Saturday, January 4th, 2014

Last month I asked the following question in an exam for the advanced image analysis course we teach here: “Given that interpolation is a convolution, describe how you would compute an interpolation using the Fourier Transform.” Unfortunately I can count on one finger the number of students that did not simply answer with something in the order of “convolution can be computed by multiplication in the Fourier domain.” And the one student that did not give this answer didn’t give an answer at all… Apparently this question is too difficult, though I thought it was interesting and only mildly challenging. In this post I’ll discuss interpolation and in passing give the correct answer to this question.

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Tags: aliasing, filtering, Fourier transform, interpolation, Lanczos, linear, pulse train, sampling, shift, zoom.

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Friday, September 25th, 2009

I read a very nice article in the latest IEEE Signal Processing Magazine: Prandoni, P. and Vetterli, M., “From Lagrange to Shannon… and back: another look at sampling,” IEEE Signal Processing Magazine 26(5):138-144, September 2009. The authors make a case for teaching signal processing starting with discrete time, and then moving to continuous time. I don’t agree, but they expose their case very nicely. But I did learn something new from this paper, which is why I am writing this. It turns out that the Lagrange interpolation polynomials converge to the sinc function as the polynomial order goes to infinity.

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Tags: interpolation, Lagrange polynomials, sinc.

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