Abstract:
The present invention relates to a method and system for measuring fluid velocity in pipes alternately transmitting two or more ultrasonic frequencies through a pipe wall into a fluid containing scatterers. For each transmission frequency, energy reflected from the scatterers is mixed with the transmission frequency and the result sampled at a rate which is a constant fraction of the transmission frequency. The combination of the Doppler effect on frequencies reflected from the moving scatterers, and the described sampling rate scheme combine to permit isolation of velocity related frequencies from extraneous frequencies in the reflected energy in a computationally efficient manner. A single frequency which represents fluid velocity is extracted from the gathered data, and the fluid velocity readily calculated therefrom using the Doppler formula. The invention provides a system and method for measuring fluid velocity which is simple, reliable, and cost effective.

Description:
BACKGROUND OF THE INVENTION 
     Often, it is necessary to measure the rate of fluid flow within a closed pipe. Non-invasive measurement methods are preferred because such methods do not detrimentally effect the fluid flow or pipe wall. There are two dominant methods of non-invasive flow rate measuring: “Doppler ultrasonic” and “Ultrasonic transit time.” Both methods utilize the transmission of ultrasound through the pipe wall and into the fluid. 
     Doppler ultrasonic uses two ultrasonic transducers coupled to the pipe. The first transducer transmits a continuous ultrasonic signal through the pipe wall and into the fluid. Assuming the moving fluid contains bubbles or solids which can act as acoustic scattering sites, or “scatterers”, the second transducer receives scattered ultrasound signals. Then, the frequency of the scattered signal is compared with that of the transmitted signal. The frequency shift between the transmitted and received signals is proportional to the velocity of the scattering sites and, therefore, indicates the velocity of the fluid in the pipe. 
     In many industrial applications, vibrations from motors and other extraneous sources create frequencies in the pipe that are received by the ultrasonic sensor along with the Doppler shifted frequencies of interest. The detection system used to determine the Doppler frequency may select noise or other ambiguous signals, causing erroneous velocity measurements. 
     One past approach to dealing with the problem of extraneous frequencies involved the use of digital filters to mask out erroneous frequencies. This method assumes the noise source is stationary and continuous. This is often not the case in industrial applications. Variable frequency motor controls are now commonly used to control pumps, resulting in the presence of a range of noise frequencies some of which can get past the filters. Further, automated system controllers continuously turn noise generating equipment off and on, resulting in still further variation in the range of extraneous frequencies. Finally the digital filters can be complex to use. 
     There is a need in the art for a method and system for measuring flow rate with improved reliability and consistency which will not be subject to the confusion caused by extraneous frequencies being received by existing Doppler flow system transducers. 
     There is a another need in the art for a method and system which will accomplish such flow rate measurement without the need for customer installed filters. 
     There is yet another need in the art for a method and system for measuring flow rate which simplifies the user&#39;s interaction with the required equipment. 
     There is yet another need in the art for a method of determining fluid flow rate in real time with maximum computational efficiency. 
     SUMMARY OF THE INVENTION 
     These and other objects, features and technical advantages are achieved by a system and method for determining the velocity of a flowing fluid by measuring the Doppler shift of two or more ultrasonic waves reflected from scatterers carried in a flowing fluid. This flowing fluid contains a dispersion of scatterers which comprise various bubbles and solids which reflect incident ultrasonic waves. 
     A series of ultrasonic waves is transmitted into the flow at a specific frequency and reflects off the flowing scatterers. The corresponding Doppler shifted reflection for this series of waves is subtracted from the transmitted waves and the result collected. A second series of waves at a different frequency is then transmitted into the flow and a second corresponding Doppler shifted reflection is subtracted from the transmitted waves and the result collected. For both series, the result of the subtraction contains Doppler beat frequencies representing the velocity of the fluid. 
     Performing a Discrete Fourier Transform (DFT) on the first subtracted series will reveal concentrations of energy at particular frequencies, some of which result from the scatterers and some of which result from extraneous noise. Similarly, a second DFT performed on the second subtracted series will also reveal frequency peaks representing both the Doppler beat frequencies and extraneous noise. The embedded noise and other extraneous signal peaks will be at similar frequencies in both subtracted signals while the Doppler beat frequencies will be separated by a difference proportional to the ratio of the transmitted frequencies. 
     This absence in variation of the noise frequencies between the two series of sampled waves permits the frequencies of interest to be isolated from the extraneous noise frequencies. The second collected series of frequencies is intentionally scaled by the ratio of the two transmission frequencies. This causes the Doppler beat frequencies to align and the noise frequencies to misalign. The “scaling” referred to above is performed on the second (and all additional sets if applicable) set of DFT data, and consists of the following: for each data point consisting of a frequency associated with an amplitude, multiplying the frequency datum by the ratio of the first transmission frequency to the second transmission frequency. This operation compensates for the inherent property of the Doppler effect which, for the same fluid and scatterer velocity, generates reflected velocity related Doppler beat frequencies (frequencies present after mixing) which are proportional to the frequency of the signal originally transmitted into the fluid. 
     A further improvement to the implementation of this method takes advantage of an inherent property of the DFT. By setting the sampling rate to be proportional to the transmission frequency for each series of data collected, the sampling time interval for the subtracted signal and the resulting frequency increment of the calculated DFT will be inversely proportional to the transmission frequency. Since the measured Doppler shifted beat frequency associated with a particular velocity is directly proportional to the transmission frequency employed, the sampling frequency adjustment mentioned above automatically compensates for the Doppler effect, thus obviating the need for mathematically scaling the frequency data after calculating the DFT. This represents an advantage because mathematically scaling the data is computationally expensive, and this invention concerns a real time process in which processing power must be optimally employed. 
     After sampling at the rate established for each transmission frequency and performing the DFT for two sets of data, the velocity related frequency data for the two data sets will converge within a reasonable frequency range without having to perform a separate calculation to mathematically scale the frequency values for the data collected at the lower transmission frequency. The scaling process effected by the variation in sampling rates will cause noise and other extraneous frequencies, which are the same between the two data sets prior to the sampling process, to misalign once the scaling is performed. 
     The aligned Doppler shifted peaks are detected by finding the maximum amplitude, or apex, of a correlation performed on the two sets of DFT data. A frequency distribution is identified as the Doppler distribution based on the location of this apex. Then, the centroid of the selected frequency distribution is determined and used as the measurement frequency, which is then used to calculate the velocity of the fluid. The fluid flow can then be determined by multiplying the cross-sectional area in the pipe by the fluid flow velocity. 
     It must be emphasized that although the above discussion has concentrated on the operations involved in determining fluid velocity using two transmission frequencies, the same principles can be readily applied for any number of additional transmission frequencies. 
     The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described hereinafter which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and specific embodiment disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
     FIG. 1 is a diagram of the control functions and mechanical operations of a hardware implementation of the present invention. 
     FIG. 2 is a flow chart illustrating the steps performed in the present invention. 
     FIG. 3 is a frequency spectrum representation of the energy arriving at the A/D converter associated with two different transmission frequencies without frequency scaling. 
     FIG. 4 is a frequency spectrum representation of energy arriving at the A/D converter associated with two different transmission frequencies where the frequency values of the curves have been scaled. 
     FIG. 5 illustrates the result of performing a correlation on the curves displayed in FIG.  4 . 
     FIG. 6 is a diagram of the control functions and mechanical operations of an alternative embodiment of the present invention. 
    
    
     DESCRIPTION OF THE INVENTION 
     This discussion assumes a familiarity with various signal processing techniques and with the Doppler effect. Those seeking background knowledge of the methods and techniques described herein are advised to consult the following references which are hereby incorporated by reference. 
     With respect to The Doppler effect, see: 
       Ultrasonic Technology,  Richard Goldman, 1962, Reinhold Publishing Corporation, London, U.K.; 
       Ultrasonics: Fundamentals,  Technology, Applications, Second Edition, Dale Ensminger, 1988, Marcel Dekker, Inc., New York, N.Y.; and 
       Ultrasonic Measurements for Process Control,  1989, L. C. Lynnworth, Academic Press, Inc. San Diego, Calif. 
     With respect to Signal processing, see: 
       Signals, Systems, and Transforms,  Charles L. Phillips &amp; John M. Parr, 1995, Prentice-Hall, Inc., Englewood Cliffs, N.J. 
       Digital Signal Processing,  in VLSI, Richard Higgins, 1990, Prentice-Hall, Inc. Englewood Cliffs, N.J. 
     FIG. 1 illustrates a diagram of a flow meter  10  according to the present invention. Microprocessor  17  is coupled to Switch Control  12  to control the frequency selection, and to A/D converter  16  to control its sampling rate and to receive digital data from it. Switch Control  12  is coupled to two generators of sinusoidal electrical signals, the high frequency generator  108  and the low frequency generator  109 . 
     The first Dual Band-Pass filter  11  is coupled to the output of the low and high frequency signal generators, and to the two piezoelectric transducer (PZT) transmitters: high frequency TxHi transmitting transducer  101 , and low frequency TxLo transmitting transducer  102 . 
     High frequency RcHi receiving transducer  103  and low frequency RcLo receiving transducer  104  are coupled to second dual band-pass filter  13 . Second dual band-pass filter  13  is also coupled to Frequency Modulation (FM) mixer  14 , which is, in turn, coupled to A/D converter  16 . A/D converter  16  is coupled to divider  15 , and microprocessor  17 . 
     Microprocessor  17  is preferably a high performance, embedded microcontroller. 
     High and low frequency generators,  108  and  109  respectively, transmit sinusoidal electrical signals at different frequencies, such as, by way of example, 500 KHz and 640 KHz. High frequency transmitting transducer  101 , and low frequency transmitting transducer  102 , convert the received electrical signals into ultrasonic waves at the respective frequencies. Conversely, high frequency receiving transducer  103 , and low frequency receiving transducer  104 , convert received ultrasonic frequencies into electrical signals. Divider  15  acts to divide the active transmission frequency by a constant “N” to optimize the sampling rate at the A/D converter. It is noted that in an alternative arrangement, the frequency division could be performed by the microprocessor and the result transmitted to the A/D converter. 
     Microprocessor  17  sends a signal to switch control  12  to switch frequencies when appropriate. A high frequency (Hi-freq) sinusoidal signal is sent by High Frequency generator  108  to dual band-pass filter  11  which in turn directs the filtered signal to high frequency transmitting transducer  101 , which converts the electrical energy to ultrasonic energy. This ultrasonic beam passes through the pipe wall  105  and into flowing fluid  107 . The fluid carries scatterers  106  which reflect the ultrasonic beam in all directions. High frequency receiving transducer  103  receives reflected ultrasonic energy containing, along with extraneous signals, velocity related frequencies which are a function of both the active transmission frequency and the velocity of the scatterers in the fluid. The velocity of the scatterers when statistically averaged equals the velocity of the fluid. These velocity related frequencies are referred to as the Doppler shifted frequencies. The signal from high frequency receiving transducer  103  is then transmitted to the Dual band-pass filter  13  which filters the signal, acts to reduce crosstalk between the sensors, and sends the filtered signal to FM mixer  14 , which subtracts the Doppler shifted frequency from the transmitted frequency, resulting in the Doppler beat frequency. This analog electrical signal is measured by an analog to digital converter (A/D)  16 , at a sampling rate equal to the active transmission frequency divided by constant “N”. 
     A series of these measurements is sent to microprocessor  17 , which stores this data and sends out a command to switch frequencies to the switch control, which proceeds to select low frequency generator  109 . The above described sequence is repeated identically for the low frequency signal using the low frequency components along the path. The following discussion states the sequence of events for the low frequency signal treatment while minimizing redundancy. 
     Low frequency generator  109  generates the signal which goes to dual band pass filter  11  which in turn transmits the filtered signal to the low frequency transmitting transducer  102 . The low frequency transmitting transducer  102  converts this signal into ultrasonic waves. The low frequency receiving transducer  104  converts the received ultrasonic signal into an electrical signal and sends it in turn to dual band-pass filter  13 . The signal is then sent to mixer  14  where the received frequency is subtracted from the transmitted frequency thereby generating the Doppler beat frequency for the case of low frequency transmission. The resulting analog electrical signal is then sent to A/D converter  16 . This anal electrical signal is measured by an A/D converter  16 , at a sampling rate equal to the active (in this case, low frequency) transmission frequency divided by constant “N”. 
     As with the high frequency case, a series of these measurements is sent to microprocessor  17  which stores the data. Microprocessor  17  then sends a command to switch control  12  to again change frequencies. It can be readily observed that this will cause the entire process to repeat, performing all processes in an alternating manner between the high and low frequencies. Of course, any number of frequencies can be used, which can be selected by different system parameters, such as pipe thickness, fluid type, scatterer type, extraneous noise, among others. 
     One skilled in the art will recognize that the hardware illustrated in FIG. 1 is merely one way to implement the method discussed below. Alternate hardware embodiments are readily apparent and are clearly within the scope of the present invention. 
     FIG. 2 illustrates a flow chart of the method of measuring flow rate according to the present invention. The first step  210  is to set the transmission frequency selection to “high” to start the process. In subsequent runs through the process, microprocessor  17  will alternate between low and high transmission frequency settings. Next, at step  225 , the selected frequency is divided by constant “N” to establish the sampling rate at which data will be sampled at the A/D converter  16 . The next step  211 , is to send a sinusoidal electrical signal of the selected frequency to dual band-pass filter  11  using the Switch Control  12 . Next at step  212 , dual band-pass filter  11  acts to selectively allow only the high or low selected frequency to pass through the filter, and then directs the filtered signal appropriately to either the high frequency transmitting transducer  101  or to the low frequency transmitting transducer  102  in accordance with the currently active transmission frequency. 
     The next step  213 , is to convert the sinusoidal electrical signal into ultrasonic energy. This is accomplished by high frequency transmitting transducer  101  for high frequency signals, and by low frequency transmitting transducer  102  for low frequency signals. Next, at step  214 , this ultrasonic energy is transmitted through the pipe wall  105  into the flowing fluid  107  so as to cause this energy to reflect off scatterers  106  dispersed throughout the fluid  107 . The frequencies emanating from the scatterers  106  result from a combination of the transmitted frequency and the velocities of the scatterers, and form a Doppler shift frequency distribution. 
     At step  215 , the reflected ultrasonic frequencies are received by the receiving transducer and converted into electrical signals by the High frequency receiving transducer  103  for high frequency transmissions, and by the low frequency receiving transducer  104  for low frequency transmissions. 
     At step  216 , the Doppler beat frequency is produced by subtracting the values of the frequencies reflected off the scatterers from the value of the transmitted frequency using the FM Mixer  14 . It is noted that the noise signals are not affected by the mixer and pass through to the A/D converter with their original frequencies intact. 
     At step  218 , the analog signal emerging from the FM Mixer  14  is sampled by the A/D converter  16  at the sampling rate calculated in step  225 . A series of measurements obtained by this sampling step is sent to the microprocessor  17 . 
     At step  219 , microprocessor  17  performs a Discrete Fourier Transform (DFT) on the series of measurements generated in step  218 , thereby generating frequency domain data associated with the transmission frequency then in operation. Specifically, a Fast Fourier Transform (FFT), an algorithm formulated to calculate DFTs rapidly, is performed on the sampled data for the cases of high and low frequency transmission. The result of the computation is the generation of a data set for each transmission frequency used. Each data set consists of data points each of which associate a frequency with an amplitude. 
     For background information on Discrete Fourier Transforms (FFTs) and Fast Fourier Transforms (FFTs), the reader is referred to the following teaching reference: DIGITAL SIGNAL PROCESSING, by Proakis and Manolakis, Third Edition, Prentice Hall 1996. This teaching reference is hereby incorporated by reference. 
     At step  220 , if data has been collected using both high and low transmission frequencies, operation continues at step  221 . If only high frequency data has been gathered, the microprocessor  17  sets frequency selection to “low”, in step  217 , and repeats steps  211  through  219 . 
     At step  221 , a correlation between the DFTs for the data resulting from the low frequency transmission and from the high frequency transmission is performed by multiplying the DFT data together. As a result of the multiplication, the Doppler beat frequencies form a large identifiable apex  502  whereas the other frequencies will be misaligned. In step  222 , the Doppler frequency distribution is identified and the centroid of the Doppler distribution is determined with precision. In step  223  the velocity is calculated from the centroid frequency using the Doppler formula and the flow is calculated by multiplying the velocity by the cross-sectional area of the pipe. Step  223  completes one full measurement of fluid flow rate. 
     At step  226 , data is cleared from the microprocessor. 
     At step  224 , the process begins anew beginning at step  210 . 
     While the embodiment above includes the desirable benefit of setting the sampling rate at the A/D converter  16  equal to the transmission frequency divided by a constant “N”, the invention may be practiced without this feature. Without establishing this relationship between transmission frequency and sampling rate, additional computation would have to performed on the frequency domain data to prepare for the correlation operation. 
     FIG. 3 presents a graphical representation  301  of the frequency spectrum of the energy arriving at AID converter  16 . This figure represents data gathered for two separate transmission frequencies, for a single fluid velocity, with no scaling of frequencies having been performed. Energy  304  is plotted as a function of Frequency  305 . The Noise frequency peaks  302  in the curve for data corresponding to low frequency transmission  306  are in line with the noise frequency peaks  302  in the curve for data corresponding to high frequency transmission  307 . The noise signals have frequencies which are too low to be affected by the mixer  14 , and are independent of the transmission frequency value. Therefore, the same noise frequencies arrive at the A/D converter for all transmission frequencies used. Consequently the noise frequency peaks  302  for the cases of different transmission frequencies are aligned. 
     By contrast, the Doppler beat frequencies emerging from the mixer vary proportionately with transmission frequency for the same fluid velocity. Accordingly, the Doppler frequency distributions  303  for the cases of high and low frequency transmission signals are misaligned. 
     FIG. 4 presents a graphical representation  401  of the frequency spectrum of the sampling data gathered at A/D converter  16  after scaling has been performed. The graph is the result of performing a Discrete Fourier Transform on the sampled data. Energy  404  on the vertical axis is plotted against Frequency  405  on the horizontal axis thereby indicating the signal strength of the various frequencies after scaling has been performed. Two separate groups of data are pictured: data collected during high frequency transmission indicated by the dotted line  407 , and data collected during low frequency transmission indicated by the solid line  406 . The frequency values for the low frequency graph have been scaled upwards by the ratio of the transmission frequencies. This scaling is preferably accomplished by appropriately setting the Sampling rate as in step  225  at the A/D converter  16 , but can also be performed arithmetically. One skilled in the art will recognize that the required scaling could also be achieved through a combination of sampling rate control and arithmetic operation so long as the combination of the two yields the same overall scaling of the frequency values. 
     The noise frequencies  402  are indicated at three separate local peaks:  402 . a,    402 . b,  and  402 . c.  The Doppler Beat frequency distribution  403  is also shown. This figure permits some visual appreciation of the present invention&#39;s mechanism for distinguishing between noise frequencies  402  and velocity related Doppler Beat frequencies  403 . The noise frequency peaks  402 . a  and  402 . b  are displaced with respect to one another, although they originate from the same noise frequency, because the peak at  402 . b  represents that noise frequency effectively multiplied by a scaling factor equal to the ratio of the transmission frequencies (i.e. TxHi/TxLo). After this scaling operation, the noise peak  402 . b  forming part of the data set gathered for low frequency transmission  406  is moved up the frequency scale by the amount of the multiplication. Frequency peak  402 . b  is thereby separated on the frequency scale from frequency peak  402 . a.    
     The Doppler Beat frequency distributions  303  of FIG. 3 which were misaligned, are now represented by element  403 , and are aligned in FIG. 4 because of the scaling of the frequency values of the data set corresponding to the low frequency transmission signal. The scaling operation has acted to cancel the Doppler characteristic which caused the signals to previously be misaligned. 
     FIG. 5 presents a graphical illustration  501  of a correlation between the two plots of sampling data in FIG.  3 . The Multiplication Result  505  on the vertical axis is plotted against frequency  506  on the horizontal axis. A single solid line  507  represents the value of the multiplication result for each frequency within the range of the graph. 
     The Multiplication result  505  is the mathematical product of the values of energy measured for the case of high frequency transmission and the case of low frequency transmission for every frequency in the frequency range  506  covered by the graph  501 . It can be readily seen that the multiplication product  507  at noise frequencies  508  is low because of the misalignment of these frequencies in the graph of FIG.  4 . 
     The relatively close alignment of the Doppler frequency distributions  403  in FIG. 4, result in a salient bulge in the multiplication result  507  within the Doppler Beat Frequency range  503 . The peak value of the multiplication result  507  within the Doppler Beat Frequency range  503  is the Apex of the Doppler Beat Frequencies  502 . The frequency at which this Apex  502  in the multiplication result  507  occurs is the Apex frequency  504 . The frequency distribution in proximity to this apex is identified and the centroid of the distribution is calculated, leading to the determination of the centroid frequency  509 . The centroid frequency  509  is used to calculate other quantities of interest such as the fluid flow velocity and the fluid flow rate. 
     The following discusses the mathematical principles underlying operations discussed in the textual description of the invention. The following derivation explains the principle of the Dual or Multiple Frequency Doppler flow meter. The general Doppler formula is:        V   =           C   ·     (     Ftx   -   Frc     )         2   ·   Ftx   ·     cos        (   a   )                         let        :                   Df     =         (     Ftx   -   Frc     )                   then                 V     =       C   ·   Df       2   ·   Ftx   ·     cos        (   a   )                                      
     Where: C is the sonic velocity of the fluid or the speed of sound in the fluid; Ftx is the transmission frequency; Frc is the reflected frequency; Df is the Doppler Beat frequency; and cos(a) is the cosine of the angle of the incident beam relative to the direction of flow. 
     If ultrasonic beams are transmitted at two different frequencies into a constantly flowing fluid containing scatterers, the following relationship exists between the Doppler frequencies for the two different transmission frequencies.                    C   ·     Df   a         2   ·     Ftx   a     ·     cos        (   a   )           =       C   ·     Df   b         2   ·     Ftx   b     ·     cos        (   a   )                  
              Df   a       Ftx   a       =       Df   b       Ftx   b              
            Df   b     =         Ftx   b       Ftx   a       ·     Df   a                 Equation                 1                                
     Equation 1 proves the second Doppler signal is equal to the first Doppler signal multiplied by the ratio of the transmission frequencies. 
     It follows from Equation 1 that if: 
     the Doppler shifted frequency is proportional to the transmit frequency: 
     
       
         DfαFtx and 
       
     
     the sample time interval is inversely proportional to the transmit frequency:          1     Δ                 t          α                 Ftx                          
     then          1     Δ                 t          α                 Df                          
     or          d     Δ                 t       =   Df                          
     where d is some constant. 
     If          d     Δ                   t   a         =     Df   a                            
     and          d     Δ                   t   b         =     Df   b                            
     replace in equation 1:          d     Δ                   t   b         =       (       Ftx   b       Ftx   a       )          d     Δ                   t   a                                  
     Rearranging, we get:          Δ                   t   b       =       (       Ftx   a       Ftx   b       )        Δ                   t   a                              
     Then:                Δ                   t   b       =         Ftx   a       Ftx   b          Δ                   t   a               Equation                 2                                
     The time domain data entering from the mixer is sampled at time intervals of At and converted to frequency domain data using a Discrete Fourier Transform (DFT). The resulting frequency data is presented in intervals of Δω (note that  2 π f=Δω). 
     The frequency domain representation of the first set of sampling data is given by:            F   a          (     Δ                     ω   a     ·   k       )       =       ∑     n   =   0     N                         x   a          (     Δ                     t   a     ·   n       )       ·     W   N       (     Δ                     t   a     ·   n       )     ·     (     Δ                   ω   a        k     )                                    
     where:          W   N     =              -   j     ·   2   ·   π     N                              
     is a constant 
     A second DFT is performed on a second set of data having time interval Δt b , which is inversely proportional to the transmission frequency. This transform produces data for N+1 frequencies at intervals of Δω b . 
     The frequency domain representation of the second set of sampling data is given by:            F   b          (     Δ                     ω   b     ·   k       )       =       ∑     n   =   0     N                         x   b          (     Δ                     t   b     ·   n       )       ·     W   N       (     Δ                     t   b     ·   n       )     ·     (     Δ                   ω   b        k     )                                    
     The frequency intervals are equal to Δω*k in the exponent term (Δt*n)(Δω*k). Within the Doppler frequency range, the value of k at the maximum amplitude is labeled “kd”. The exponent value is then (Δt*n*Δω)*kd. 
     Inserting equations 1 and 2 into this exponent form, we get:            (     Δ                     t   b     ·   n   ·   Δ                     ω   b       )     ·   kd     =         [       (           Ftx   a       Ftx   b       ·   Δ                     t   a       )     ·   n     ]     ·     [       (           Ftx   b       Ftx   a       ·   Δ                     ω   a       )     ·   kd     ]       =       (     Δ                     t   a     ·   n   ·     Δω   a         )     ·   kd                              
     The maximum amplitude will therefor occur at the same increment, kd, in both DFTs. If the data is sampled at a rate proportional to the ratio of the transmit frequencies, the maximum Doppler beat signal for both DFTs will occur at the same frequency value Δω*kd. All other constant frequency sources (noise and other extraneous signals) will be shifted in the DFTs due to the difference in the sampling time intervals between the two DFTs. Correlating the two frequency spectra will produce a large apex at the frequency Δω*kd, clearly identifying the Doppler signal from all other signals. The centroid of this frequency can then be readily calculated. This centroid frequency will be treated as representing the velocity of the fluid. 
     The velocity is calculated using this centroid frequency with the general Doppler formula. The volumetric flow is then determined by multiplying by the velocity by the cross-sectional area of the pipe. 
     FIG. 6 illustrates a block diagram of an alternative embodiment of a flow meter  60  according to the present invention. In contrast to the embodiment of FIG. 1, this embodiment provides for more than two possible transmission frequencies. This would be useful in the event that a clearer and more accurate apex would be achievable with the addition of transmission frequencies beyond the first two. 
     Microprocessor  617  selects the desired transmission frequency from the Variable Frequency Signal Generator  608 . The signal is then converted into ultrasonic energy by the transducer  601  and transmitted through the pipe wall  105  into the fluid  107  containing scatterers  106 . Transducer  601  could include a plurality of piezoelectric transducers operating in different frequency ranges. 
     Reflected ultrasonic energy is received at Receiver  603  and there converted into an electrical signal. Receiver  603  could include a plurality of piezoelectric transducers operating in different frequency ranges. The electrical signal is then passed through controllable band-pass filter  613  whose characteristics are controlled by the Microprocessor  617 . The filtered signal is then subtracted from the currently active transmission frequency in the FM mixer  14 . 
     The signal resulting from the subtraction in Mixer  14  is then sampled at A/D Converter  16 . In a preferred embodiment, the sampling rate at the A/D converter is always the currently active transmission frequency divided by a constant “N”. Establishing this relationship between the A/D sampling rate and the transmission frequency obviates the requirement to perform the computationally demanding task of scaling frequency information in the DFT, while still ensuring that the sampling rate will remain high enough (i.e. above the Nyquist limit) to faithfully reproduce the frequencies appearing at the A/D converter  16 . 
     The A/D sampling data is continuously sent to microprocessor  617 , where sampling data associated with a particular transmission frequency is stored. The process of gathering data associated with a particular transmission frequency will be conducted at least twice, but can be conducted for an essentially unlimited number of frequencies. 
     The calculations of the DFTs, Correlation data, frequency distribution apex, and centroid frequency, as discussed in FIGS. 2,  3  and  4  are performed in the same manner in the embodiment of FIG.  6 . 
     An advantage presented by the embodiment of FIG. 6 is that if the centroid (velocity representing) frequency cannot be determined with sufficient precision, or if there is still noise data which disrupts the velocity calculation after an initial set of transmission frequencies has been employed, microprocessor  617  can decide to select and send yet another transmission frequency and collect sampling data associated therewith. The above process may continue until sampling data sufficient for accurate determination of the fluid velocity has been collected. 
     Another advantage presented by the embodiment of FIG. 6 is the ability to select transmission frequencies based on the material properties and the size of the scatterers. By way of example, fine particles reflect higher frequencies, while coarse particles reflect lower frequencies. 
     Of course, one skilled in the art will recognize that the hardware illustrated in FIG. 6 is merely one way to implement the present invention. Alternate hardware embodiments are readily apparent and are clearly within the scope of the present invention. 
     Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.