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What is the ideal reconstruction formula or ideal interpolation formula for x(t) = _________(a) \(\sum_{-\infty}^\infty x(nT) \frac{sin⁡(π/T) (t-nT)}{(π/T)(t-nT)}\)(b) \(\sum_{-\infty}^\infty x(nT) \frac{sin⁡(π/T) (t+nT)}{π/T)(t+nT}\)(c) \(\sum_{-\infty}^\infty x(nT) \frac{sin⁡(2π/T) (t-nT)}{2π/T)(t-nT}\)(d) \(\sum_{-\infty}^\infty x(nT) \frac{sin⁡(4π/T) (t-nT)}{(4π/T)(t-nT)}\)I got this question in homework.Question is taken from Digital to Analog Conversion Sample and Hold in portion Sampling and Reconstruction of Signals of Digital Signal Processing

Answer»

The correct answer is (a) \(\sum_{-\infty}^\infty x(NT) \FRAC{sin⁡(π/T) (t-nT)}{(π/T)(t-nT)}\)

To explain: x(t) = \(\sum_{-\infty}^\infty x(nT) \frac{sin⁡(π/T) (t-nT)}{(π/T)(t-nT)}\) where the SAMPLING interval T = 1/Fs=1/2B, Fs is the sampling frequency and B is the bandwidth of the ANALOG SIGNAL.



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