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Fourier analysis convolution theorem

The entire analysis of synchronous detection, or lock-in amplification as it is sometimes called, can be conveniently analyzed by straightforward application of the Fourier transform techniques, transform directory, and convolution theorem developed in Section IV of Chapter 1. [Pg.53]

Fourier analysis is used to find the velocity and attenuation of surface waves. Let the range in z over which data is available be (. If there were no attenuation, then by the convolution theorem the Fourier transform F ( ) would be a sine function centred at a spatial frequency... [Pg.135]

According to the convolution theorem of Fourier analysis, the Fourier transform of a product of two functions is given by the convolution (here indicated by the symbol ) of their individual Fourier transforms. Hence, the effect of multiplying 1(8) by the boxcar function D(8) is to yield a spectrum that is the convolution of the Fourier transform of 1(8) measured with an infinitely long retardation and the Fourier transform of D(8). The Fourier transform of 1(8) is the true spectrum 5(v), while the Fourier transform of D(8), /(v), is given by... [Pg.42]

Turning now to a closer inspection of these quantities representing the detection signals, we note that each of the detection amplitudes (69) and (72) is a Fourier integral function. Then, according to the time convolution theorem of Fourier analysis (Papoulis, 1962), expression (69) of the scattered photon detection amplitude can also be written as the convolution product of... [Pg.297]


See other pages where Fourier analysis convolution theorem is mentioned: [Pg.390]    [Pg.390]    [Pg.226]    [Pg.355]    [Pg.617]   
See also in sourсe #XX -- [ Pg.448 ]




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