...and the transfer function in the frequency domain. It can be shown that the Fourier transform of a convolution of two functions is the product of the Fourier transforms of the two functions : C(f) = S(f)G(f) (3.7) The amplitude spectrum is the product of the amplitude spectra, and the phase...

...more- agreeable form using the Fourier convolution theorem which states that the Fourier transform of a convolution of two functions is the product of the Fourier transforms of the two functions. 7(f ) = 6(f)S(f) (2) Therefore in the Fourier-plane the effect becomes a multiplication, point by point,...

...The Fourier transform of a Fourier transform yields the original function 2. The Fourier transform of the convolution of two functions is the product of the Fourier transforms of the individual functions. 0M] = F(x) • G(x) These two properties together mean that the nasty-looking...

...advantage of the convolution theorem for Fourier Transforms which states that the Fourier Transform of the convolution of two functions is the product of the Fourier Transforms of the individual functions. Hence the "solution" of equation (2) is given by dividing the Fourier Transform...

...convolution form of (23.12) as Y. = 6,L (23.18) where we have used the fact that the Fourier transform of the convolution of two functions is the product of the Fourier transformed variables. We define the spectrum for the process as (23.19) where the brackets denote...

...object in measurement space). We use the convolution theorem which states that the Fourier transform of the convolution of two functions is the product of the Fourier transforms of the individual functions. We can therefore write this transform in the form Fc = [Tfc] = [Tfm].[Tf|] (1.3)...

...(4.2), we have (p(q) = e-'lql. (4.3) The convolution theorem states that the Fourier transform of a convolution of two functions is the product of the Fourier transforms of the two functions, ] = F(q)G(q). (4.4) For iid random variables, S2 = x, + x2. (4.5) The pdf P2(S2) of the sum of two...

...the Fourier transform of the convolution of Fu with L. Mathematics shows that the Fourier transform of the convolution of two functions is the product of the Fourier transforms of the two functions. Thus (see Fig. 3.l20 and Inset Ml, the wave W is the product of the Fourier transforms of L and Fu....

...the Fourier transform of the convolution of Fu with L. Mathematics shows that the Fourier transform of the convolution of two functions is the product of the Fourier transforms of the two functions. Thus (see Fig. 3.120 and Inset M), the wave W is the product of the Fourier transforms of L and Fu....

...This deconvolution can be performed in Fourier space by utilizing the fact that the Fourier transform of the convolution of two functions is the product of the Fourier transforms of the functions. A Gaussianlike (with variance of crc) derivative profile of EDP is shown [Figure 4. Bottom...