Signal_Reconstruction - Signal Reconstruction the Cardinal...

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Signal Reconstruction – the Cardinal Series Author: John M. Cimbala, Penn State University Latest revision: 13 February, 2006, 5:30 p.m. Introduction In a previous learning module, we discuss how to convert an analog signal into a digital signal. In this learning module, we discuss how to reconstruct a digital signal back into an analog signal. Signal Reconstruction As long as the Nyquist criterion is met (sampling frequency f s is at least twice the maximum signal frequency), we can theoretically reconstruct the original analog waveform from a set of discrete samples. One method of reconstruction is the cardinal series . It is the only reconstruction technique we discuss here. For N discrete data points, the cardinal series is () 1 0 sin 1 nN d n t n t ft f nt t n t π =− = ⎛⎞ ⎜⎟ Δ ⎝⎠ Δ , where t is time (we assume that the signal starts at t = 0), n is the data point number (the summation is over all N discrete data points, from n = 0 to n = N – 1), f
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