Let x n be a discrete time signal obtained by sampling a continuous time signal x c (t) with some sampling period T so that x n x c (nT) Assume x c (t) is bandlimited to 100 Hz, i e, X c (j) 0 for 2(100) We wish to estimate the continuous time spectrum X c (j) by computing a 1024 point DFT of x n , X k What is the smallest value of T such that the equivalent frequency spacing between consecutive DFT samples X k corresponds to I Hz or less in continuous time frequency

Question: Let x[n] be a discrete-time signal obtained by sampling a continuous-time signal x c (t) with some sampling period T so that x[n] = x

Let x[n] be a discrete-time signal obtained by sampling a continuous-time signal x_c(t) with some sampling period T so that x[n] = x_c(nT). Assume x_c(t) is bandlimited to 100 Hz, i.e, X_c(jΩ) = 0 for |Ω| ≥ 2π(100). We wish to estimate the continuous-time spectrum X_c(jΩ) by computing a 1024-point DFT of x[n], X[k]. What is the smallest value of T such that the equivalent frequency spacing between consecutive DFT samples X[k] corresponds to I Hz or less in continuous-time frequency?

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