Method apparatus and system for the identification of the relationship between two signals

Claim 2

A multiport linear passive lumped-parameter network consisting of only linear passive elements with one input port and at least four output ports, means for providing an input signal at said input port, passive coupling means within said network for producing four output signals at the four output ports, each frequency component of said signals being described by an envelope magnitude and phase the frequency response of each of said output signals with respect to said input signal being finite (including zero) at all real frequencies, the second output signal having a phase leading the phase of the first output signal by 90* and the second output signal envelope magnitude being proportional to W times the first output signal of radian frequency W, the third output signal for each input signal having a phase leading the phase of the first output signal by 180 degrees and the third output signal envelope magnitude being proportional to omega 2 times the first output signal envelope magnitude, the fourth output signal for each input signal having a phase leading the phase of the first output signal by 270* and the fourth output signal envelope magnitude being proportional to omega 3 times the first output signal envelope magnitude for each input signal of radian frequency omega .

Claim 3

A multiport network consisting of only linear passive elements with one input port and three output ports, means for providing a voltage excitation signal having a parameter T at said input port, coupling means within the network to generate first, second, and third output signals responsive to said excitation at the three output portS respectively, such that when the excitation (after a preselected time t equals zero) produces a first output signal changing in magnitude proportional to s1 (t) T2 (1 - (1 + t/T) e t/t) then the corresponding second output signal for positive time is proportional to s2(t) t e116 t/T and the corresponding third output signal for positive time is proportional to s3(t) (1 - t/T(e t/T for all T

Claim 4

A multiport network consisting of only linear passive elements with one input port and three output ports, means for providing a voltage excitation signal having a parameter T at said input port, coupling means within the network to generate first, second, and third output signals responsive to said excitation at the three output portS respectively, such that when the excitation (after a preselected time t equals zero) produces a first output signal changing in magnitude proportional to s1 (t) T2 (1 - (1 + t/T) e t/t) then the corresponding second output signal for positive time is proportional to s2(t) t e116 t/T and the corresponding third output signal for positive time is proportional to s3(t) (1 - t/T(e t/T for all T

Claim 5

A claim as in claim 2 wherein s1(t) is proportional to the time integral of s2(t) and s2(t) is proportional to the time integral of s3(t).

Claim 6

A claim as in claim 2 wherein s2(t) is proportional to the time derivative of s1(t) and s3(t) is proportional to the time derivative of s2(t).

Claim 7

A linear passive multiport circuit consisting of only linear passive elements comprising a two-terminal input with a source of voltage supplies to said input, a first pair of two impedances with different phase angles in series between the said two terminals with a first tap between the said two impedances, a second pair of two impedances with different phase angles in series between said first tap and one of said input terminals, with a second tap between the two said impedances of said second pair, a third pair of two impedances with different phase angles in series between said second tap and one of said input terminals, with a third tap between the two said impedances of said third pair, passive said first pair of two impedances generating a second signal proportional to the voltage between said first tap and said one input terminal, said second pair of two impedances generating a third signal proportional to the voltage between said second tap and said one input terminal, said third pair of two impedances generating a fourth signal proportional to the voltage between said third tap and said one input terminal, and passive means responsive to an algebraically linearly weighted combination of said, second, third and fourth signals to generate a fifth signal.

Claim 8

A linear passive multiport circuit consisting of only linear passive elements comprising a two-terminal input with a source of voltage supplies to said input, a first pair of two impedances with different phase angles in series between the said two terminals with a first tap between the said two impedances, a second pair of two impedances with different phase angles in series between said first tap and one of said input terminals, with a second tap between the two said impedances of said second pair, a third pair of two impedances with different phase angles in series between said second tap and one of said input terminals, with a third tap between the two said impedances of said third pair, passive said first pair of two impedances generating a second signal proportional to the voltage between said first tap and said one input terminal, said second pair of two impedances generating a third signal proportional to the voltage between said second tap and said one input terminal, said third pair of two impedances generating a fourth signal proportional to the voltage between said third tap and said one input terminal, and passive means responsive to an algebraically linearly weighted combination of said, second, third and fourth signals to generate a fifth signal.

Claim 9

A circuit as in claim 5 whereby said third signal is proportional to the time derivative of said second signal, and said fourth signal is proportional to the time derivative of said third signal.

Claim 10

A circuit as in claim 5 whereby said third signal is proportional to the time integral of said second signal, and said fourth signal is proportional to the time intergral of said third signal.

Claim 11

A linear passive circuit consisting of onlp linear passive resistors and capacitors for producing a plurality of state variable signals from a measured signal, comprising means for performing a dynamic passive operation on said measured signal to produce a first output, means for performing a second passive dynamic operation on said measured signal to provide a second output, means for performing a third passive dynamic operation on said measured signal to provide a third output, means for performing a fourth passive dynamic operation on said measured signal to provide a fourth output, whereby said second output is the derivative with respect to time of said first output and said third output is the time derivative of said second output, and said fourth output is the time derivative of said third output, and whereby the roots of the denominators of the transferences from said measured signal to each of said outputs are equal

Claim 12

A linear passive circuit consisting of onlp linear passive resistors and capacitors for producing a plurality of state variable signals from a measured signal, comprising means for performing a dynamic passive operation on said measured signal to produce a first output, means for performing a second passive dynamic operation on said measured signal to provide a second output, means for performing a third passive dynamic operation on said measured signal to provide a third output, means for performing a fourth passive dynamic operation on said measured signal to provide a fourth output, whereby said second output is the derivative with respect to time of said first output and said third output is the time derivative of said second output, and said fourth output is the time derivative of said third output, and whereby the roots of the denominators of the transferences from said measured signal to each of said outputs are equal

Claim 13

A multiport circuit consisting of linear passive resistors and capacitors for producing a plurality of state variable signals from an input signal, passive means for generating from said input signal a first state variable signal, passive means for generating from said input signal a second state variable signal which is a time derivative of the first state variable signal, and means For generating from said input signal a third state variable signal which is a time derivative of the second state variable signal, and passive means for generating from said input signal a fourth state variable signal which is a time derivative of the third state variable signal, each of said means for generating a state variable signal having a gain less than a predetermined finite value of gain, the roots of the denominator of the complex gain as a function of frequency from said input signal to said first state variable signal being equal to the roots of the denominator of the complex gain from said input signal to said second state variable signal and being equal to the roots of the denominator of the complex gain from said input signal to said third state variable signal and being equal to the roots of the denominator of the complex gain from said input signal to said fourth state variable signal.

Claim 14

A multiport circuit consisting of linear passive resistors and capacitors for producing a plurality of state variable signals from an input signal, passive means for generating from said input signal a first state variable signal, passive means for generating from said input signal a second state variable signal which is a time derivative of the first state variable signal, and means For generating from said input signal a third state variable signal which is a time derivative of the second state variable signal, and passive means for generating from said input signal a fourth state variable signal which is a time derivative of the third state variable signal, each of said means for generating a state variable signal having a gain less than a predetermined finite value of gain, the roots of the denominator of the complex gain as a function of frequency from said input signal to said first state variable signal being equal to the roots of the denominator of the complex gain from said input signal to said second state variable signal and being equal to the roots of the denominator of the complex gain from said input signal to said third state variable signal and being equal to the roots of the denominator of the complex gain from said input signal to said fourth state variable signal.

Claim 15

A linear passive dynamic circuit consisting of only linear passive elements for producing a plurality of state variable signals from an input signal, passive means for generating a first state variable signal from said input signal, passive means for generating second, third, and fourth state variable signals from said input signal, said state variable signals being related such that a polynomial in the frequency variable times the Laplace transform of the first state variable signal using the frequency variable equals the Laplace transform of said input signal and so that the fourth state variable signal is the time integral of the third state variable and so that the third state variable signal is the time integral of the second state variable signal and the second state variable signal is the time integral of the first state variable signal, each of said passive means for generating a state variable signal having a gain from input to state variable signal less than a predetermined value.

Claim 16

A linear passive dynamic circuit consisting of only linear passive elements for producing a plurality of state variable signals from an input signal, passive means for generating a first state variable signal from said input signal, passive means for generating second, third, and fourth state variable signals from said input signal, said state variable signals being related such that a polynomial in the frequency variable times the Laplace transform of the first state variable signal using the frequency variable equals the Laplace transform of said input signal and so that the fourth state variable signal is the time integral of the third state variable and so that the third state variable signal is the time integral of the second state variable signal and the second state variable signal is the time integral of the first state variable signal, each of said passive means for generating a state variable signal having a gain from input to state variable signal less than a predetermined value.

Claim 17

A circuit as in claim 8 wherein said transference from measured signal to the said third output has a numerator polynomial order not greater than its denominator polynomial order.

Claim 18

A circuit as in claim 9 wherein each means for generating a state variable signal contains an R-C ladder network.

Claim 19

A circuit as in claim 10 wherein each of said gains is limited to less than said predetermined value only by the linear dynamic properties of each of said means for generating a state variable signal.