Abstract:
A transducer system with transducer and circuitry for applying a pulse train at a single frequency to excite the transducer. The transducer is operable to receive an echo waveform in response to the pulse train. The system also comprises circuitry for determining a time of flight as between a first reference time associated with the pulse train and a second reference time associated with the echo waveform.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
       [0001]    This application claims priority to, the benefit of the filing date of, and hereby incorporates herein by reference, U.S. Provisional Patent Application 62/205,821, entitled “METHOD AND SYSTEM FOR ULTRASOUND TIME-OF-FLIGHT MEASUREMENT,” and filed Aug. 17, 2015. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable. 
       BACKGROUND OF THE INVENTION 
       [0003]    The preferred embodiments relate to ultrasonic transducers and more particularly to a method and system for ultrasound time of flight (TOF) measurement. 
         [0004]    Ultrasound transducers are known in the art for transmitting ultrasound waves and detecting a reflection or echo of the transmitted wave. Such devices are also sometimes referred to as ultrasound or ultrasonic transducers or transceivers. Ultrasound transducers have myriad uses that produce an output or other result based on a distance determination from the operation of the transceiver, whereby the transceiver emits a series of pulses toward a target and then receives back an echo waveform of the signal off the target, and signal processing determines a distance to the target based in part on the elapsed timing between the transmitted pulses and the echo waveform. The output of such a system may be the distance determination itself, or the distance determination may be part of an additional determination or action based on the distance, such as displacement measurement, level sensing, material characterization, structure monitoring, vibration sensing, medical diagnostics, and the like. In any event, for various of these applications, precision of the distance measurement may be very important. 
         [0005]    By way of further background,  FIG. 1  illustrates a signal diagram of the operation of a typical prior art ultrasound transducer, in first transmitting a signal and then receiving an echo waveform. Specifically, at a time t 0 , an excitation pulse train is applied to the transducer, which in response transmits a corresponding ultrasonic pulse train signal, where both the applied and transmitted pulse trains consist of a number of pulses, such as 5 to 20 such pulses, shown beginning therefore at time t 0  and ending at time t 1 . The transmitted pulses are directed toward a target item, which reflects a signal back toward the transducer. Time passes as these signals pass along a channel or medium between the transducer and the target. This time may be referred to in the art as time of flight (TOF) and therefore occurs between times t 0  and t 2 . Note also that TOF may be measured as between offset times from either or both of times t 0  and t 2 . For example, rather than TOF starting at t 0  when the pulse train commences, it may be started later, such as when the pulse train completes. Similarly, rather than TOF ending at t 2  when the echo waveform commences, it may be ended later, such as when the echo waveform reaches a threshold. Additional details as to the latter are described later in this document. 
         [0006]    At time t 2 , the transducer begins to receive back an echo waveform WF 1  signal, reflected by the target, as shown by the echo waveform that begins at time t 2 . Echo waveform WF 1  is generally a sinusoid that starts at or near time t 2  with a relatively low amplitude and then the amplitude continues to increase for some amount of time. While not shown in  FIG. 1 , the waveform WF 1  (and amplitude) will eventually decay, although for sake of the teachings in this document the decay period is not of particular relevance as signal processing relies instead on the increasing amplitude period of the echo waveform WF 1 . Specifically, processing circuitry (e.g., a processor), associated with or coupled to the transducer, is operable to sample this received waveform WF 1  so as to develop a time reference from t 0  to a detected point in the waveform. This detected point is also sometimes referred to as TOF, although it occurs in the echo waveform after t 2 . Further, by detecting a certain time event in the waveform, a reference is created in one pulse repetition cycle (PRC), that is, in one instance of a pulse train followed by an echo waveform, so that this reference may be compared against a similar time reference in subsequent PRCs, whereby a change in reference thereby indicates a change in distance between the transducer and the target. In any event, there are various prior art approaches for detecting this time event in the echo waveform. 
         [0007]      FIG. 2  illustrates a signal diagram in connection with explaining one prior art approach for detecting a time reference in a received echo waveform. First in connection with  FIG. 2 , note that the echo waveform of  FIG. 1  is received, and it applied to a rectifier so that any negative portion of the signal is thereby converted to a positive signal, so that the entire sinusoid is at or above zero amplitude. Moreover, per one prior art approach, the waveform time reference for a PRC is determined once the amplitude (or magnitude, if not rectified) reaches a threshold THR. Thus, as shown in  FIG. 2 , this occurs at what is shown as a first TOF at t OF1 , that is, where the waveform amplitude reaches THR. In this approach, therefore, the first TOF at t OF1  becomes a first reference that may be compared to the reference TOF for comparably-performed time detections for subsequent (or earlier) PRCs. 
         [0008]      FIG. 3  illustrates a signal diagram in connection with explaining another prior art approach for detecting a time reference in a received echo waveform WF 1 , and for sake of contrast the first TOF at t OF1  from  FIG. 2  is also copied into  FIG. 3 . In  FIG. 3 , an envelope detector is also used to process the echo waveform, thereby creating an envelope ENV 1  signal or measure, as shown by an additional dashed line in  FIG. 3 . Moreover, per this prior art approach, the waveform time reference for a PRC is determined once the envelope reaches the threshold THR. Thus, in  FIG. 3 , this occurs at what is shown as a TOF at t OF2 , that is, where the waveform envelope ENV 1  reaches THR. Note, however, that the envelope reaches the threshold THR at t OF2 , which is before the actual increasing amplitude of the echo waveform does so at t OF1 . Thus, the envelope ENV 1  has a smoothing and interpolating function as between the successive increasing amplitude signal swings of the waveform so as to give a better approximation of when the energy of the waveform exceeds the threshold THR, and may provide better detection thereof, as compared to the approach of  FIG. 2 . 
         [0009]    While the envelope approach of  FIG. 3  performs better than the amplitude approach of  FIG. 2 ,  FIG. 4  illustrates a limitation of the envelope approach. Specifically,  FIG. 4  includes the same waveform WF 1  (and its envelope ENV 1 ) of  FIGS. 1 and 3 , but to make the illustration clear that waveform is shown in a dashed line. Particularly,  FIG. 4  also illustrates a second waveform WF 2  intending to depict the echo waveform from a second set of transmitted pulses (i.e., a second PRC). As shown in  FIG. 4 , therefore, the second waveform WF 2  has a slightly increased amplitude, as compared to the first waveform WF 1 . Such a response may be received due to noise or the shape or size of the target. With the increase in amplitude in the second waveform WF 2 , then its envelope ENV 2  necessarily increases in value at a faster rate than that of the envelope ENV 1  of the first waveform WF 1 . Thus, note in  FIG. 4  that the time when the envelope ENV 2  crosses the threshold THR occurs at t OF4 , which is earlier than the t OF2  time that envelope ENV 1  (of waveform WF 1 ) crossed that threshold. Note that such a change in detected timing, therefore, can create erroneous results in the distance measure of the transducer system. Specifically, even if the target did not move from the time of the first PRC to the time of the second PRC, the system detects a change in TOF (i.e., between t OF4  and t OF2 ), which is thereby interpreted as a change in distance as between the PRCs. Thus, the noise or other cause in the amplitude variations between successive PRCs creates error in the distance measure. 
         [0010]    Given the preceding, the preferred embodiments seek to improve upon the prior art, as further detailed below. 
       BRIEF SUMMARY OF THE INVENTION 
       [0011]    In a preferred embodiment, there is a transducer system. The system comprises a transducer and circuitry for applying a pulse train at a single frequency to excite the transducer. The transducer is operable to receive an echo waveform in response to the pulse train. The system also comprises circuitry for determining a time of flight as between a first reference time associated with the pulse train and a second reference time associated with the echo waveform. The circuitry for determining comprises: (i) circuitry for estimating an amplitude waveform envelope for at least a portion of the echo waveform; (ii) circuitry for identifying a first time when the amplitude waveform envelope reaches a threshold; and (iii) circuitry for adjusting the first time to the second reference time, in response to a phase of the echo waveform. 
         [0012]    Numerous other inventive aspects are also disclosed and claimed. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         [0013]      FIG. 1  illustrates a signal diagram of the operation of a typical prior art ultrasound transducer, in first transmitting a signal and then receiving an echo waveform. 
           [0014]      FIG. 2  illustrates a prior art received rectified echo waveform evaluated for when the signal amplitude reaches a threshold. 
           [0015]      FIG. 3  illustrates a prior art received echo waveform evaluated for when an envelope of the signal amplitude reaches a threshold. 
           [0016]      FIG. 4  illustrates a prior art received echo waveform evaluated for when an envelope of the signal amplitude reaches a threshold, wherein successive instances of the echo waveform have differing envelopes. 
           [0017]      FIG. 5  illustrates a block diagram of a transducer  10  according to a preferred embodiment. 
           [0018]      FIG. 6  illustrates a flowchart of a method of operation of the system from  FIG. 5 . 
           [0019]      FIG. 7  illustrates a sampled reflected echo waveform according to a preferred embodiment and for which a waveform envelope is evaluated to detect when a threshold is reached. 
           [0020]      FIG. 8  illustrates a plot of phase versus time of a linear regression fit for three lines corresponding to respective 2π periods of the waveform of  FIG. 7 . 
           [0021]      FIG. 9  illustrates a functional block diagram to summarize preferred embodiment implementation details. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0022]      FIGS. 1 through 4  were described in the earlier Background of the Invention section of this document and the reader is assumed to be familiar with the principles of that discussion. 
         [0023]      FIG. 5  illustrates a block diagram of transducer system  10  according to a preferred embodiment. System  10  includes an ultrasonic transducer  12  that for illustrative purposes is shown having a transmitting T and receiving R element, where those elements may be combined as known in the art. Transducer  12  is constructed of known (e.g., piezoelectric) materials and is operable to transmit ultrasound waves toward a target  14  and receives an echo waveform in response to reflections of the transmitted signal. More specifically, a processor  16  is coupled (e.g., via general purpose input/output GPIO) to an optional voltage booster  18 , whereby processor  16  can output a pulse width modulated pulse train that is thereby voltage boosted and applied to the transmitting element T of transducer  12 . The voltage boosted and pulsing input signal causes vibrations in the material of the transmitting element T of transducer  12 , thereby emitting a typically directional wave signal toward target  14 . When an echo waveform is reflected back to the receiving element R of transducer  12 , that receiving element R responds with an electrical signal corresponding to the echo waveform. In system  10 , the echo waveform is applied to a gain stage  20 , which in a preferred embodiment amplifies the signal and also performs an analog-to-digital (ADC) conversion. The resultant digital signal is then connected to processor  16 , which samples the digital signal at some desired sampling frequency, f S , and processor  16  is further programmed to perform additional processing of the digital samples as detailed in the remainder of this document. Among such processing, processor  16  is able to determine an indication of time of flight (TOF) between the transmitted pulse signal and the received echo waveform (or a reference point in that waveform), thereby representing a distance between transducer  12  and target  14 , where that distance may be the desired output from processor  16  or may be further processed in connection with other common transducer applications which process the distance measure further for additional determinations. 
         [0024]      FIG. 6  illustrates a flowchart of a method  30  of operation of processor  16  from system  10 , as may be implemented with appropriate software instructions stored in or accessible by, and or via hardware/firmware of, processor  16 , or any combination thereof. Method  30  commences with a step  32 , where system  10  transmits an excitation pulse train such as shown in  FIG. 1 , where for reference the frequency of the pulses is referred to a f PT . Thus, in system  10 , processor  16  outputs the pulse train via GPIO, and it is optionally boosted by booster  18  and applied to the transmitting element T of transducer  12 . In response, ultrasonic waves are directed toward target  14 , and an echo waveform, also having a frequency of f PT , is reflected back toward the receiving element R of transducer  12 . For continuing discussion in this document,  FIG. 7  illustrates such a reflected echo waveform WF 3 , which as introduced earlier has an increasing amplitude for a period of time after which it will begin to decay. Next, method  30  continues to step  34 . 
         [0025]    In step  34 , processor  16  captures digital values (i.e., samples) of the reflected waveform amplitude into on-chip or off-chip memory, preferably at an integer multiple IM of f PT  so that IM samples are captured for each period of transmitted pulse; in one preferred embodiment, IM=4, so the sampling frequency, f S , for step  34  is 4*f PT . In  FIG. 7 , therefore, for each 2π period of the generally sine wave shape of waveform WF 3 , four circles are shown along each 2π wave period, each intending to illustrate a respective one of four samples captured during that period and per step  34 . Note that for each digital captured sample amplitude, also stored is the timing of the sample. Such timing may be determined by a count either of processor clock cycles or by a sequentially incrementing number of samples captured, as knowledge of the number of a sample necessarily can provide the timing of the sample by multiplying the sample number times the sample period, T S =1/f S . Next, method  30  continues to step  36 . 
         [0026]    In step  36 , the peak of the received samples is identified as the sample indicating the largest amplitude (i.e., largest absolute value), where a later discussion indicates the determination of amplitude given a sample value. Once the peak is identified, a number of samples within a time window centered about the time of the detected peak are retained (e.g., in memory) for processing. The width of the time window may be selected by one skilled in the art. For example, in one preferred embodiment, the time window equals twice the length of time, T W , to transmit the pulses in step  32  (e.g., from t 0  to t 1  in  FIG. 1 ). Next, method  30  continues to step  38 . 
         [0027]    In step  38 , a waveform envelope, shown by way of example in  FIG. 7  as envelope ENV 3 , is determined from the stored data samples remaining after step  36 . As shown graphically in  FIG. 7 , such an envelope generally represents a relatively smooth curve passing in proximity to the peak amplitude for each 2π period of waveform WF 3 . Various techniques may be selected for determining envelope ENV 3 , where as detailed later, in a preferred embodiment one method is to filter each sample as real data to provide an imaginary counterpart (e.g., I and Q data, respectively), and then trigonometry is used to determine an approximate sine wave amplitude in response. Further in step  38 , in addition to determining the envelope, detection is made of the time (either clock time or sample time) when the envelope ENV 3  crosses a threshold THR, as illustrated in  FIG. 7  to occur at a time t THR . The value of the threshold THR may be selected by one skilled in the art, such as at ½ the peak amplitude determined in step  36 ; for sake of illustrative purposes, however, in  FIG. 7  the threshold THR is shown larger than ½ of the peak, so as to facilitate the remaining discussing of inventive aspects. Next, method  30  continues to step  40 . 
         [0028]    In step  40 , a linear regression is performed to determine the phase of ±N step  34  (or step  36 ) samples, where those samples occurred relative to the time when the step  38  peak was determined. In one preferred embodiment N=10, so the phase is determined on 10 samples before t THR  and the phase is determined on 10 samples after t THR . Various techniques for determining phase also may be selected by one skilled in the art, and as introduced earlier where I and Q data are generated for each sample, then in that instance trigonometry also may be used to determine phase for each sample, as also detailed later. Thus, for each of the N samples, known or determined are its sample time st x  and its respective phase θS, which may be represented by a coordinate pair of its sample time and phase thereby creating a sample set with 2N coordinates, as [(st 0 , θS 0 ), (st 1 , θS 1 ), . . . (st 2N , θS 2N-1 ). In general, for a sinusoid of either fixed or varying amplitude, the wave may be described by the following Equation 1: 
         [0000]      amplitude= A  sin(θ S )= A  sin(2π( f )( st )+ø)  Equation 1
 
         [0000]    where, 
         [0029]    A is the peak amplitude, 
         [0030]    θS is the phase of a sample, 
         [0031]    f is the frequency of the waveform, which here is the same as the frequency, f PT , of the originally transmitted pulses; 
         [0032]    st is sample time; and 
         [0033]    ø is the phase offset (i.e., y-axis intercept). 
         [0000]    Note, therefore, that the parenthetical of (2π(f)(st)+ø) in Equation 1 is a line (i.e., typically referred to in geometry as y=mx+b) having slope of m=2πf and a y-intercept of b=ø. In this regard, therefore, and by definition, linear regression will model or fit a line to the phase of the sampled data and matching the parenthetical of Equation 1, depicting the increasing phase, among the 2N (e.g., 20) samples. In this regard,  FIG. 8  illustrates a plot of sample phase along the vertical axis and sample time along the horizontal axis, with a first phase line PL THR  that results from the above-described linear regression. Thus, from samples shown also in  FIG. 8  by way of circles both before and after time t THR , line phase line PL THR  is best fit to those samples, although to simplify the drawing only six samples are shown, rather than 20. Since phase and time are known for each sample in the set, then this line may be defined and extrapolated as desired, for example to provide the phase offset ø (i.e., y-axis intercept). Note therefore that while a sample may not have occurred at time t THR  since that time is detected from an envelope amplitude, rather than a single sample amplitude, exceeding a threshold THR, then the line PL THR  thereby estimates phase and timing other than at the finite sample times. Thus, an estimated phase {circumflex over (θ)} can be determined from the line PL THR  as of the time t THR . In addition, therefore, the line PL THR  also indicates phase and timing for other points along the line, as will be useful as further described below. Next, method  30  continues to step  42 . 
         [0034]    In step  42 , processor  16  estimates a time of the zero-phase crossing of waveform WF 3  that corresponds to the ±N data samples closest to time t THR . Thus, looking to  FIG. 7 , where time t THR  occurs during a 2π period for waveform WF 3 , then step  42  attempts to determine the time t ZCTHR  of the zero phase crossing that occurred at the beginning of the 2π period during which t THR  occurred. In a preferred embodiment, step  42  is accomplished using the linear regression result from step  40 , as is further appreciated with respect to  FIG. 8 . Specifically, recall that step  42  produced line PL THR , a linear fit to phase data of the ±N data samples closest to time t THR . As a result, this line extends to and intersects with the 0 radian axis, that is, where the estimated phase {circumflex over (θ)} equals zero. Graphically and computationally, therefore, the zero crossing of the phase axis (i.e., when phase equals 0) may be determined given Equation 1 as modeled by line PL THR , namely, by rearranging the parenthetical of Equation 1 as shown in the following Equation 2: 
         [0000]      0=(2π( f   PT )( st )+ø)  Equation 2
 
         [0000]    Rearranging Equation 2 to solve for the time when the zero crossing occurs gives the following Equation 3: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       - 
                       ∅ 
                     
                     
                       2 
                        
                       
                         π 
                          
                         
                           ( 
                           
                             f 
                             PT 
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     t 
                     ZCTHR 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0035]    Given the preceding, note that t ZCTHR  provides a reference time relative to waveform WF 3 , where that reference relates to phase (i.e., as defined by zero-crossing) of the waveform WF 3 , rather than solely to its amplitude. In this manner, therefore, a preferred embodiment may calculate TOF as to this reference time, and thereafter distance is a straightforward relationship to rate (i.e., speed of sound) times TOF. The distance measurement therefore is responsive to a phase-related timing as between successive received echo waveforms, that is, so long as the target  14  is not moving, while the amplitude of successive echo waveforms may vary, the phase as between such successive echo waveforms is typically constant, absent any disturbance or change in the channel between transducer  12  and target  14 . Thus, the preferred embodiment, in determining distance based on phase, is more accurate than prior art, amplitude-detecting-only, schemes. Moreover, in the preferred embodiment the echo waveform is efficiently created from a single frequency transmission of a pulse train. Still further, and as detailed below, an additional aspect of a preferred embodiment can incorporate still further considerations so as to reduce the chance of phase (or cycle) slip, further improving the accuracy of the resultant distance measurement, as is accomplished as shown in remaining steps in method  30 , which next proceeds to step  44 . 
         [0036]    It is recognized in connection with a preferred embodiment that cycle slip may occur as between successively-received echo waveforms, that is, an erroneous detection of a single cycle away from the actual cycle in which the threshold is exceeded corresponds to one wavelength in error measurement; for example, for 40 kHz, one wavelength (i.e., λ) is 8.5 mm, so a cycle slip of a single cycle will result in a distance calculation error of 8.5 mm, which is a very large error for high resolution systems. Such an error is more likely to occur in prior art where envelope detectors are used to evaluate the reaching of a threshold. In contrast, therefore, the preferred embodiment, by identifying a zero crossing as revealed by the phase of the echo waveform, can detect changes in distance to the target as low as fractions of the wavelength λ, thereby providing the ability to detect movement down to the 100 um levels, meaning the preferred embodiment can detect very small shifts in target distance, as low as 1/85th of the wavelength, for example. This is traditionally not achievable using envelope methods, since changes in envelope at such small displacements are usually not a very robust indicator, whereas the preferred embodiment can capture such changes by evaluating relative to phase variations, rather than amplitude envelope variations. In this regard, step  44  is directed at reducing the chance for cycle slip, as may occur if t THR  was particularly close to the 2π period of the echo waveform immediately before the period in which t THR  occurred, or likewise if t THR  was particularly close to the 2π period of the echo waveform immediately after the period in which t THR  occurred. To mitigate the possibility of cycle slip, step  44  determines two additional zero crossing times, one designated as t ZCTHR−  as the zero crossing for the 2π period of the echo waveform immediately before the period in which t THR  occurred, and one designated as t ZCTHR+  as the zero crossing for the 2π period of the echo waveform immediately after the period in which t THR  occurred. In one preferred embodiment, these two additional two zero crossings are readily achievable given line PL THR  in  FIG. 8 , as t ZCTHR−  will occur at one period earlier of the echo waveform relative to t ZCTHR , and t ZCTHR+  will occur at one period later of the echo waveform relative to t ZCTHR . Thus, in  FIG. 8 , a phase line PL THR−  is shown having a phase of 2π earlier than line PL THR , and a phase line PL THR+  is shown having a phase of 2π later than line PL THR . Moreover, phase line PL THR−  therefore has a respective zero crossing as t ZCTHR− , and phase line PL THR−  therefore has a respective zero crossing as t ZCTHR+ . Next, method  30  continues to step  46 . 
         [0037]    Step  46  determines a final reference time t final  to be used as the time reference to determine TOF for the determination of distance between transducer  12  and target  14 . Thus, whereas earlier in connection with step  42  it was noted that t ZCTHR  may be used for such a time reference, step  46  provides an alternative whereby one of either t ZCTHR− , t ZCTHR , or t ZCTHR+ , is selected as that reference time, so as to reduce the chance of cycle slip. In one preferred embodiment, this selection of reference time is as follows. 
         [0038]    It is noted that t THR  is not likely to occur exactly at a time of a sample, so in terms of sample time (i.e., an integer multiple of the time when a sample is taken), then t THR  is a fractional value, that is, some non-integer multiple of sample time. Hence, to improve the fractional delay part of t THR  toward a final time reference to determine TOF, a preferred embodiment determines the fractional delay portion, t THRfrac , of t THR , according to the following Equation 4: 
         [0000]        t   THRfrac   =t   THR −roun( t   THR )  Equation 4
 
         [0039]    Next, the preferred embodiment calculates the time difference between the fractional delays derived from the envelope and phase, so as to improve robustness of the fractional delay computation to mitigate cycle slips due to 2π uncertainty in phase. This sub-step determines if the envelope time crossing at time t THR  falls within the same 0 to 2π radians of the waveform WF 3  period when t THR  occurred, or if it was closer to the immediately-preceding 2π cycle or to the immediately-following 2π cycle, depending on when the t THR  crossing happened. Hence, three differential values are determined, as shown in the following Equations 5 through 7: 
         [0000]      Δ t   ZCTHR−   =t   THRfrac   −t   ZCTHR−   Equation 5
 
         [0000]      Δ t   ZCTHR   =t   THRfrac   −t   ZCTHR   Equation 6
 
         [0000]      Δ f   ZCTHR+   =t   THRfrac   −t   ZCTHR+   Equation 7
 
         [0040]    Next, the preferred embodiment selects from the results of Equations 5 through 7 the one fractional delay estimate from phase that is closest to the fractional delay estimate from the envelope, as shown in the following Equation 8, selecting the minimum of the absolute values listed therein: 
         [0000]      t fracfinal =min[abs(Δ f   ZCTHR−   ,Δt   ZCTHR   ,Δt   ZCTHR+ )]  Equation 8
 
         [0041]    Finally, the preferred embodiment computes the final absolute time reference for use in the TOF determination by correcting the original t THR  estimate (from when the envelope waveform reached threshold THR) with the newer estimate, as shown in Equation 9: 
         [0000]        t   final   =t   THR   −t   fracfinal   Equation 9
 
         [0042]    Given the results of Equation 9, step  48  determines the distance from transducer  12  to target  14  using t final  as the ultimate timing reference, again in that distance relates to TOF and the speed of sound, as shown in the following Equation 10: 
         [0000]      target distance=( t   final   −t   0 )* c/ 2  Equation 10
 
         [0000]    where, 
         [0043]    t 0  is the time when the pulse train began transmission (see  FIG. 1 ); and 
         [0044]    c is the speed of sound. 
         [0000]    Note also that the calculation may include some offset from the result of this product because the detected time reference is not the beginning of the echo waveform (t 2  in  FIG. 1 ), where the offset can be removed as a constant bias (i.e., calibration constant). Note also that any other potential cycle slips due to noise can be cleaned up by using a 3/N-tap median filter at the cost of latency, as the application demands. 
         [0045]      FIG. 9  illustrates a functional block diagram to summarize various of the above teachings and to complete various additional detail as to certain preferred embodiment implementation details. In general, therefore,  FIG. 9  again illustrates, from  FIG. 5 , transducer  12  and the receiver portion communicating a signal to gain stage  20 , where recall the signal is amplified and converted from analog to digital and connected to processor  16 . In  FIG. 9 , processor  16  is shown in dashed outline, so as to further illustrate various computational functions that may be implemented by software programming and/or hardware on processor  16 , either alone or in conjunction with other devices communicating with processor  16 . 
         [0046]    Turning to the functionality achieved in processor  16  so as to perform method  30  of  FIG. 6 , a digital bandpass filter  50  processes the received signal so as to eliminate noise beyond certain frequencies, based on the expected operating frequency bandwidth of transducer  12 . For example, bandpass filter  50  may filter the signal so as to pass the pulse waveform frequency f PT ±2 kHz. The filtered signal therefore provides a real component, which is treated as the I data of the eventual I/Q data pair. This real data, I, is coupled to a Hilbert filter  52  (or other discrete Fourier transformation) to convert the real signal to I/Q data, that is, to provide the Q data counterpart. Both the I data (from bandpass filter  50 ) and the Q data (from Hilbert filter  52 ) are connected to an amplitude determination block  54  and a phase angle detection block  56 . For each sample (I,Q), amplitude determination block  54  determines the amplitude A (in Equation 1) given an understanding of phase vectors in the complex plane, whereby the Pythagoras equation shown in  FIG. 9  determines the wave amplitude as the hypotenuse length given the sampled size of I and Q. Note, therefore, that this amplitude provides a measure of envelope ENV 3  in  FIG. 7 , as the amplitude rises with the increase of the sine wave amplitude (and likewise later decays). Thus, this amplitude is connected as one input to a comparator  58 , which compares that amplitude to its second input, the threshold THR value, so as to achieve step  38  in  FIG. 6 . At the same time, also for each sample (I,Q), phase angle detection block  56  determines the momentary phase θ (in Equation 1) based on the arctangent of Q relative to I. Thus, for each sample (I,Q), the sample time st, of the sample is known and the respective momentary phase θ x  is determined, thereby providing the above discussed sample set with 2N coordinates, as [(st 0 , θS 0 ), (st 1 , θS 1 ), . . . (st 2N , θS 2N-1 ). With this information, the remaining steps  40  through  46  of  FIG. 6  may be accomplished by a TOF estimator  60 , from which a distance determination may be concluded per step  48  of  FIG. 6 . 
         [0047]    From the above, the preferred embodiments are shown to provide a an improved ultrasonic transducer system and method for ultrasound time of flight (TOF) measurement and the resultant distance determination therefrom. The preferred embodiments have been shown in a favorable implementation with respect to distance detection, but note numerous aspects may apply to other systems that render additional processing from the TOF information. In view of the above, therefore, while various alternatives have been provided according to the disclosed embodiments, still others are contemplated and yet others can ascertained by one skilled in the art. Given the preceding, therefore, one skilled in the art should further appreciate that while some embodiments have been described in detail, various substitutions, modifications or alterations can be made to the descriptions set forth above without departing from the inventive scope, as is defined by the following claims.