• Express the signal x (t) as,

  x (t) = sin$ (2πf_0t)$

  Using Euler’s identity express x (t) as follows:

We know that,

Hence equation (1) can be written as follows:

• The term δ$(f- f_0 t)$ is a delta function in the frequency domain which is shifted right by frequency “$f_0$” .Its amplitude is +1/2 and the term δ$(f+ f_0 $t) represents a delta function which is shifted left by frequency “$f0$”.Its amplitude is -1/2.