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 reconstructa digital signal back into an analog signal. Signal Reconstruction•As long as the Nyquist criterion is met (sampling frequency fsis 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 Ndiscrete data points, the cardinal series is ()10sin1nNdntntftf nttntπ=−=⎡⎤⎛⎞−⎜⎟⎢⎥Δ⎝⎠⎣⎦=Δ−Δ∑, where tis time (we assume that the signal starts at t= 0), nis the data point number (the summation is over all Ndiscrete data points, from n= 0 to n= N– 1), f
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