
6. An ultrasonic pulse Doppler flow meter according to claim 3
further comprising display means for simultaneously displaying flow
speeds transformed from the first average value and the second average
value.
7. An ultrasonic pulse Doppler flow meter comprising:
transmitter-receiver means for transmitting an ultrasonic pulsed
continuous wave repeatedly toward an object at predetermined intervals,
receiving a reflected wave from the object, and generating a reception
signal from the received reflected wave;
phase detecting means for generating a power value indicative of
a power of the reception signal each time the reception signal is
generated;
phase detecting means for generating a phase vector indicative
of a phase of the reception signal each time the reception signal
is generated;
phase difference detecting means for generating a phase difference
value representing a phase difference between a present phase vector
and a preceding phase vector each time the phase vector is generated;
phase difference classifying means for classifying a plurality
of phase difference values outputted from the phase difference detecting
means into a first group consisting of positive phase difference
values and a second group consisting of negative phase difference
values;
means for calculating a first average angle from the phase difference
values belonging to the first group and obtaining a cosine value
and a sine value of the first average angle, the first average angle
being calculated in accordance with a weighted averaging method
in which the phase difference values belonging to the first group
are weighted by corresponding power values outputted from the power
detecting means;
means for calculating a second average angle from the phase difference
values belonging to the second group and obtaining a cosine value
and a sine value of the second average angle, the second average
angle being calculated in accordance with a weighted averaging method
in which the phase difference values belonging to the second group
are weighted by corresponding power values outputted from the power
detecting means;
means for calculating a weighted sum of the cosine values of the
first and second average angles by adding a first product to a second
product, the first product being a product of the cosine value of
the first average angle and a first sum of power values outputted
from the power detecting means corresponding to the phase difference
values belonging to the first group, the second product being a
product of the cosine value of the second average angle and a second
sum of power values outputted from the power detecting means corresponding
to the phase difference values belonging to the second group;
means for calculating a weighted sum of the sine values of the
first and second average angles by adding a third product to a fourth
product, the third product being a product of the sine value of
the first average angle and the first sum of power values, the fourth
product being a product of the sine value of the second average
angle and the second sum of power values;
means for calculating an argument of a vector from real and imaginary
parts of the vector which are equal to the weighted sum of the cosine
values and the weighted sum of the sine values, respectively, the
argument being a first total average value of the phase difference
values outputted from the phase difference detecting means; and
means for transforming the first total average value into a flow
speed.
8. An ultrasonic Doppler flow meter according to claim 7 further
comprising:
means for transforming the phase difference values outputted from
the phase difference detecting means into angles in a new polar
coordinate system in which a direction of the first total average
value serves as a reference axis;
means for adding and averaging the angles in the new polar coordinate
system; and
means for transforming an output of the adding and averaging means
into a value in an original polar coordinate system of the phase
difference values outputted from the phase difference detecting
means, the value in the original polar coordinate system being a
second total average value of the phase difference values outputted
from the phase difference detecting means;
wherein the means for transforming transforms at least one of the
first total average value and the second total average value into
a flow speed.
9. An ultrasonic Doppler flow meter comprising:
transmitter-receiver means for transmitting an ultrasonic pulsed
continuous wave repeatedly toward an object at predetermined intervals,
receiving a reflected wave from the object, and generating a reception
signal from the received reflected wave;
phase detecting means for generating a phase vector indicative
of a phase of the reception signal each time the reception signal
is generated;
phase difference detecting means for generating a phase difference
value representing a phase difference between a present phase vector
and a preceding phase vector each time the phase vector is generated;
phase difference classifying means for classifying a plurality
of phase difference values outputted from the phase difference detecting
means into a first group consisting of positive phase difference
values and a second group consisting of negative phase difference
values;
means for calculating a first total average value of the phase
difference values outputted from the phase difference detecting
means in accordance with the positive phase difference values of
the first group and the negative phase difference values of the
second group; and
means for transforming the first total average value into a flow
speed.
10. An ultrasonic Doppler flow meter according to claim 9 further
comprising:
means for transforming the phase difference values outputted from
the phase difference detecting means into angles in a new polar
coordinate system in which a direction of the first total average
value of the phase difference values outputted from the phase difference
detecting means serves as a reference axis; and
means for calculating a second total average value of the phase
difference values outputted from the phase difference detecting
means based on the angles in the new polar coordinate system;
wherein the means for transforming transforms at least one of the
first total average value and the second total average value into
a flow speed.
## Description CROSS-REFERENCE TO RELATED APPLICATIONS
The present application relates to the subject matter described
in application Ser. No. 611541 filed on Nov. 13 1990 (claiming
priority based on Japanese Patent Application No. 01-292338 filed
on Nov. 13 1989), entitled "ULTRASONIC DOPPLER FLOW METER",
by the same inventors and assigned to the same assignees of the
present application.
BACKGROUND OF THE INVENTION
The present invention relates to a pulse doppler measuring apparatus,
and more particularly to an apparatus for detecting the speed of
a moving object by using an ultrasonic wave, for example, a pulse
doppler measuring apparatus capable of measuring the flow speed
of blood in a living body in realtime with a high signal-to-noise
ratio.
Various kinds of apparatuses have hitherto been known which detect
the flow speed of an object by utilizing the Doppler effect of an
acoustic wave. Specifically, in an apparatus using the pulse Doppler
method which is described in, for example, an article entitled "Pulsed
Ultrasonic Doppler Blood Flow Sensing" by D. W. Baker (IEEE
Trans. Vol. SU-17 No. 3 July 1970 pages 170 to 185), a pulsed
continuous wave is sent out repeatedly, and a time gate corresponding
to the distance to a measured part is set on a received signal to
specify the measured part.
An ultrasonic Doppler blood flow measuring apparatus has been known,
in which, as disclosed in, for example, JP-A-58-188433 JP-A-60-119929
and JP-A-61-25527 an ultrasonic wave is transmitted toward a blood
vessel, and the Doppler shift frequency of the ultrasonic wave reflected
from the blood in the blood vessel is measured to detect vcos.theta.,
where .theta. represents an angle between the direction of blood
flow and the transmission direction of the ultrasonic wave, and
v indicates a blood flow speed.
Further, a technique called "color flow mapping", in
which the distribution of blood flow speed in a cross section of
a living body is measured and displayed in color on a tomographic
image, is described in an article entitled "Real-Time Two-Dimensional
Blood Flow Imaging Using an Autocorrelation Technique" by C.
KASAI et al. (IEEE Trans. Vol. SU-32 No. 3 May 1985 pages 458
to 464). In order to carry out the color flow mapping at a desired
image frame rate, the blood flow speed at each of a plurality of
pixels is determined by averaging the measured values of Doppler
shift due to a relatively small number of measurements. In the example
mentioned in the above article, a difference vector between a vector
indicated by a Doppler signal detected currently and a vector indicated
by the preceding Doppler signal is obtained by an autocorrelator
for each of the measurements, and the average speed is calculated
from the argument of a vector which represents the sum of a plurality
of difference vectors. That is, the autocorrelation method is used
in the above example.
Meanwhile, U.S. Pat. No. 4809703 discloses the so-called two
axial component method, in which a phase difference .DELTA..theta.
of a Doppler signal obtained for each measurement is decomposed
into a cosine component and a sine component, a plurality of values
of each of the cosine and sine components are added and averaged,
and a phase difference indicated by the average cosine and sine
components thus obtained is transformed into a velocity.
Further, an article entitled "Blood Flow Imaging Using a Discrete-Time
Frequency Meter" by M. A. Brandestini and F. K. Forster (1978
Ultrasonics Symposium Proceedings pages 348 to 352) shows a method
in which the phase difference of a Doppler signal is detected for
each of a plurality of repetitions of measurement, and an average
phase difference is calculated by adding a plurality of values of
phase difference directly, to be converted into a velocity. This
method will hereinafter be referred to as "phase difference
averaging method".
Meanwhile, it is pointed out in U.S. Pat. No. 4905206 that the
phase difference averaging method produces a large calculation error
when a true average phase difference is close to +.pi. or -.pi.,
that is, a moving object is put in a high-speed region, and that
the autocorrelation method and the two axial component method produce
a large calculation error when the true average phase difference
is close to zero, that is, the moving object is put in a low-speed
region. U.S. Pat. No. 4905206 further discloses that one of the
phase difference averaging method and the autocorrelation method
(or the two axial component method) can be changed over to the other
so that the above difficulties are eliminated, and that values of
phase difference obtained for a plurality of measurements are transformed
into those in a new polar coordinate system using a direction which
is indicated by the average phase difference angle according to
the autocorrelation method, as a reference axis, and the values
of phase difference thus obtained are added and averaged.
SUMMARY OF THE INVENTION
The further investigation conducted by the present inventors has
shown that the calculation of an average phase difference in the
new polar coordinate system which is described in U.S. Pat. No.
4905206 fails to eliminate the sources of the errors completely.
In other words, the new polar coordinate system is formed so that
the direction of a central angle indicative of an average value
of dispersed phase difference values obtained for a plurality of
measurements is used as a reference axis to bring phase difference
values which are to be averaged close to .+-.0. However, when the
average phase difference for determining the reference axis is calculated
by the autocorrelation method, a large error is produced in the
low speed region, because the measured phase difference value fluctuates
widely on the basis of noise. In such a case, the reference axis
of the new polar coordinate system does not agree with the direction
of the central angle of the dispersed phase difference values. That
is, an angle greater than .pi. and an angle less than -.pi. are
folded back, and thus it is impossible to perform a correct arithmetic
operation for obtaining an average phase difference.
It is accordingly an object of the present invention to provide
an ultrasonic Doppler flow meter capable of producing an output
which does not deviate from a true average flow speed much, even
when the phase difference detected for each measurement varies widely.
It is another object of the present invention to provide an ultrasonic
Doppler flow meter which can carry out the phase difference averaging
method appropriately even when the detected phase difference value
varies widely, and thus can reduce an error in measurement greatly.
According to an aspect of the present invention, there is provided
an ultrasonic Doppler flow meter which comprises means for classifying
a plurality of phase difference values detected from a reflected
ultrasonic wave into a first group consisting of positive phase
difference values and a second group consisting of negative phase
difference values, means for calculating an average value of the
phase difference values belonging to the first group to obtain cosine
and sine values of an angle indicated by the average value, means
for calculating an average value of the phase difference values
belonging to the second group to obtain cosine and sine values of
an angle indicated by the average value, means for adding the cosine
components while using a weight corresponding to one of the number
of phase difference values included in each of the first and second
groups and the power of each phase difference signal, and for adding
the sine components while using a weight corresponding to one of
the number of phase difference values included in each of the first
and second groups and the power of each phase difference signal,
and means for calculating the argument of a vector of which the
real and imaginary parts are given by the sum of the cosine components
and the sum of the sine components, respectively, to obtain a total
average phase difference.
According to another aspect of the present invention, there is
provided an ultrasonic Doppler flow meter which comprises the above
means, and in which a plurality of measured phase difference values
are transformed into values in a new polar coordinate system using
a direction which is indicated by the total average phase difference
angle, as a reference axis, and the phase difference values in the
new polar coordinate system are added and averaged, to transform
the average value thus obtained into a velocity.
According to the calculation of the total average phase difference
based upon the grouping of measured phase difference values, even
when the phase difference value obtained for each measurement varies
widely, a large error due to the autocorrelation method and the
conventional two axial component method will never appear. Accordingly,
when the total average phase difference is transformed into a velocity,
a flow speed is obtained which is hardly affected by noise.
Further, the total average phase difference does not deviate so
greatly from the center value of dispersed phase difference values
obtained for a plurality of measurements. Accordingly, the direction
indicated by the total average phase difference angle is suited
to be used as the reference axis of a new polar coordinate system
which is introduced to add and average angles (namely, phase difference
angles).
Other features and advantages of the present invention will become
apparent from the following detailed explanation taken in conjunction
with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram showing the whole construction of an
embodiment of a pulse Doppler measuring apparatus according to the
present invention.
FIG. 2 is a block diagram showing a main part of the embodiment
of FIG. 1 in detail.
FIG. 3 is a problem analysis diagram showing a program which is
executed by the data processor of FIG. 1.
FIG. 4 is a graph which shows a phase change characteristic for
explaining the function of the program of FIG. 3.
FIG. 5 is a block diagram showing a main part of another embodiment
of a pulse Doppler measuring apparatus according to the present
invention, in detail.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The principle of the present invention and embodiments thereof
will be explained below in detail, with reference to the drawings.
First, explanation will be made of the outline of the construction
of a pulse Doppler measuring apparatus according to the present
invention and the operation principle of the apparatus.
FIG. 1 is a block diagram showing an embodiment of a pulse Doppler
measuring apparatus according to the present invention.
The present embodiment includes a transmitting circuit 2 a receiving
circuit 3 a phase comparator 4 an A/D converter 5 a fixed substance
removing filter, that is, an MTI (moving target indication) filter
6 an average phase difference calculating circuit 7 a selector
8 for changing an output, a data processor 9 a divider 10 a display
device 11 a controller 12 and an operator's console 13. The transmitting
circuit 2 gives a pulsed continuous wave to a transducer 1 at intervals
of a predetermined time T. Thus, the transducer 1 emits an ultrasonic
pulsed continuous wave toward a reflecting body 11 at intervals
of T. The reflected acoustic wave thus produced is incident on the
transducer 1 and the reflection signals therefrom are successively
detected by the receiving circuit 3. In the phase comparator 4
each of the detected received signals is mixed with two kinds of
reference signals .alpha.=Acos.omega.t and .alpha.'=Asin.omega..sub.o
t, to obtain Doppler signals V.sub.R and V.sub.I having phase information
of the reflection signal. In the A/D converter 5 the signals V.sub.R
and V.sub.I of the wave reflected from the reflecting body 11 located
at a predetermined depth are sampled at intervals of T, to be transformed
into digital signals. The digital signals thus obtained are expressed
b V'.sub.Rn and V'.sub.In, when the number of the repetition of
ultrasonic transmission is indicated by n (=1 2 3 and so on).
The signals V'.sub.Rn and V'.sub.In are given by the following equations:
The MTI filter 6 produces a first-order difference of the output
of the A/D converter 5 to remove the unvaried reflected wave signal
coming from a fixed substance. For the sake of simplicity, let us
rewrite the equations (1) and (2) as follows:
Then, the output V.sub.n of the MTI filter is given by the following
equation:
The output V.sub.n will hereinafter be referred to as "phase
vector".
FIG. 2 shows an example of the average phase difference calculating
circuit 7. Referring to FIG. 2 each time the phase vector V.sub.n
is supplied from the MTI filter to a power calculating circuit,
the power calculating circuit calculates the power P.sub.n of the
phase vector from the real part R.sub.n and imaginary part I.sub.n
of the phase vector in accordance with the following equation:
The phase vector V.sub.n is also applied to an ATAN memory 731.
The memory 731 stores therein a transformation table for obtaining
the argument of the phase vector from the values of real and imaginary
parts thereof, to deliver the phase angle (that is, argument) .theta..sub.n
of the phase vector V.sub.n. A phase difference detecting circuit
732 produces the difference between a phase vector at the present
time and a phase vector at the time preceding by one time period,
to obtain a phase difference .DELTA..theta..sub.n. It is to be noted
that the phase difference .DELTA..theta..sub.n is detected as an
angle lying in a range from +.pi. to -.pi., and thus is given by
the following equation: ##EQU1##
Phase difference values .DELTA..theta..sub.n thus obtained are
successively applied to each of a correction value detecting circuit
740 and a phase difference averaging circuit 730.
The correction value detecting circuit 740 and the phase difference
averaging circuit 730 calculate values .DELTA..theta. and .DELTA..theta.'
of average phase difference, respectively, by a method peculiar
to the present invention, each time a predetermined number N of
phase difference data .DELTA..theta..sub.n (for example, eight or
sixteen phase difference data) are applied to the circuits 740 and
730. The above method will be explained below.
In the correction value detecting circuit 740 a positive-negative
discriminating/counting circuit 741 discriminates between positive
phase difference data and negative phase difference data, counts
the number K of positive phase difference data and the number L
of negative phase difference data, and delivers positive phase difference
data .DELTA..theta..sub.k (where k=1 k) and negative phase difference
data .DELTA..theta..sub.l (where l=1 L) separately. That is, the
above operation is written as follows: ##EQU2##
The positive phase difference data .DELTA..theta..sub.k (where
k=1 . . . K) are successively applied to a weight center calculating
circuit 742 in which an average value .DELTA..theta..sub.u of the
positive phase difference data .DELTA..theta..sub.k is calculated.
In more detail, those ones P.sub.k of power values P.sub.n delivered
from the power calculating circuit 736 which correspond to the positive
phase difference data .DELTA..theta..sub.k are added by an adder
737 to obtain ##EQU3## The sum ##EQU4## obtained from the adder
733 which sequentially add the P.sub.k is used to perform a weighted,
averaging operation as follows: ##EQU5##
Meanwhile, those ones P.sub.l of power values P.sub.n which correspond
to the negative phase difference data .DELTA..theta..sub.l are added
by an adder 738 to obtain ##EQU6## The negative phase difference
.DELTA..theta..sub.l (l=1 . . . is applied to another weight center
calculating circuit 743 to perform a weighted, averaging operation
as follows: ##EQU7##
The average value .DELTA..theta..sub.u thus obtained indicates
the weight center of the phase difference angles .DELTA..theta..sub.n
in the first and second quadrants, and the average value .DELTA..theta..sub.L
indicates the weight center of the phase difference angles .DELTA..theta..sub.n
in the third and fourth quadrants.
A COS memory 744 stores therein a transformation table for transforming
an angle into the cosine value thereof, and a SIN memory 745 stores
therein a transformation table for transforming an angle into the
sine value thereof. The central angle .DELTA..theta..sub.U is applied
to the memories 744 and 745 to obtain the cosine and sine values
of the angle .DELTA..theta..sub.U. Similarly, the central angle
.DELTA..theta..sub.L is applied to a COS memory 746 and a SIN memory
747 to obtain the cosine and sine values of the angle .DELTA..theta..sub.L.
The cosine components thus obtained are added by an adder 754 in
the following special manner. The cosine value cos .DELTA..theta..sub.U
outputted from the COS memory 744 is multiplied by the power sum
##EQU8## corresponding to the positive phase difference by means
of a multiplier 748 and the cosine value cos.DELTA..theta..sub.L
outputted from the COS memory 746 is multiplied by the power sum
##EQU9## corresponding to the negative phase difference by means
of a multiplier 750. The outputs of the multipliers 748 and 750
are added by an adder 754. That is, weighted addition is carried
out for the cosine values cos.DELTA..theta..sub.U and cos.DELTA..theta..sub.L.
Similarly, the sine value sin.DELTA..theta..sub.U outputted from
the SIN memory 745 is multiplied by the power sum ##EQU10## by means
of a multiplier 749 and the sine value sin.DELTA..theta..sub.l
outputted from the SIN memory 747 is multiplied by the power sum
##EQU11## by means of a multiplier 751. The outputs of the multipliers
749 and 751 are added by an adder 755. That is, weighted addition
is carried out for the sine values sin.DELTA..theta..sub.U and sin
.DELTA..theta..sub.L. Respective outputs XR and XI of the adders
754 and 755 are given by the following equations: ##EQU12##
As mentioned above, the weight center of positive phase difference
angles and the weight center of negative phase difference angles
are delivered from the weight center calculating circuits 742 and
743 respectively. Alternatively, the simple average angle of the
positive phase difference angles and the simple average angle of
the negative phase difference angles may be calculated by the circuits
742 and 743 respectively. That is, the output .DELTA..theta..sub.U
and .DELTA..theta..sub.L of the circuits 742 and 743 are calculated
not by the equations (8) and (9) but by the following equations:
##EQU13## In this case, the power calculating circuit 736 and the
adders 737 and 738 can be omitted, and signal lines which extend
from the positive-negative discriminating/counting circuit 741 and
is indicated by a broken line in FIG. 2 is used. Further, in the
multipliers 748 and 750 the number K of positive phase difference
data .DELTA..theta..sub.k is used as a weight coefficient in place
of the power sum ##EQU14## In the multipliers 749 and 751 the number
L of negative phase difference data .DELTA..theta..sub.l is used
as a weight coefficient in place of the power sum ##EQU15## In the
above case, the output X.sub.R of the adder 754 and the output X.sub.I
of the adder 755 are given by the following equations: ##EQU16##
An ATAN memory 752 stores therein a transformation table for obtaining
the argument of a vector from the values of real and imaginary parts
of the vector. The outputs X.sub.R and X.sub.I of the adders 754
and 755 are applied to the ATAN memory 752 which delivers the argument
.DELTA..theta. of a vector X given by the following equation:
The argument .DELTA..theta. is given by the following equation:
The value of argument .DELTA..theta. thus obtained is delivered
as the output of the correction value detecting circuit 740. The
argument .DELTA..theta. is an average phase difference which is
obtained in such a manner that N phase difference data are classified
into a first group consisting of positive phase difference data
and a second group consisting of negative phase difference data,
a central or average angle of phase difference angles belonging
to the first group and a central or average angle of phase difference
angles belonging to the second group are calculated, each central
(or average) angle is transformed into cosine and sine values thereof,
and an average value of cosine values and an average value of sine
values are calculated. When the above average values are calculated,
the power sum corresponding to each of the first and second groups
or the number of phase difference data included in each of the first
and second groups is used as a weight coefficient. Hence, the argument
.DELTA..theta. indicates a substantially central value of N dispersed
phase difference data.
In the present embodiment, it is possible to select one of two
modes, that is, a mode in which the value of .DELTA..theta. is transformed
into a velocity and the velocity thus obtained is displayed as an
average flow speed, and a mode in which the value of .DELTA..theta.
is used as a correction value, that is, N phase difference data
are transformed into values in a new polar coordinate system using
the direction indicated by .DELTA..theta. as a reference axis, and
the values in the new polar coordinate system are added and averaged
to obtain a more accurate average phase difference. In the phase
difference averaging circuit of FIG. 2 N phase difference data
in the new polar coordinate system are added and averaged. That
is, in an angle correcting circuit 733 the correction value .DELTA..theta.
is subtracted from each phase difference data .DELTA..theta..sub.n,
and the principal value of the difference angle .DELTA..theta..sub.n
-.DELTA..theta. is determined. When this principal value is expressed
by .DELTA..theta..sub.m, the principal value .DELTA..theta..sub.m
is given by the following equation: ##EQU17##
In an adding/averaging circuit 734 N phase difference data .DELTA..theta..sub.m
thus obtained are added and averaged. Thus, the output .DELTA..theta."
of the circuit 734 is given by the following equation: ##EQU18##
The value of .DELTA..theta." is the average value of phase
difference data .DELTA..theta..sub.m in the new polar coordinate
system where the direction indicated by the output .DELTA..theta.
of the correction value detecting circuit 740 is used as the reference
axis, an angle in a range from 0.degree. to 180.degree. is defined
in the counterclockwise direction from the reference axis, and an
angle in a range from 0.degree. to -180.degree. is defined in the
clockwise direction from the reference axis. Accordingly, an error
which is produced in averaging phase difference data distributed
in the vicinity of .+-..pi., is reduced, and an accurate average
value is obtained. In an adder 735 the correction value .DELTA..theta.
is added to the average value .DELTA..theta." to carry out
inverse transformation for the average value .DELTA..theta.".
Thus, the average value .DELTA..theta." is transformed into
an average phase difference .DELTA..theta.' in an original polar
coordinate system. The average phase difference .DELTA..theta.'
is given by the following equation:
As mentioned above, in the average phase difference calculating
circuit 7 two kinds of average phase difference data .DELTA..theta.
and .DELTA..theta.' are calculated each time N phase vectors are
detected.
Referring back to FIG. 1 one of .DELTA..theta. and .DELTA..theta.'
is selected by the selector 8 in accordance with a control signal
which is sent out from the controller 12 on the basis of a command
from the operator's console 13 to be applied to the data processor
9. After having been subjected to necessary processing in the data
processor 9 the selected average phase difference .DELTA..theta.
or .DELTA..theta.' is applied to the divider 10 to be divided by
the transmission interval T of the ultrasonic wave, thereby being
transformed into a Doppler angular frequency .omega..sub.d. That
is, the Doppler angular frequency .omega..sub.d is given as follows:
##EQU19##
In the present embodiment, the data processor 9 stores therein
a phase difference correcting program. Accordingly, even if the
average phase difference .DELTA..theta.' obtained in the above manner
has a calculation error, the average phase difference .DELTA..theta.'
can be corrected.
The phase difference correcting program uses a basic algorithm
which is applicable to various methods of adding and averaging phase
difference data. In more detail, when one true phase difference
data exceeds 180.degree. in a process for adding phase difference
data, the true phase difference data is folded back, and thus the
result of addition will differ from the true sum by -360.degree..
Accordingly, the average value of N phase difference data will differ
from a true average value by -360.degree./N. When two true phase
difference data exceed 180.degree., the average value of N phase
difference data will differ from a true average value by -720.degree./N.
Further, when one true phase difference data is less than -180.degree.,
the value of phase difference data will differ from a true average
value by 360.degree./N. The function of the phase difference correcting
program is to presume a plurality of average values having such
errors and to estimate the presumed average values for the purpose
of selecting the most appropriate average value.
FIG. 3 shows an example of the phase difference correcting program
in the form of a problem analysis diagram (PAD). In the present
example, five kinds of presumed average values are estimated. Referring
to FIG. 3 the program is started (step 801). In step 802 the number
k of the repetition of processing is specified in a range from 1
to M (M=5 in the present example). Repeated processing includes
steps 803 to 805. In the step 803 the initial value of an error
S is set to zero. In the step 804 the initial value .theta..sub.0
of an angle is set to zero. In the step 805 the number of the repetition
of processing is specified in a range from 1 to N (where N indicates
the number of angles to be averaged). The contents of the repeated
processing are as follows. In step 806 phase difference data .DELTA..theta..sub.1
to .DELTA..theta..sub.N from the phase difference detecting circuit
732 are successively summed up to obtain .theta..sub.n. FIG. 4 shows
the change of .theta..sub.n with the number n (where n=1 2 . .
. N). Meanwhile, by using the average value .DELTA..theta.' from
the average phase difference calculating circuit 7 five presumed
average values to be estimated are given by the following equation:
##EQU20##
Now, let us assume a case where phase difference data are not dispersed
at all, and each phase difference data is equal to the average phase
difference .DELTA..theta..sub.k. In this case, the value .theta..sub.n
which is obtained by summing up the phase difference data successively
will travel on one of five dot-dash lines shown in FIG. 4. In step
807 the difference D between the sum .theta..sub.n of actual phase
difference data .DELTA..theta..sub.1 to .DELTA..theta..sub.n and
a corresponding value on the dot-dash line is calculated as follows:
##EQU21## In steps 811 to 822 the difference angle D is transformed
into a principal value (namely, an angle within a range from -180.degree.
to +180.degree.). In step 823 the absolute value of the principal
value of the difference angle D is added to the error S which is
obtained at the preceding stage, to update the error S. This processing
is repeated till the number n becomes N. The value of S thus obtained
is an index for indicating the degree of coincidence between the
solid line shown in FIG. 4 and one of the dot-dash lines. Accordingly,
in step 826 the above error S is used as a total error A(k). In
the step 802 the above processing is repeated for values 1 to M
of the number k. Thus, five total errors A(1) to A(5) for indicating
the degree of coincidence between the solid line of FIG. 4 and each
of five dot-dash lines are obtained. Strictly speaking, the total
error A(k) does not indicate the total sum of errors between the
solid line and one of the dot-dash lines, but indicates the total
sum of absolute values of principal values of the above errors,
since the program includes the process of the steps 811 to 822 for
transforming the difference angle D into a principal value. When
the repetition in the step 802 is completed, five values of total
error A(k) for k=1 2 3 4 5 are compared with one another to
find the smallest one of five values, and the number k producing
the smallest total error is referred to as "k.sub.min"
(step 827). Thus, that one of five dot-dash lines which can indicate
a correct average value more appropriately than the remaining dot-dash
lines is determined. In steps 828 and 829 the most appropriate
average value .DELTA..theta..sub.c is given by the following equation:
##EQU22## Specifically, the average value .DELTA..theta..sub.c for
k.sub.min =3 as shown in step 829 is given by the following equation:
The solid line of FIG. 4 shows a case where the true value of the
i-th phase difference exceeds 180.degree., and is folded back. In
this case, the average value .DELTA..theta.'+360.degree./N for k=4
is a correct average value. According to the above-mentioned program,
the i-th and following phase difference data are transformed into
principal values on the broken line of FIG. 4 by the processing
in the steps 811 to 822 and the difference between each of the
values thus obtained and a corresponding value on the dot-dash line
for k=4 is used to update the error S. Accordingly, it is judged
by calculation that the total error A(4) is the smallest one of
the errors A(1), A(2), A(3), A(4) and A(5). Thus, the correct average
value is selected.
The average phase difference which has been checked by the phase
difference correcting program is transformed by the divider 10 into
a speed value which is displayed on the display screen of the display
device 11. It is indicated by the operator's console 13 whether
or not the phase difference correcting program is used for the average
value .DELTA..theta.' outputted from the average phase difference
calculating circuit 7. Further, speed values corresponding to the
average values .DELTA..theta., .DELTA..theta.' and .DELTA..theta..sub.c
can be displayed on the display screen in parallel.
FIG. 5 shows another example of the average phase difference calculating
circuit 7. In FIG. 5 the ATAN memory 731 the phase difference
detecting circuit, 732 the power calculating circuit 736 and the
correction value detecting circuit 740 are equal in construction
to those shown in FIG. 2. Accordingly, each of these circuits performs
the same operation as mentioned above. In the correction value detecting
circuit 740 the central angle of positive ones of phase difference
data .DELTA..theta..sub.n and the central angle of negative phase
difference data are calculated, each central angle is transformed
into cosine and sine values thereof, and the correction value .DELTA..theta.
indicative of the substantially central angle of dispersed phase
difference data .DELTA..theta..sub.n is calculated from the sum
of cosine values and the sum of sine values. Meanwhile, in a phase
difference averaging circuit 730', the phase difference data .DELTA..theta..sub.n
are transformed into values .DELTA..theta..sub.m in a new polar
coordinate system where the direction indicated by the correction
value .DELTA..theta. is used as a reference axis, and not the simple
arithmetic mean of phase difference data .DELTA..theta..sub.m but
the central angle thereof is calculated by utilizing the output
P.sub.n of the power calculating circuit 736. That is, in the angle
correcting circuit 733 each phase difference data .DELTA..theta..sub.n
is transformed on the basis of the equation (16) into the angle
.DELTA..theta..sub.m in the new polar coordinate system where the
direction of the correction angle .DELTA..theta. is used as the
reference axis. In a weight center calculating circuit 734', the
power P.sub.m of each phase signal delivered from the power calculating
circuit 736 is used as a weight coefficient (it is to be noted that
the power P.sub.n of the phase signal indicating the phase difference
.DELTA..theta..sub.n is the same as the power P.sub.m of the phase
signal indicating the phase difference .DELTA..theta..sub.m and
thus the output of the power calculating circuit 736 may be expressed
by P.sub.m), and the central angle of phase difference data .DELTA..theta..sub.m
(that is, central phase difference angle .DELTA..theta.") is
calculated by the following equation: ##EQU23## In the adder 735
as in FIG. 2 the correction angle .DELTA..theta. is added to the
central angle .DELTA..theta." to transform the central angle
.DELTA..theta." into an average phase angle .DELTA..theta.'
in an original polar coordinate system. By calculating an average
phase difference while using a weight coefficient corresponding
to the power of each phase signal, the effect of noise on the average
phase difference is reduced. |