Apparatus and method to calibrate one or more transducers in a noisy environment

A method to calibrate a servo sensor disposed on a magnetic tape head disposed adjacent a magnetic tape moving along a tape path, wherein said magnetic tape includes at least one servo edge comprising an interface between a first recorded signal and a second recorded signal, wherein said servo sensor detects said first recorded signal and said second recorded signal, and wherein an independent position sensor provides an IPS signal comprising the position of said tape head with respect to said tape path, said method comprising the steps of:

• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• providing an IPS signal;
• providing a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining at each of four harmonics of that reference frequency the real and imaginary components of said measured servo signal waveform;
• calculating the magnitude M of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• calculating the phase φ of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• forming a filtered servo signal ratio waveform using the equation
• 6 M servo ⁡ ( 0 ) + ∑ M servo ⁡ ( i ) * cos [ φ servo ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein Mservo(0) comprises the DC component of said measured servo signal waveform, and wherein (i) is an integer greater than or equal to 1 and less than or equal to 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining at four harmonics of that reference frequency the real and imaginary components of said measured IPS signal waveform;
• calculating the magnitude MIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• calculating the phase φIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• forming a filtered IPS signal waveform using the equation
• 7 ∑ M IPS ⁡ ( i ) * cos [ φ IPS ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein (i) is an integer between 1 and 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining a plurality of actual datapoints;
• forming an X/Y array comprising said plurality of actual datapoints;
• calculating a transfer function using a third order curve fitting algorithm and said X/Y array;
• determining a plurality of calculated datapoints using said transfer function;
• determining if said transfer function models said actual datapoints;
• and
• operative if said transfer function models said actual datapoints, calculating using said transfer function one or more expected position error signals.

An article of manufacture comprising a computer useable medium having computer readable program code disposed therein for calibrating a servo sensor disposed on a magnetic tape head disposed adjacent a moving magnetic tape, wherein said magnetic tape includes at least one servo edge comprising an interface between a first recorded signal and a second recorded signal, wherein said servo sensor is capable of detecting said first recorded signal and said second recorded signal, and wherein an independent position sensor provides an IPS signal comprising the lateral position of said magnetic tape with respect to said tape head, the computer readable program code comprising a series of computer readable program steps to effect:

• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• providing an IPS signal;
• providing a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining at (P) harmonics of said reference frequency the real components and the imaginary components of said measured servo signal waveform;
• forming a filtered servo signal waveform;
• determining at (P) harmonics of said reference frequency the real components and imaginary components of said measured IPS signal waveform;
• forming a filtered IPS signal waveform;
• calculating a transfer function comprising the mathematical relationship between said filtered IPS signal waveform and said filtered servo signal waveform;
• and
• calculating one or more expected position error signals using said transfer function.

An article of manufacture comprising a computer useable medium having computer readable program code disposed therein for calibrating a servo sensor disposed on a magnetic tape head disposed adjacent a moving magnetic tape, wherein said magnetic tape includes at least one servo edge comprising an interface between a first recorded signal and a second recorded signal, wherein said servo sensor is capable of detecting said first recorded signal and said second recorded signal, and wherein an independent position sensor provides an IPS signal comprising the lateral position of said magnetic tape with respect to said tape head, the computer readable program code comprising a series of computer readable program steps to effect:

• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• providing an IPS signal;
• providing a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining at each of four harmonics of that reference frequency the real and imaginary components of said measured servo signal waveform;
• calculating the magnitude M of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• calculating the phase φ of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• forming a filtered servo signal ratio waveform using the equation
• 10 M servo ⁡ ( 0 ) + ∑ M servo ⁡ ( i ) * cos [ φ servo ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein Mservo(0) comprises the DC component of said measured servo signal waveform, and wherein (i) is an integer greater than or equal to 1 and less than or equal to 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining at four harmonics of that reference frequency the real and imaginary components of said measured IPS signal waveform;
• calculating the magnitude MIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• calculating the phase φIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• forming a filtered IPS signal waveform using the equation
• 11 ∑ M IPS ⁡ ( i ) * cos ⁡ [ φ IPS ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein (i) is an integer between 1 and 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining a plurality of actual datapoints;
• forming an X/Y array comprising said plurality of actual datapoints;
• calculating a transfer function using a third order curve fitting algorithm and said X/Y array;
• determining a plurality of calculated datapoints using said transfer function;
• determining if said transfer function models said actual datapoints;
• and
• operative if said transfer function models said actual datapoints, calculating using said transfer function one or more expected position error signals.

A computer program product usable with a programmable computer processor having computer readable program code embodied therein to calibrate a servo sensor disposed on a magnetic tape head disposed adjacent a moving magnetic tape, wherein said magnetic tape includes at least one servo edge comprising an interface between a first recorded signal and a second recorded signal, wherein said servo sensor is capable of detecting said first recorded signal and said second recorded signal, and wherein an independent position sensor provides an IPS signal comprising the lateral position of said magnetic tape with respect to said tape head, comprising:

• computer readable program code which causes said programmable computer processor to move said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• computer readable program code which causes said programmable computer processor to provide an IPS signal;
• computer readable program code which causes said programmable computer processor to provide a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• computer readable program code which causes said programmable computer processor to provide a sampling rate;
• computer readable program code which causes said programmable computer processor to sample said servo signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to sample said IPS signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to provide a measured servo signal waveform;
• computer readable program code which causes said programmable computer processor to provide a measured IPS signal waveform;
• computer readable program code which causes said programmable computer processor to determine the real components and the imaginary components of said measured servo signal waveform;
• computer readable program code which causes said programmable computer processor to form a filtered servo signal waveform;
• computer readable program code which causes said programmable computer processor to determine the real components and imaginary components of said measured IPS signal waveform;
• computer readable program code which causes said programmable computer processor to form a filtered IPS signal waveform;
• computer readable program code which causes said programmable computer processor to calculate a transfer function comprising the mathematical relationship between said filtered IPS signal waveform and said filtered servo signal waveform;
• and
• computer readable program code which causes said programmable computer processor to calculate one or more expected position error signals using said transfer function.

A computer program product usable with a programmable computer processor having computer readable program code embodied therein for to calibrate a servo sensor disposed on a magnetic tape head disposed adjacent a moving magnetic tape, wherein said magnetic tape includes at least one servo edge comprising an interface between a first recorded signal and a second recorded signal, wherein said servo sensor is capable of detecting said first recorded signal and said second recorded signal, and wherein an independent position sensor provides an IPS signal comprising the lateral position of said magnetic tape with respect to said tape head, comprising:

• computer readable program code which causes said programmable computer processor to move said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• computer readable program code which causes said programmable computer processor to provide an IPS signal;
• computer readable program code which causes said programmable computer processor to provide a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• computer readable program code which causes said programmable computer processor to provide a sampling rate;
• computer readable program code which causes said programmable computer processor to sample said servo signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to sample said IPS signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to form a measured servo signal waveform;
• computer readable program code which causes said programmable computer processor to form a measured IPS signal waveform;
• computer readable program code which causes said programmable computer processor to determine at each of four harmonics of that reference frequency the real and imaginary components of said measured servo signal waveform;
• computer readable program code which causes said programmable computer processor to calculate the magnitude Mservo of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to calculate the phase φservo of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to form a filtered servo signal ratio waveform using the equation
• 14 M servo ⁡ ( 0 ) + ∑ M servo ⁡ ( i ) * cos ⁡ [ φ servo ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein Mservo(0) comprises the DC component of said measured servo signal waveform, and wherein (i) is an integer greater than or equal to 1 and less than or equal to 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• computer readable program code which causes said programmable computer processor to determine at four harmonics of that reference frequency the real and imaginary components of said measured IPS signal waveform;
• computer readable program code which causes said programmable computer processor to calculate the magnitude MIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to calculate the phase φIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to form a filtered IPS signal waveform using the equation
• 15 ∑ M IPS ⁡ ( i ) * cos ⁡ [ φ IPS ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein (i) is an integer between 1 and 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• computer readable program code which causes said programmable computer processor to determine a plurality of actual datapoints;
• computer readable program code which causes said programmable computer processor to form an X/Y array using said plurality of actual datapoints;
• computer readable program code which causes said programmable computer processor to calculate a transfer function using a third order curve fitting algorithm and said X/Y array;
• computer readable program code which causes said programmable computer processor to determine a plurality of calculated datapoints using said transfer function;
• computer readable program code which causes said programmable computer processor to compare said plurality of actual datapoints to said plurality of calculated datapoints;
• computer readable program code which causes said programmable computer processor to determine if said transfer function models said actual datapoints;
• and
• computer readable program code which, if said transfer function models said actual datapoints, causes said programmable computer processor to calculate using said transfer function one or more expected position error signals.

A servo system to calibrate one or more index positions for a magnetic tape, wherein said magnetic tape comprises at least one or more continuous servo edges comprising an interface between a first recorded signal and a second recorded signal, comprising:

• a tape head capable of moving alternatingly in a first direction and an opposing second direction along a first axis as said magnetic tape moves alternatingly in a third direction and an opposing fourth direction along a second axis, wherein said first axis and said second axis are substantially orthogonal,
• one or more servo sensors disposed on said tape head, wherein said one or more servo sensors are capable of detecting said first recorded signal and said second recorded signal;
• a servo detector, wherein said servo detector is capable of communication with each of said one or more servo sensors, and wherein said servo detector provides a servo signal comprising the ratio of the detected first recorded signal and the detected second recorded signal;
• an independent position sensor, wherein said independent position sensor provides an IPS signal comprising a measurement of the position of said tape head with respect to said tape path;
• a servo loop, wherein said servo loop is capable of moving said tape head in said first direction and in said second direction;
• logic, wherein said logic is capable of communicating with said servo detector, said independent position sensor, and said servo loop, said logic:
• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• receiving an IPS signal;
• receiving a servo signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining the real components and the imaginary components of said measured servo signal waveform;
• forming a filtered servo signal waveform;
• determining the real components and imaginary components of said measured IPS signal waveform;
• forming a filtered IPS signal waveform;
• calculating a transfer function comprising the mathematical relationship between said filtered IPS signal waveform and said filtered servo signal waveform;
• and
• calculating one or more expected position error signals using said transfer function.

A servo system to calibrate one or more index positions for a magnetic tape, wherein said magnetic tape comprises at least one or more continuous servo edges comprising an interface between a first recorded signal and a second recorded signal, comprising:

• a tape head capable of moving alternatingly in a first direction and an opposing second direction along a first axis as said magnetic tape moves alternatingly in a third direction and an opposing fourth direction along a tape path, wherein said first axis and said tape path are substantially orthogonal,
• one or more servo sensors disposed on said tape head, wherein each of said one or more servo sensors are capable of detecting said first recorded signal and said second recorded signal;
• a servo detector, wherein said servo detector is capable of communication with each of said one or more servo sensors, and wherein said servo detector provides a servo signal comprising the ratio of the detected first recorded signal and the detected second recorded signal;
• an independent position sensor, wherein said independent position sensor provides an IPS signal comprising a measurement of the position of said tape head with respect to said tape path;
• a servo loop, wherein said servo loop is capable of moving said tape head in said first direction and in said second direction;
• logic, wherein said logic is capable of communicating with said servo detector, said independent position sensor, and said servo loop, said logic:
• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• receiving an IPS signal;
• receiving a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining at each of four harmonics of that reference frequency the real and imaginary components of said measured servo signal waveform;
• calculating the magnitude Mservo of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• calculating the phase φservo of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• forming a filtered servo signal ratio waveform using the equation
• 18 M servo ⁡ ( 0 ) + ∑ M servo ⁡ ( i ) * cos ⁡ [ φ servo ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein Mservo(0) comprises the DC component of said measured servo signal waveform, and wherein (i) is an integer greater than or equal to 1 and less than or equal to 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining at four harmonics of that reference frequency the real and imaginary components of said measured IPS signal waveform;
• calculating the magnitude MIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• calculating the phase φIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• forming a filtered IPS signal waveform using the equation
• 19 ∑ M IPS ⁡ ( i ) * cos ⁡ [ φ IPS ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein (i) is an integer between 1 and 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• correlating said form a first calibration curve;
• determining a plurality of actual datapoints;
• forming an X/Y array using said plurality of actual datapoints;
• calculating a transfer function using a third order curve fitting algorithm and said X/Y array;
• determining a plurality of calculated datapoints using said transfer function;
• determining a plurality of calculated datapoints using said transfer function;
• determining if said transfer function models said actual datapoints;
• and
• operative if said transfer function models said actual datapoints, calculating using said transfer function one or more expected position error signals.

A tape drive for reading and/or writing information to a magnetic tape, wherein said magnetic tape comprises at least one or more continuous servo edges comprising an interface between a first recorded signal and a second recorded signal, comprising:

• a motion system capable of moving said magnetic tape alternatingly in a first direction and an opposing second direction along a tape path;
• a tape head capable of moving alternatingly in a third direction and an opposing fourth direction along a second axis, wherein said tape path and said second axis are substantially orthogonal,
• one or more servo sensors disposed on said tape head, wherein each of said one or more servo sensors are capable of detecting said first recorded signal and said second recorded signal;
• a servo detector, wherein said servo detector is capable of communication with each of said one or more servo sensors, and wherein said servo detector provides a servo signal comprising the ratio of the detected first recorded signal and the detected second recorded signal;
• an independent position sensor, wherein said independent position sensor provides an IPS signal comprising a measurement of the lateral position of said magnetic tape with respect to said tape head;
• a servo loop, wherein said servo loop is capable of moving said tape head in said third direction and in said fourth direction;
• logic, wherein said logic is capable of communicating with said servo detector, said independent position sensor, and said servo loop, said logic:
• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• receiving an IPS signal;
• receiving a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining at (P) harmonics of said reference frequency the real components and the imaginary components of said measured servo signal waveform;
• forming a filtered servo signal waveform;
• determining at (P) harmonics of said reference frequency the real components and imaginary components of said measured IPS signal waveform;
• forming a filtered IPS signal waveform;
• calculating a transfer function comprising the mathematical relationship between said filtered IPS signal waveform and said filtered servo signal waveform;
• and
• calculating one or more expected position error signals using said transfer function.

A tape drive for reading and/or writing information to a magnetic tape, wherein said magnetic tape comprises at least one or more continuous servo edges comprising an interface between a first recorded signal and a second recorded signal, comprising:

• a motion system capable of moving said magnetic tape alternatingly in a first direction and an opposing second direction along a tape path;
• a tape head capable of moving alternatingly in a third direction and an opposing fourth direction along a second axis, wherein said tape path and said second axis are substantially orthogonal,
• one or more servo sensors disposed on said tape head, wherein each of said one or more servo sensors is capable of detecting said first recorded signal and said second recorded signal;
• a servo detector, wherein said servo detector is capable of communication with each of said one or more servo sensors and wherein said servo detector provides a servo signal comprising the ratio of the detected first recorded signal and the detected second recorded signal;
• an independent position sensor, wherein said independent position sensor provides an IPS signal comprising a measurement of the position of said tape head with respect to said tape path;
• a servo loop, wherein said servo loop is capable of moving said tape head in said third direction and in said fourth direction;
• logic, wherein said logic is capable of communicating with said servo detector, said independent position sensor, and said servo loop, said logic:
• moving said tape head alternatingly in a first direction and an opposing second direction along a first axis as said tape moves along a second axis, wherein said first axis and said second axis are substantially orthogonal, wherein the position of said magnetic head along said first axis as a function of time comprises a periodic function having a reference frequency;
• receiving an IPS signal;
• receiving a servo signal comprising the ratio of said detected first recorded signal and said detected second recorded signal;
• establishing a sampling rate;
• sampling said servo signal at said sampling rate;
• sampling said IPS signal at said sampling rate;
• forming a measured servo signal waveform;
• forming a measured IPS signal waveform;
• determining at each of four harmonics of that reference frequency the real and imaginary components of said measured servo signal waveform;
• calculating the magnitude Mservo of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• calculating the phase φservo of said measured servo signal waveform at each of said four harmonics of said reference frequency;
• forming a filtered servo signal ratio waveform using the equation
• 22 M servo ⁡ ( 0 ) + ∑ M servo ⁡ ( i ) * cos ⁡ [ φ servo ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein Mservo(0) comprises the DC component of said measured servo signal waveform, and wherein (i) is an integer greater than or equal to 1 and less than or equal to 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining at four harmonics of that reference frequency the real and imaginary components of said measured IPS signal waveform;
• calculating the magnitude MIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• calculating the phase φIPS of said measured IPS signal waveform at each of the four harmonics of said reference frequency;
• forming a filtered IPS signal waveform using the equation
• 23 ∑ M IPS ⁡ ( i ) * cos ⁡ [ φ IPS ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ]
• wherein (i) is an integer between 1 and 4, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• correlating said form a first calibration curve;
• determining a plurality of actual datapoints;
• forming an X/Y array using said plurality of actual datapoints;
• calculating a transfer function using a third order curve fitting algorithm and said X/Y array;
• determining a plurality of calculated datapoints using said transfer function;
• determining a plurality of calculated datapoints using said transfer function;
• determining if said transfer function models said actual datapoints;
• and
• operative if said transfer function models said actual datapoints, calculating using said transfer function one or more expected position error signals.

A method to calibrate a transducer, wherein said transducer provides a first signal, and wherein a reference provides a reference signal, said method comprising the steps of:

• providing said first signal;
• providing said reference signal;
• establishing a sampling rate comprising a reference frequency;
• sampling said first signal at said sampling rate;
• sampling said reference signal at said sampling rate;
• forming a measured first signal waveform;
• forming a measured reference signal waveform;
• determining at (P) harmonics of said reference frequency the real components and the imaginary components of said measured first signal waveform;
• forming a filtered first signal waveform;
• determining at (P) harmonics of said reference frequency the real components and imaginary components of said measured reference signal waveform;
• forming a filtered reference signal waveform;
• calculating a transfer function comprising the mathematical relationship between said filtered reference signal waveform and said filtered first signal waveform;
• and
• forming a calibration curve using said transfer function.

A method to calibrate a transducer, wherein said transducer provides a first signal, and wherein a reference provides a reference signal, said method comprising the steps of:

• providing said first signal;
• providing said reference signal;
• establishing a sampling rate comprising a reference frequency;
• sampling said first signal at said sampling rate;
• sampling said reference signal at said sampling rate;
• forming a measured first signal waveform;
• forming a measured reference signal waveform;
• determining at four harmonics of said reference frequency the real components and the imaginary components of said measured first signal waveform using a Goertzel algorithm;
• calculating the magnitude Mfirst(i) of said measured first signal waveform at each of said four harmonics of said reference frequency;
• calculating the phase φfirst(i) of said measured first signal waveform at each of said four harmonics of said reference frequency;
• and
• forming a filtered first signal waveform using the equation
• 26 ∑ M first ⁡ ( i ) * cos ⁡ [ φ first ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ] ;
• wherein (i) is an integer greater than or equal to 0 and less than or equal to (P), wherein Mfirst(0) and cos[φfirst(0)+(2i+2)(π)(t)/x] represent a DC component, and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• determining at four harmonics of said reference frequency the real components and imaginary components of said measured reference signal waveform using a Goertzel algorithm;
• calculating the magnitude Mref(i) of said measured reference signal waveform at each of said four harmonics of said reference frequency;
• calculating the phase φref(i) of said measured reference signal waveform at each of said 4 harmonics of said reference frequency;
• forming a filtered reference signal waveform using the equation
• 27 ∑ M ref ⁡ ( i ) * cos ⁡ [ φ ref ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ] ;
• wherein (i) is an integer greater than or equal to 1 and less than or equal to (P), and wherein (t)/x is greater than or equal to 0 and less than or equal to 1.
• determining a plurality of actual datapoints;
• forming an X/Y array comprising said plurality of actual datapoints.
• using a third order curve fitting program to form a transfer function using said X/Y array;
• determining a plurality of calculated datapoints using said transfer function;
• comparing said plurality of actual datapoints with said plurality of calculated datapoints;
• forming a calibration curve using said transfer function.

A computer program product usable with a programmable computer processor having computer readable program code embodied therein to calibrate a transducer, wherein said transducer provides a first signal, and wherein a reference provides a reference signal, comprising:

• computer readable program code which causes said programmable computer processor to provide said first signal;
• computer readable program code which causes said programmable computer processor to provide said reference signal;
• computer readable program code which causes said programmable computer processor to provide a sampling rate comprising a reference frequency;
• computer readable program code which causes said programmable computer processor to sample said first signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to sample said reference signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to provide a measured first signal waveform;
• computer readable program code which causes said programmable computer processor to provide a measured reference signal waveform;
• computer readable program code which causes said programmable computer processor to determine at (P) harmonics of said reference frequency the real components and the imaginary components of said measured first signal waveform;
• computer readable program code which causes said programmable computer processor to form a filtered first signal waveform;
• computer readable program code which causes said programmable computer processor to determine at (P) harmonics of said reference frequency the real components and imaginary components of said measured reference signal waveform;
• computer readable program code which causes said programmable computer processor to form a filtered reference signal waveform;
• computer readable program code which causes said programmable computer processor to calculate a transfer function comprising the mathematical relationship between said filtered reference signal waveform and said filtered first signal waveform;
• and
• computer readable program code which causes said programmable computer processor to form a calibration curve using said transfer function.

A computer program product usable with a programmable computer processor having computer readable program code embodied therein to calibrate a transducer, wherein said transducer provides a first signal, and wherein a reference provides a reference signal, comprising:

• computer readable program code which causes said programmable computer processor to providing said first signal;
• computer readable program code which causes said programmable computer processor to providing said reference signal;
• computer readable program code which causes said programmable computer processor to establishing a sampling rate comprising a reference frequency;
• computer readable program code which causes said programmable computer processor to sampling said first signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to sampling said reference signal at said sampling rate;
• computer readable program code which causes said programmable computer processor to forming a measured first signal waveform;
• computer readable program code which causes said programmable computer processor to forming a measured reference signal waveform;
• computer readable program code which causes said programmable computer processor to determining at four harmonics of said reference frequency the real components and the imaginary components of said measured first signal waveform using a Goertzel algorithm;
• computer readable program code which causes said programmable computer processor to calculating the magnitude Mfirst(i) of said measured first signal waveform at each of said four harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to calculating the phase φfirst(i) of said measured first signal waveform at each of said four harmonics of said reference frequency;
• and
• computer readable program code which causes said programmable computer processor to forming a filtered first signal waveform using the equation
• 30 ∑ M first ⁡ ( i ) * cos ⁡ [ φ first ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ] ;
• wherein (i) is an integer greater than or equal to 0 and less than or equal to (P), and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• computer readable program code which causes said programmable computer processor to determining at four harmonics of said reference frequency the real components and imaginary components of said measured reference signal waveform using a Goertzel algorithm;
• computer readable program code which causes said programmable computer processor to calculating the magnitude Mref(i) of said measured reference signal waveform at each of said four harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to calculating the phase φref(i) of said measured reference signal waveform at each of said 4 harmonics of said reference frequency;
• computer readable program code which causes said programmable computer processor to forming a filtered reference signal waveform using the equation
• 31 ∑ M ref ⁡ ( i ) * cos [ φ ref ⁡ ( i ) + ( 2 ⁢ i + 2 ) ⁢ ( π ) ⁢ ( t ) / x ] ;
• wherein (i) is an integer greater than or equal to 1 and less than or equal to (P), and wherein (t)/x is greater than or equal to 0 and less than or equal to 1;
• computer readable program code which causes said programmable computer processor to determining a plurality of actual datapoints;
• computer readable program code which causes said programmable computer processor to forming an X/Y array comprising said plurality of actual datapoints.
• computer readable program code which causes said programmable computer processor to using a third order curve fitting program to form a transfer function using said X/Y array;
• computer readable program code which causes said programmable computer processor to determining a plurality of calculated datapoints using said transfer function;
• computer readable program code which causes said programmable computer processor to comparing said plurality of actual datapoints with said plurality of calculated datapoints;
• computer readable program code which causes said programmable computer processor to forming a calibration curve using said transfer function.