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EE200_Weber_11-25

# EE200_Weber_11-25 - EE 200 Sampling Theorem A...

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12 EE 200 Sampling Theorem A continuous-time signal can be completely recovered from the discrete-time signal if we obey the Nyquist- Shannon sampling theorem: If x(t) is a band limited signal with X( ω ) = 0 for | ω | > ω M , then x(t) is uniquely determined by its samples x(nT) if ω s > 2 ω m where ω s =2 π /T . Note: This depends on being able to use a ideal low pass filter for reconstruction of the signal.

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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 Real Complex Sampled signal Integer Complex Output signal Real Complex DiscToCont T
14 EE 200 Sampling and Reconstruction The discrete-to-continuous step can be divided into two parts. The first part changes a discrete time signal with values T apart into a continuous-time signal with Dirac delta functions T apart, each with a weight equal to the value of the sampled signal at that time. Sampled signal Integer Complex Impulse signal Real Complex ImpulseGen T n t

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15 EE 200 Sampling and Reconstruction To understand what happens during the sampling process, and how to best reconstruct the signal, we can analyze the frequency response of the system that goes from a continuous-time input signal to a continuous-time series of impulses Sampled signal Integer Complex Impulse signal Real Complex ImpulseGen T n t Sampler T Input signal Real Complex x(t) x p (t)
16 EE 200 Impulse-Train Sampling We can model how a signal is sampled by using a

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EE200_Weber_11-25 - EE 200 Sampling Theorem A...

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