EE200_Weber_9-23

EE200_Weber_9-23 - t p ( t ) = 1 + t / T if " T s <...

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13 EE 200 Sampling and Reconstruction The process of sampling the signals is only half of the task. We also need to reconstruct a new continuous time signal, preferably as close as possible to the original continuous-time signal. The discrete-to-continuous converter takes discrete values as input and outputs a continuous signal. Sampler T Input signal x(t) Sampled signal x[n] Output signal y(t) DiscToCont T
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14 EE 200 Interpolation The reconstruction process must interpolate between the sample values to create a continuous signal. The choice of how to interpolate between the samples affects the accuracy of the output signal. n t x(nT s ) y(t)
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15 EE 200 Interpolation The simplest form of interpolation is to output the value of the input for a time T s , known as a “zero-order hold”. t p(t) t 1 T s /2 t y(t) p ( t ) = 1 " 1 2 T s < t # 1 2 T s 0 otherwise $ % & -T s /2 x(nT s )
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16 EE 200 Interpolation A linear interpolator creates a line between the values of the last pulse and the current one.
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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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This note was uploaded on 10/13/2009 for the course EE 200 at USC.

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EE200_Weber_9-23 - t p ( t ) = 1 + t / T if " T s <...

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