Homework1_Solutions

Homework1_Solutions - I. HOMEWORK #1 SOLUTIONS 1) a)...

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I. HOMEWORK #1 SOLUTIONS 1) a) f(2,-3) b) f(x+4,y-1) 2) R R (( x - ξ 0 ) + ( y - η 0 )) exp - ξ 0 2 exp - η 0 2 0 0 R ( R (( x - ξ 0 ) + y ) exp - ξ 0 2 0 ) exp - η 0 2 0 R ( x - ξ 0 + y ) exp - xi 0 2 0 = x π - 0 + y π π R ( x + ( y - η 0 )) exp - η 0 2 0 π ( x π + y π - 0) = π ( x + y ) 3) a) i) Perfectly replicates image ii) This depends on how you interpreted the problem. When you convolve a function with a kernel, it actually ﬂips the kernel and then drags it across the image. If you assumed that the kernel was unﬂipped, then it moves the image up and to the left. If you assumed the kernel was already ﬂipped, it moves the image down and to the right. Sorry for the confusing/ambiguous question. iii) Blurs image b) i) δ ( x,y ) ii) Again, this depends on how you read the problem. I accepted either δ ( x + 1 ,y - 1) or δ ( x - 1 ,y + 1). iii) I intended the answer to be a rect function, but I also accepted a comb function, provided you expressed it in the correct terms and with the correct limits. You should note, though, that comb functions aren’t convolved with anything in real space. They don’t represent a PSF of a system, but instead can be thought

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This note was uploaded on 10/30/2010 for the course MP 230 taught by Professor Macfall during the Fall '10 term at Duke.

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Homework1_Solutions - I. HOMEWORK #1 SOLUTIONS 1) a)...

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