Journal of the Franklin Institute, Volume 250Pergamon Press, 1950 |
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Page 45
... transforms ( Sec . 6 ) . Included among the special cases of ( 1 ) are the Fourier transform ( Sec . 7 ) , the Hilbert transform ( Sec . 9 ) , and the convolution integral ( Sec . 10 ) . The proposed instrument makes it possible to ...
... transforms ( Sec . 6 ) . Included among the special cases of ( 1 ) are the Fourier transform ( Sec . 7 ) , the Hilbert transform ( Sec . 9 ) , and the convolution integral ( Sec . 10 ) . The proposed instrument makes it possible to ...
Page 49
... TRANSFORMS It is often desirable ( see Sec . 13 ) to be able to iterate transforms , that is to take the transform of a function f ( t ) with the kernel K ( x , t ) , thereby obtaining a function F ( x ) , and then to take the transform ...
... TRANSFORMS It is often desirable ( see Sec . 13 ) to be able to iterate transforms , that is to take the transform of a function f ( t ) with the kernel K ( x , t ) , thereby obtaining a function F ( x ) , and then to take the transform ...
Page 51
... TRANSFORMS 7. THE FOURIER TRANSFORMS The oldest and most common integral transform is the Fourier transform . The Fourier cosine transform is the special case of ( 1 ) for which we may take ( a , b ) ( - , + ) , and = K ( x , t ) = cos ...
... TRANSFORMS 7. THE FOURIER TRANSFORMS The oldest and most common integral transform is the Fourier transform . The Fourier cosine transform is the special case of ( 1 ) for which we may take ( a , b ) ( - , + ) , and = K ( x , t ) = cos ...
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