7.37 An NRZ data stream of amplitude levels +1 is passed through a low-pass filter whose impulse response is defined by the Gaussian function h(t) = exp where a is a design parameter defined in terms of the filter's 3dB bandwidth by In 21 a = 2 W a. Show that the transfer function of the filter is defined by H(f) = exp(-a?f?) Hence, demonstrate that the 3dB bandwidth of the filter is indeed equal to W. You may use the list of Fourier-transform pairs in Table 2.1. b. Determine the response of the filter to a rectangular pulse of unit amplitude and duration T centered on the origin.
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