In real continuous-time signal x c (t) is bandlimited to frequencies below 5 kHz; i.e., X c

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In real continuous-time signal xc(t) is bandlimited to frequencies below 5 kHz; i.e., Xc(jΩ) = 0 for |Ω| ≥ 2π(5000). The signal xc(t) is sampled with a sampling rate of 10,000 samples per second (10kHz) to produce a sequence x[n] = xc(nT) with T = 10−4.

Let X[k] be the 1000-point DFT of x[n].

(a) To what continuous-time frequency does the index k = 150 in X[k] correspond?

(b) To what continuous-time frequency does the index k = 800 in X[k] correspond? 

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Discrete Time Signal Processing

ISBN: 978-0137549207

2nd Edition

Authors: Alan V. Oppenheim, Rolan W. Schafer

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