Method and apparatus for extracting derivatives from surface acoustic waves

Claim 1

An apparatus for extracting the second derivative from an acoustic wave, comprising: a first bus bar; a second bus bar spaced apart from said first bus bar; three pairs of parallel fingers coupled to a piezoelectric material and oriented transversely to the direction of travel of the acoustic waves, and wherein the first, fourth, and fifth fingers are coupled to said first bus bar and the second, third, and sixth fingers are coupled to said second bus bar, the center-to-center spacing of the fingers in each pair is equal to one-half the acoustic wavelength, and the end portions of the outer pairs each overlap by an equal amount, and the end portions of the inner pair overlap by an amount equal to two times said equal amount of overlap of said outer pairs, whereby the amplitude contribution of each pair is weighted by an amount equal to the amount of overlap of said fingers in each pair and the difference in amplitude contribution between said outer pairs and said inner pairs is obtained so that the second derivative is extracted from the acoustic wave according to the finite difference approximation of the pulse amplitudes, as follows: Δ .sup.2 Y.sub.k = Y.sub.k - 2Y.sub.K-1 + Y.sub.k-2, wherein Y k equals the amplitude of the acoustic wave passing a reference point at time k.

Claim 2

An apparatus for extracting the second derivative from an acoustic wave, comprising: a first bus bar; a second bus bar spaced apart from said first bus bar; three pairs of parallel fingers coupled to a piezoelectric material and oriented transversely to the direction of travel of the acoustic waves, and wherein the first, fourth, and fifth fingers are coupled to said first bus bar and the second, third, and sixth fingers are coupled to said second bus bar, the center-to-center spacing of the fingers in each pair is equal to one-half the acoustic wavelength, and the end portions of the outer pairs each overlap by an equal amount, and the end portions of the inner pair overlap by an amount equal to two times said equal amount of overlap of said outer pairs, whereby the amplitude contribution of each pair is weighted by an amount equal to the amount of overlap of said fingers in each pair and the difference in amplitude contribution between said outer pairs and said inner pairs is obtained so that the second derivative is extracted from the acoustic wave according to the finite difference approximation of the pulse amplitudes, as follows: Δ .sup.2 Y.sub.k = Y.sub.k - 2Y.sub.K-1 + Y.sub.k-2, wherein Y k equals the amplitude of the acoustic wave passing a reference point at time k.

Claim 6

An apparatus for extracting derivatives of the n th order from an acoustic wave, where n is any real, positive integer greater than 1 comprising: a first bus bar; a second bus bar spaced from said first bus bar; pairs of overlapping parallel fingers coupled to a piezoelectric material and oriented transversely to the direction of travel of the acoustic wave, one finger of each pair extending from said first bus bar and the other finger extending from said second bus bar, the center-to-center spacing of said fingers in each pair being equal to one-half the acoustic wavelength; and means for weighting said pairs of fingers according to the finite difference approximation series; Δ .sup.n Y.sub.k = Δ .sup.n-1 Y.sub.k - Δ .sup.n-1 Y.sub.k-1, wherein n = the derivative being extracted and Y k = the amplitude of the acoustic wave passing a reference point at time k, and wherein the number of pairs of fingers contributing a signal is equal to the number of terms in said series, the weight given to each contributing pair is an integral multiple equal to the coefficient of the respective term in said series, and the phase of the contributing pair is the same as the sign of said coefficient, whereby a signal equal to the n th derivative of the acoustic wave is obtained from said bus bars.

Claim 7

An apparatus for extracting derivatives of the n th order from an acoustic wave, where n is any real, positive integer greater than 1 comprising: a first bus bar; a second bus bar spaced from said first bus bar; pairs of overlapping parallel fingers coupled to a piezoelectric material and oriented transversely to the direction of travel of the acoustic wave, one finger of each pair extending from said first bus bar and the other finger extending from said second bus bar, the center-to-center spacing of said fingers in each pair being equal to one-half the acoustic wavelength; and means for weighting said pairs of fingers according to the finite difference approximation series; Δ .sup.n Y.sub.k = Δ .sup.n-1 Y.sub.k - Δ .sup.n-1 Y.sub.k-1, wherein n = the derivative being extracted and Y k = the amplitude of the acoustic wave passing a reference point at time k, and wherein the number of pairs of fingers contributing a signal is equal to the number of terms in said series, the weight given to each contributing pair is an integral multiple equal to the coefficient of the respective term in said series, and the phase of the contributing pair is the same as the sign of said coefficient, whereby a signal equal to the n th derivative of the acoustic wave is obtained from said bus bars.

Claim 10

An apparatus for extracting derivatives of the n th order from an acoustic wave, where n is any real, positive integer greater than 1, comprising: a first bus bar; a second bus bar spaced apart from said first bus bar; and pairs of parallel fingers coupled to a piezoelectric material and oriented transversely to the direction of travel of the acoustic wave, one finger of each pair extending from said first bus bar and the other finger extending from said second bus bar, the center-to-center spacing of said fingers in each pair being equal to one-half the acoustic wavelength, the end portions of said fingers in each pair overlapping by an integral multiple of the minimum overlap of said fingers in any pair, the geometrical relationship of said pairs being governed by the series: Δ .sup.n Y.sub.k = Δ .sup.n-1 Y.sub.k - Δ .sup.n-1 Y.sub.k-1 , wherein n = the derivative being extracted and Y k = the amplitude of the acoustic wave passing a reference point at time k, and wherein the number of pairs of fingers in the apparatus is equal to the number of terms in said series, said integral multiple of overlap for each pair is equal to the coefficient of the respective term in said series, and the leading finger, with respect to the acoustic wave, of each of said pairs extends from said first bus bar when said coefficient is positive, whereby the amplitude contribution of each pair is weighted by said overlap and either added or subtracted from the derivative depending upon the sequence of connection of each finger in said pairs to said bus bars.

Claim 11

An apparatus for extracting derivatives of the n th order from an acoustic wave, where n is any real, positive integer greater than 1, comprising: a first bus bar; a second bus bar spaced apart from said first bus bar; and pairs of parallel fingers coupled to a piezoelectric material and oriented transversely to the direction of travel of the acoustic wave, one finger of each pair extending from said first bus bar and the other finger extending from said second bus bar, the center-to-center spacing of said fingers in each pair being equal to one-half the acoustic wavelength, the end portions of said fingers in each pair overlapping by an integral multiple of the minimum overlap of said fingers in any pair, the geometrical relationship of said pairs being governed by the series: Δ .sup.n Y.sub.k = Δ .sup.n-1 Y.sub.k - Δ .sup.n-1 Y.sub.k-1 , wherein n = the derivative being extracted and Y k = the amplitude of the acoustic wave passing a reference point at time k, and wherein the number of pairs of fingers in the apparatus is equal to the number of terms in said series, said integral multiple of overlap for each pair is equal to the coefficient of the respective term in said series, and the leading finger, with respect to the acoustic wave, of each of said pairs extends from said first bus bar when said coefficient is positive, whereby the amplitude contribution of each pair is weighted by said overlap and either added or subtracted from the derivative depending upon the sequence of connection of each finger in said pairs to said bus bars.