Use parts (b) and (a) of Exercise [1.2] to show that Equation (50c) can be rewritten as where, for a complex number Conclude that with an appropriate definition for fm. Use this to show that, for...

Use parts (b) and (a) of Exercise [1.2] to show that Equation (50c) can be rewritten as

where, for a complex number

Conclude that

with an appropriate definition for fm. Use this to show that, for all t,

where gp( ) is given by Equation (50b) and

(This result shows that we can in fact replace the

in the Fourier series representation of

by =; i.e., the Fourier series representation of gp(t) is in fact equal to gp(t) itself for all t.)