Since is a real signal, . But from the given hypothesis, for k > 2. This implies that
for k > 2.
Also, it is given that . Therefore the only non-zero Fourier coefficients are , , and.
It is also given that is a positive real number. Therefore . Thus we have,
=
=
=
Since and are both periodic with period 3, we have
But, by given hypothesis we have , which implies that
Therefore we have,
Finally, it is given that
Therefore, and the constants A = 1, B = and C = 0.
is a real signal, 
. But from the given hypothesis, 
for k > 2. This implies that 
for k > 2.
Also, it is given that 
. Therefore the only non-zero Fourier coefficients are 
, 
, 
and
.
It is also given that 
is a positive real number. Therefore 
. Thus we have, 
= 
and 
are both periodic with period 3, we have 
, which implies that 
and the constants A = 1, B = 
and C = 0. 
