What are the absolute bandwidths of the signals shown in Pro

What are the absolute bandwidths of the signals shown in Problem 2 above? What is the null-null bandwidth of the waveform in Problem 2 - Part(iv)? What is the 3 dB bandwidth of x(t)=2e^-3t u(t)?

Solution

I am solving only last part. For rest part problem2 required.

X(t)= 2e^(-3t) u(t)

X(jw)= Fourier transform of x(t)

= 2/(3+jw)

=(2/3)/(1+jw/3)

|X(jw) |= magnitude of X(jw)

= (2/3)/(1+w^2/9)^0.5

At 3db frequency , (1+w^2/9)=2

W^2/9=1

W= 3 rad/s

Fc=3db frequency= 2/3 hz