Reduce the level of inter symbol interference

Question

Solve the following problem:

Suppose a digital communication system employs Gaussian-shaped pulses of the form

x(t) = exp(-πa² t²)

To reduce the level of inter symbol interference to a relatively small amount, we impose the condition that x(T ) = 0.01, where T is the symbol interval.

The bandwidth W of the pulse x(t) is defined as that value of W for which X(W)/X(0) = 0.01, where X( f ) is the Fourier transform of x(t). Determine the value of W and compare this value to that of raised cosine spectrum with 100 percent roll off.