Sampling, Reconstruction of Unsampled Signal.

Cuthbert Nyack
The original unsampled signal can be recovered from the samples by passing the samples through a low pass filter with a bandwidth of half the sampling frequency. In the applet below, the unsampled signal which is a sine in this case is in gray, samples are in magenta, the response of the filter to the first 5 samples are shown by the sinc functions in orange, yellow, green, cyan and pink, and the sum of the responses is in red. The parameter BW is the bandwidth of the ideal low pass filter. The applet illustrates the effect of the sampling time and filter bandwidth on the reconstructed signal.
eg parameters (1.0, 5.0, 0.4, 2.5, na, na, na, na, na, 1.0) show that when the bandwidth is half the sampling frequency, the sum of the sincs is equal to the sampled signal in the range of t where the included sincs are dominant.

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© 2000 Cuthbert A. Nyack.