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**Unformatted text preview: **t p ( t ) = 1 + t / T if " T s < t < 1-t / T if # t < T s 0 otherwise $ % & ’ & p(t) t 1 T s-T s t y(t) x(nT s ) 17 EE 200 Interpolation An ideal interpolator is the sinc function and recreates the original input exactly. The peak of one sinc function aligns with zeros of all the other sinc function. The resulting summation perfectly recreates the signal. p ( t ) = sin( " t / T s ) t / T s p(t) t 1 T-T y(t) t 1 T-T 18 EE 200 Interpolation While the sinc function may be an ideal interpolator, it has some problems that make it impossible to actually implement. The pulse is non-causal, and it also has infinite extent in both positive and negative time. If we truncate the response to something that can be built this will introduce errors in the resulting output. p(t) t 1 T-T...

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