Let xa(t) be a bandlimited signal to max, i.e., Xa(N) = 0,|N| > Nmax. Suppose that...

  

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Let xa(t) be a bandlimited signal to max, i.e., Xa(N) = 0,|N| > Nmax. Suppose that the signal is sampled with sampling frequency Fs Z2Fmax (frequencies in Hz). Denote by Ed the energy of x[n] = xa(nTs), i.e., Ed = _- |x[n]|2 and by Ea the energy of xa(t), i.e., Ea = |xa(t)|²dt. Show that Ea Ts Ed = Verify the energy relationship for the bandlimited signal xa (t) with Xa(N) = 2 for 2 € [-1000, 1000TT] and 0 otherwise. Assume that the signal is sampled at the Nyquist rate. Let xa(t) be a bandlimited signal to max, i.e., Xa(N) = 0,|N| > Nmax. Suppose that the signal is sampled with sampling frequency Fs Z2Fmax (frequencies in Hz). Denote by Ed the energy of x[n] = xa(nTs), i.e., Ed = _- |x[n]|2 and by Ea the energy of xa(t), i.e., Ea = |xa(t)|²dt. Show that Ea Ts Ed = Verify the energy relationship for the bandlimited signal xa (t) with Xa(N) = 2 for 2 € [-1000, 1000TT] and 0 otherwise. Assume that the signal is sampled at the Nyquist rate.

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To show that Ed Ea Ts we need to demonstrate that the energy of the discretetime signal xn is equal to the energy of the continuoustime signal xat mul... View the full answer