Fourier transform for angular frequency In Section 2.2, the Fourier transform is defined in terms of frequency

f. To avoid confusion here, it is denoted as Xf ( f ). The Fourier transform is often defined in terms of radians per second, i.e., the angular frequency !

X!ð!Þ ¼

Z1

1 xðtÞej!tdt:

Derive the formula of inverse Fourier transform from X!(!) to x(t) and the relationship between X!(!) and Xf (f).