an embodiment of the present invention provides a method for processing a “ raw ” or filtered intracardiac signal , which may be unipolar or bipolar . typically the processing comprises fitting the intracardiac signal to a predetermined waveform , and deriving an annotation time of the signal from the fitted signal , rather than from the raw signal . typically , a unipolar signal is fitted to an equation representative of a single complete oscillation . a bipolar signal may be fitted to an equation representative of a difference of two single complete oscillations , typically separated by a temporal difference . in some embodiments the single complete oscillation corresponds to a differential of a gaussian function . an asymmetry factor may be applied to the differential , and in some embodiments the asymmetry factor corresponds to a gaussian function . the inventors have found that fitting raw or filtered signals to a predetermined equation , and measuring an annotation time from the fitted signals , reduces variation of the annotation times , as compared to annotation times determined directly from the raw or filtered signals . reference is now made to fig1 , which is a schematic illustration of an electrocardiograph ( ecg ) analysis system 20 , according to an embodiment of the present invention . system 20 receives at least one , and typically a plurality , of electrical signals from one or more electrodes positioned within an organ of a human patient . typically , the signals are received from a multiplicity of electrodes placed on one or more probes in the organ . for example , during an invasive procedure on a heart , a first probe with one or more electrodes may be positioned in a reference region of the heart , and used to sense a reference ecg signal from the region . a second probe having multiple electrodes may be used to detect and record other ecg signals from other regions of the heart . for simplicity and clarity , the following description , except where otherwise stated , assumes an investigative procedure that senses electrical signals from a heart 34 , using a single probe 24 . furthermore , a distal end 32 of the probe is assumed to have two substantially similar electrodes 22 a . 22 b . electrodes 22 a , 22 b , may be referred to herein as electrodes 22 . those having ordinary skill in the art will be able to adapt the description for multiple probes having one or more electrodes , as well as for signals produced by organs other than a heart . typically , probe 24 comprises a catheter which is inserted into the body of a subject 26 during a mapping procedure performed by a user 28 of system 20 . in the description herein user 28 is assumed , by way of example , to be a medical professional . during the procedure subject 26 is assumed to be attached to a grounding electrode 23 . in some embodiments , electrodes 29 may be attached to the skin of subject 26 , in the region of heart 34 . system 20 may be controlled by a system processor 40 , comprising a processing unit 42 communicating with a memory 44 . processor 40 is typically mounted in a console 46 , which comprises operating controls 38 . controls 38 typically include a pointing device 39 , such as a mouse or a trackball , that professional 28 uses to interact with the processor . the processor uses software , including a probe navigation module 30 and an ecg module 36 , stored in memory 44 , to operate system 20 . ecg module 36 comprises a reference ecg sub - module 37 and a map ecg sub - module 41 , whose functions are described below . results of the operations performed by processor 40 are presented to the professional on a display 48 , which typically presents a graphic user interface to the operator , a visual representation of the ecg signals sensed by electrodes 22 , and / or an image of heart 34 while it is being investigated . the software may be downloaded to processor 40 in electronic form , over a network , for example , or it may , alternatively or additionally , be provided and / or stored on non - transitory tangible media , such as magnetic , optical , or electronic memory . ecg module 36 is coupled to receive electrical signals from electrodes 22 . the module may also be coupled to receive signals from one or more of electrodes 29 . the ecg module is configured to analyze the signals and may present the results of the analysis in a standard ecg format , typically a graphical representation moving with time , on display 48 . probe navigation module 30 tracks sections of probe 24 while the probe is within subject 26 . the navigation module typically tracks both the location and orientation of distal end 32 of probe 24 , within the heart of subject 26 . in some embodiments module 30 tracks other sections of the probe . the navigation module may use any method for tracking probes known in the art . for example , module 30 may operate magnetic field transmitters in the vicinity of the subject , so that magnetic fields from the transmitters interact with tracking coils located in sections of the probe being tracked . the coils interacting with the magnetic fields generate signals which are transmitted to the module , and the module analyzes the signals to determine a location and orientation of the coils . ( for simplicity such coils and transmitters are not shown in fig1 .) the carto ® system produced by biosense webster , of diamond bar , calif ., uses such a tracking method . alternatively or additionally , navigation module 30 may track probe 24 by measuring impedances between electrode 23 , electrodes 29 and electrodes 22 , as well as the impedances to other electrodes which may be located on the probe . ( in this case electrodes 22 and / or electrodes 29 may provide both ecg and tracking signals .) the carto3 ® system produced by biosense webster uses both magnetic field transmitters and impedance measurements for tracking . fig2 shows schematic graphs of typical ecg signals processed by system 20 , according to an embodiment of the present invention . graphs 100 , 102 show exemplary potential vs . time plots of “ raw ” ( i . e ., unprocessed ) bipolar intracardiac ecg signals . the signals are assumed to be derived from the potential differences between electrode 22 a and electrode 22 b while the electrodes contact a wall of the heart . as is known in the art , intracardiac ecg signals are noisy , the noise typically being generated by a number of factors , such as line radiation , the proximity of other electrical equipment , and other electrical sources derived from patient 26 , such as patient muscular contraction ( apart from heart muscles ). the noise typically causes problems in making quantitative measurements of annotation times from the raw signals . for example , an annotation time , t p , comprising the time of the “ r ” peak of the signal , may be required , the time being measured from the onset of the signal . graph 100 illustrates that t p is measured to be approximately 30 ms , whereas graph 102 illustrates that t p is measured to be approximately 25 ms . as is illustrated in the graphs , the measured value of t p varies . as stated above , graphs 100 , 102 illustrate bipolar graphs generated by difference signals between electrode 22 a and 22 b . the signal on each electrode 22 a or 22 b , when measured relative to a common reference electrode , is a unipolar signal , so that the bipolar signal may be considered as a difference between two unipolar signals . the reference electrode may be any convenient electrode , such as grounding electrode 23 , and / or one or more of skin electrodes 29 , and / or one or more other electrodes in contact with the heart . fig3 and 4 show schematic graphs produced by equations used for fitting to ecg signals , according to embodiments of the present invention . embodiments of the present invention fit a predetermined equation to signals such as the ecg signals illustrated in fig2 . the equation corresponds to a predetermined oscillating waveform , typically a waveform that is in the form of a single complete oscillation , i . e ., a waveform that has beginning and end points that have a substantially zero signal level , and that encompasses all the electrical activity between the two points . typically , the graph of a single complete oscillation has a single local minimum and a single local maximum . the local maximum and local minimum may be separated by a single inflection . in some embodiments , and as exemplified herein , the predetermined equation fitted to the signals is derived from the first differential of a gaussian function , skewed by an asymmetry factor . thus , for unipolar ecg signals received from electrodes 22 a or 22 b , processor 40 fits an equation having the general form given by equation ( 1 ) below to the signals : where v unipolar ( t ) represents the varying unipolar potential signal measured at the electrode at a time t ; t i is a temporal displacement of the signal , with respect to the time t = 0 . t i corresponds to the time when an activation wave passes through the electrode position ; t s is a parameter defining an asymmetry of the signal ; and inspection of equation ( 1 ) shows that the asymmetry factor provided by the equation corresponds to a gaussian function . thus , equation ( 1 ) sums a gaussian function and a first differential of a gaussian function . in the description below , parameters t i1 , a 1 , t s1 , and w 1 , are also referred to collectively as the unipolar fitting parameters of equation ( 1 ). graphs 110 , 112 , and 114 ( fig3 ) illustrate the effects of values of parameters t s and w on the waveform generated by equation ( 1 ). for simplicity , the units of the ordinate and the abscissa of each graph are assumed to be arbitrary . as shown by graph 110 , for t s = 0 , the graph has two - fold symmetry , having a center of symmetry at ( 3 , 0 ). ( in other words , under a rotation of 180 ° in the plane of the graph the graph transforms into itself .) graph 112 shows that for a positive value of t s = 3 , the graph becomes asymmetric . the asymmetry increases with increasing t s . as shown by graph 114 , the value of w changes the overall width of the graph , so that increasing the value of w reduces the width . if the ecg signal is a bipolar signal , it may be assumed to be generated by the difference between a unipolar signal v unipolar ( t ) 1 on electrode 22 a and a unipolar signal v unipolar ( t ) 2 on electrode 22 b . for bipolar signals such as these the processor fits an equation ( 2 ), derived from equation ( 1 ), to the signal : where v bipolar ( t ) represents the varying bipolar potential signal measured at the electrode at a time t ; v unipolar ( t ) 1 , v unipolar ( t ) 2 , also termed v 1 and v 2 , are as defined above for equation ( 1 ); t i1 , t i2 are temporal displacements of v 1 , v 2 ; t s1 , t s2 define asymmetries of v 1 , v 2 ; and for a bipolar signal there is a temporal difference , δt i = t i1 − t i2 , equal to a difference between the temporal displacements of the two unipolar signals v unipolar ( t ) 1 and v unipolar ( t ) 2 . the temporal difference between the two unipolar signals is typically a function of the spatial separation of the two electrodes generating the bipolar signal , and of an electrode orientation relative to a propagation direction of the activation wave . thus , in the case of two electrodes , at least a component of the propagation direction of the activation wave may be determined from the temporal difference of the unipolar signals . it will be appreciated that for more than two electrodes , the temporal differences between the respective unipolar signals detected by the more than two electrodes , as well as the positions of the electrodes , typically allow multiple components of the propagation direction to be found . from the multiple components , the propagation direction ( not just a component ) of the activation wave may be estimated . in the description below , parameters t i1 , t i2 , a 1 , a 2 , t s1 , t s2 , and w 1 , w 2 are also referred to collectively as the bipolar fitting parameters of equation ( 2 ). graphs 120 , 122 , and 124 ( fig4 ) illustrate the application of equation ( 2 ). graphs 120 and 122 are graphs of two unipolar equations of voltage vs . time , respectively having temporal displacements ( in arbitrary units ) of t = 3 and t = 4 . 5 , and widths of 4 and 2 . graph 124 is the graph of the difference of the two expressions , illustrating a bipolar voltage vs . time function having a temporal difference of δt = 4 . 5 − 3 = 1 . 5 . generated intracardiac unipolar and bipolar signals depend , inter alia , on the positions of the electrodes used to measure the signals . the generated signals also depend on the condition of the heart being measured , i . e ., whether the heart is functioning in a healthy or unhealthy manner . if a heart is unhealthy because of a specific defect , it also produces standard intracardiac signals , different from those of a healthy heart ( similar differences may be used in diagnoses using skin ecg signals , i . e ., body surface signals ). in the case of a specific defect , the unhealthy heart generates standard deficient unipolar or bipolar signals , the deficiency in the signals being caused by the respective heart defect . fig5 is a flowchart 200 showing steps performed by processor 40 in analyzing intracardiac signals , according to an embodiment of the present invention . in the following description the signals are assumed to comprise bipolar signals . those having ordinary skill in the art will be able to adapt the description , mutatis mutandis , for unipolar signals . in an initial step 202 , professional 28 inserts probe 24 into heart 34 , so that electrodes 22 a and 22 b are in contact with a section of the heart wall . processor 40 acquires intracardiac bipolar ecg signals from the electrodes , each ecg signal comprising ordered pairs of potentials v and times t : {( v , t )}. in a heartbeat selection step 204 , one complete heartbeat is selected . thus , if the duration of the selected heartbeat is t , and the acquisition in step 202 is performed at a sample rate samplerate , there are approximately t / samplerate samples of bipolar signals in the selected heartbeat . in an analysis step 206 , the processor fits equation ( 2 ) to the selected heartbeat to derive a set of values of the fitting parameters of equation ( 2 ) that give a best fit to the selected heartbeat . in a comparison step 208 , the processor uses navigation module 30 to check if electrodes 22 a and 22 b are in the same position with respect to the heart . if the comparison returns a positive result , so that the electrodes are in the same position , then in an averaging step 210 the processor averages the fitting parameters for all the heartbeats at the position , to generate a set of averaged fitting parameters . the flowchart then continues at an annotation time step 212 . if the comparison returns a negative result , so that the electrodes have moved , then no averaging is performed , and the flowchart continues directly to step 212 . in annotation time step 212 , the fitting parameters derived either in step 210 ( if averaging has occurred ) or in step 206 ( if there has been no averaging ) are used to estimate an annotation time . the annotation time is a reference time of occurrence of a characteristic of the ecg signal . the annotation time may be defined with respect to the body surface ecg , or with respect to an intracardiac reference ecg , for example from a catheter placed in the coronary sinus . typical signal characteristics used to define the reference annotation time include , but are not limited to , the time at which the r - peak maximum of the qrs complex occurs , the time at which the minimum derivative of the qrs complex occurs , the time at which a center of energy of the complete signal occurs , or the time at which a first indication of the complete signal occurs . the reference annotation time is typically dependent on the position in the heart at which the signal is measured . definitions for the reference annotation times and their values are stored in reference ecg sub - module 37 . in a map building step 214 , the processor constructs a point of an electro - anatomical map of heart 34 . to construct the map point , the processor incorporates the difference of annotation times estimated in step 212 and the relevant reference annotation time ( stored in sub - module 37 ) into a map of the heart ( using navigation module 30 ) ( fig1 ). sub - module 41 is also used in this step . the repetition of steps 202 - 214 is indicated by a continuation condition 216 returning a positive result . if condition 216 returns a negative result , typically by professional 28 deciding to stop the mapping procedure of step 214 , the flowchart ends . as stated above , steps 202 - 214 can be typically performed for different situations comprising different positions of the electrodes in healthy hearts and in unhealthy hearts with known defects . fig6 shows schematic graphs illustrating the results of applying the methods described above , according to an embodiment of the present invention . intracardiac ecg signals were recorded from several different cases , to create a data pool . approximately 5 , 900 heartbeats were extracted from the data pool . all heartbeats were organized into eleven groups , each group containing a heartbeat with an amplitude less than a pre - determined threshold . the threshold is a measure of the noise of the signal , so that signals having lower thresholds have higher noise levels . for each heartbeat in a specific group the time of occurrence t rk of the r - peak maximum , and the time of occurrence t ck of the passing of the activation wave , were estimated . k is an index representing a number of the heartbeat being measured . t ck was estimated using a fitting analysis similar to that described for flowchart 200 , herein also referred to as a fit annotation method . the method for estimating t rk is also referred to herein as the maximum annotation method . where σ ( δt ) is a standard deviation of all δt values , and the expressions of equations ( 4 ) give a measure of the variability of the annotation times by the maximum annotation method or by the fit annotation method of heartbeats within a given group . a graph 300 plots the variability var r vs . the threshold of a group , and a graph 302 is a linear regression of graph 300 . a graph 310 plots the variability var c vs . the threshold of a group , and a graph 312 is a linear regression of graph 310 . by comparison of the two sets of graphs , it is apparent that for low values of the threshold , i . e ., for signals with high noise values , the variability of the signals processed according to methods described herein , i . e ., using the fit annotation method , is less than the variability of signals that have not been processed with these methods . it will be appreciated that the embodiments described above are cited by way of example , and that the present invention is not limited to what has been particularly shown and described hereinabove . rather , the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove , as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art .
a method for analyzing signals , including : sensing a time - varying intracardiac potential signal and finding a fit of the time - varying intracardiac potential signal to a predefined oscillating waveform . the method further includes estimating an annotation time of the signal responsive to the fit .