PHYS 408 HOMEWORK 6 SOLUTIONS

62 reasoning included in part a notably inverse

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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 higher-frequency 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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