Problem 4 Suppose x(t) = sinc(t)^2. [20 points] (a) Use...

Problem 4 Suppose $x(t) = sinc(t)^2$. [20 points] (a) Use Parseval's relationship to determine the energy $E_x$. (b) Determine the energy in the frequency band [0, 1]. What percentage is this of the total energy? (c) Determine the absolute bandwidth. (d) Determine the 3-dB bandwidth.

Consider a signal g(t). Recall that |G(f)|^2 is called the energy spectral density of g(t). Integrating the energy spectral density over all frequency gives the signal's total energy. Furthermore, the energy contained in the frequency band I can be found from the integral ∫_I |G(f)|^2 df where the integration is over the frequencies in band I. In particular, if the band is simply an interval of frequency from f1 to f2, then the energy contained in this band is given by ∫_{f1}^{f2} |G(f)|^2 df. In this problem, assume g(t) = 1[-1 ≤ t ≤ 1]. (a) Find the (total) energy of g(t). (b) Figure define the main lobe of a sinc pulse. It is well-known that the main lobe of the sinc function contains about 90% of its total energy. Check this fact by first

Adi S.

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Problem 4 Suppose $x(t) = sinc(t)^2$. [20 points] (a) Use Parseval's relationship to determine the energy $E_x$. (b) Determine the energy in the frequency band [0, 1]. What percentage is this of the total energy? (c) Determine the absolute bandwidth. (d) Determine the 3-dB bandwidth.

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