Unformatted text preview: as is the case for the otherwise simple gaussian functions 2 and 3, and this multiplicative factor will shift the k space
representation by an amount k , thus shifting function 3 further than function 2 in k space for the higherfrequency carrier
wave in function 3. 6.2 reasoning Included in part (a), notably inverse proportionality of width in direct space to width in inverse space, and shifting of k space
representation by introduction of an oscillatory factor in real space. 7 7 Convolution of rectangular functions Ignore contributions from edges for the reason they contribute nothing to the integral of interest. 2
f (x ) =
0 1
h(x ) =
0 1
h(x − x ) =
0 1 < x < 2
otherwise 3 < x < 5
otherwise 3 + x < x < 5 + x
otherwise 0
x<4 2(x − 4) 4 < x < 5
g (x) = dx f (x )h(x − x ) =
2
5<x<6 2(7 − x) 6 < x < 7 0
7<x Figure 3: p7.jpg 8 (31) (32) (33) (34) 8 copy and paste convolution 8.1 function, single delta function...
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This document was uploaded on 03/11/2014 for the course PHYS 408 at University of British Columbia.
 Fall '11
 KirkW.Madison
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