A non-return-to-zero data stream (of amplitude levels ?1) is passed through a low-pa filter whose impulse response is defined by the Gaussian function where ? is a design parameter defined in terms of the filter?s 3-dB bandwidth by?

(a) Show that the transfer function of the filter is defined by H(f) = exp(? ?²f²) hence demonstrate that the 3-dB bandwidth of the filter is indeed equal to W. you may use Table A6.3 on Fourier-transform pairs.

(b) Show that the response of the filter to a rectangular pulse of unit amplitude and duration T centered on the origin is defined by Equation (6.135)

h(t) exp a? log2 1 2