Sketch graphs of the real andimaginary parts of X (jω) from Exercise 1 as functions of ω a...

Sketch graphs of the real andimaginary parts of X (jω) from Exercise 1 as functions of ω and compare them to Figures 1.

Exercise 1.

The signal x(t) = eb'u(-t) is an example of a left-sided real exponential signal. Sketch this signal for b > 0 and then show that the Fourier transform of this signal is

if b > 0. Also, using (11.15), show that the Fourier transform does not exist if b<0.

Figures 1. Right-sided exponential signal; (a) Time function x(t ) = e-at u (t) , and (b) Real part of X(jω); (c) imaginary part of X(jω).